南昌大学“材料热力学”补充习题及答案

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高等热力学习题集补充题参考答案

补充题五、即ref(1) p343 习题11－2 解：kT kTi i kTkT i i kTi i ii ii i e hm p kT e hm kT p kT N g NkTpV e hm kT N V e N Z N g e g NN εεεεεπππ32325232232)2()()2()2(2======-ii i i iN g e N g m T p kT>>∴⨯≈⋅⨯⨯⋅⨯⨯=====----823334232623252326a 3107.2S)J 10626.6(kg)102(N/m 10K)300J/K 1038.1(kg 10K,300,p 10,23πε代入将补充题六、选作题 ref(1) p.371 习题12－2试以德拜近似，证明N A 个阵点（3N A 个独立的一维简谐振子）的总能量U 为：⎰-+=TH xD D D e dxx T H RT H R U /)(0331)/)((9)(89 如何解释项？D H R )(89解：根据一维简谐振子能级公式及其配分函数得出的一个一维谐振子能量121/-+=kThv A v e hvhv N U 则频率从0到D v 的总数3N A 个的一维谐振子的总能量为：⎰-+=Dv kT hv dv v g e hvhv U 0/)()12(频率为ν的振动方式数239)(v v N v g DA =⎰-+=∴Dv DA RT hv dv v v N e hvhv U 023/9)12(⎰⎰-+=-+⋅=====TH x D D T H x DD A D D D D D e dxx T H RTH R e dx x h v h v N U TH kT hv x dx x h kTdv v kT hv x /)(033/)(03433431)/)((9)(89]142[9)(,)(,代入则令为基态能，零点能所以时，当D T H x D D x TH x H R e dx x T H RT H R U e dx x e dx x T D D )(891)/)((9)(8915110/)(033403/)(03=-+==-=-→⎰⎰⎰∞π补充题八、用ref(3).P.40－43表2－8、表2－9计算31摄氏度对应饱和压力120195Kpa 饱和NH 3液的比容v’和饱和NH 3蒸气的比容v ’’。

南昌大学“材料热力学”补充习题及答案

1、At 300K, 1 mole ideal gas expands from p =10⨯pΘ to p= pΘ isothermally and reversibly calculate (1) Calculate the q, w, ∆H m, ∆U m, ∆G m, ∆F m and ∆S m; (2) If the gas expands isothermally to a vacuum until the pressure reaches p= pΘ, calculate q, w, ∆H m, ∆U m, ∆G m, ∆F m and ∆S m.2. Calculate the equilibrium vapour pressure (atm) of sodium for an aluminum melt containing 0.005 mol% sodium(Na). The activity coefficient of sodium in aluminum is 320 and the vapor pressure of pure sodium at 750 °C is 0.23 atm.3、At 413.15K，the vapor pressure of pure C6H5Cl and C6H5Br are 125.238kPa and 66.104kPa. Given that the two pure liquids are mixed and form ideal solution. If a solution formed by the two pure liquids boils at 413.15K、101.325kPa, please calculate the composition of the solution and the vapor above it.4、Given that when a specie A in a binary solution, its vapor pressure varies with its concentration in the pattern illustrated below. Make a table to indicate the activity, activity coefficient and chemical potential of A in different concentration sections I 、II and III，using its pure substance as standard state.III III5、At 300K, the vapor pressure of liquid A and liquid B are 37.33kPa and 22.66kPa.When 2 moles of A and 2 moles of B are mixed to form a solution, the vapor pressure above the solution is 50.66kPa, and the molar fraction of A in the vapor is 0.60. Given that vapors can be taken as ideal gases. ①Calculate a A( R )and a B( R) in the solution, ②γA and γB , ③∆mix G , ④ If the solution is an ideal solution, what is the value of ∆mix G id ? ⑤ What is the value of ∆mix G ex of this solution?6、The variation, with composition, of G E for Fe-Mn alloys at 1863K is listedbelow:X Mn 0.1 0.20.30.40.50.60.7 0.80.9G m E , Joules395703 925 1054 1100 1054 925 703 395a 、Is the process to form Fe-Mn alloy at 1863K an exothermic one or an endothermic one ?b. Does the system exhibit regular solution behavior?c. Calculate E Fe μ and E Mn μ at X Mn = 0.6;d. Calculate m mix G ∆ at X Mn = 0.4;e. Calculate the partial pressures of Mn and Fe exerted by the alloy of X Mn = 0.27、Melts in the system Pb-Sn exhibit regular solution behavior. At 473︒C, a Pb =0.055 in a liquid solution of X Pb = 0.1. Calculate the value of PbSn ωfor the system and calculate the activity of Sn in the liquid solution of X Sn = 0.5 at 500︒C.93.23ln 27.145390)(ln *+--=T Tatm p Fe68.37ln 02.333440)(ln *+--=T Tatm p Mn8、With respect to the Ellingham diagram, answer the following questions:a) Explain the slope changes for the reaction 2Mg + O 2 = 2MgO; b) You want to heat up and a piece of silicon metal to 1600︒C, decide on a suitable crucible material;c) What is the value of ∆H Θ of formation of TiO 2 ? d) Find ∆G Θfor the reaction Fe + 0.5O 2 =FeO at 1200 ︒C;e) Find ∆G Θ for the reaction 3Mg + AlO 3 = 3MgO + 2A1 at 1500 ︒C; f) What is the equilibrium oxygen pressure when metallic titanium is in equilibrium with TiO 2 at 1000 ︒C?g) If you want to reduce pure TiO 2 to pure metallic titanium at 1000︒C using a CO/CO 2 gas mixture, what is the minimum CO/CO 2 ratio that can achieve such a reduction.9、Answer the following questions according to Ellingham diagram:① At what temperature(s) C can reduce SnO 2(s)、Cr 2O 3(s) and SiO 2(s) ？ ② At what temperature, the decomposition pressure of CuO reaches 1.01325⨯105 Pa ?③ The temperature(s) at which Fe 3O 4 can be reduced to FeO by H 2 ? ④ ∆G Θ when Mg reduces Al 2O 3 at 1000︒C, ⑤ Atwhattemperature,forthereaction)(322)(3234S S O Cr O Cr =+,Pa 1019'2－（平）is p O ? ⑥ Calculate the ∆G when Fe reacts with O 2 at 10－5Pa and 10－10Pa respectivelyat1000︒C, and '(2平）O p as well.⑦ Calculate the equilibrium constant of reaction 2)()(CO Mn CO MnO s s +=+ at 1100︒C (CO CO p p K /2=)⑧ At what temperature, for reaction )(2)(2)(g s s O H Mn H MnO +=+, the （平）)/(22O H H is 104/1 ? 10、The standard Gibbs free energy change for reaction I:Ni （s ） + 1/2 O2 == NiO （s ）is -244560 + 98.53TlnT J/ mol , question: a) How much is the standard Gibbs free energy change for reaction II : 2Ni （s ） + O2 == 2 NiO （s ）b) Calculate the equilibrium constants for reaction I and reaction II respectively at 1000︒ C.c) At 1000︒ C, when oxygen pressure is maintained at 10-4 atm, how much is theGibbs free energy change for reaction I ? Can reaction I proceed forward ? Is Ni stable under this condition ? Is NiO stable under this condition ? d) At 1000︒ C, how much should be the oxygen pressure if we want the Gibbs free energy change for reaction I to be 0, and how much should be the oxygen pressure if we want a Ni-NiO-O 2 system to be at equilibrium ?e) At 1000 C, what is the condition to prevent Ni from being oxidized ? and whatis the condition to reduce NiO ?11、Liquid FeO is reduced to metallic iron at 1600 °C with CO(gas) accordingto the following reaction:FeO(liquid) + CO(g) = Fe(liquid) + CO 2 a) Calculate ∆G Θ at 1600 °C for this reactionb) Detennine the minimum CO/C02 ratio required to reduce pure liquid FeO to pure metallic iron at 1600 °C.c) Determine the minimum CO/CO2 ratio required to reduce FeO dissolved in a liquid slag to metallic iron at 1600 °C. The metallic iron formed has a purity of 96 mole % iron. The activity of FeO in the liquid slag is 0.3.CO(g) at 1600 °C: ∆GΘ= -274.9 kJ/molCO2(g) at 1600 °C: ∆GΘ = -396.3 kJ/molFeO at 1600 °C: ∆GΘ = -144.6 kJ/molR= 8.314 J/ mol.K= 1.987 ca1/mol.K12、In an experiment, it was found that the Ar was not pure enough. So a setup was devised in an attempt to purify the Ar, as illustrated below. Ar which was at 2 atm was let to flow through a glass tube and the Cu powder pile in it. Given that the temperature in the glass tube is 600︒C and gas pressure is constant at 2 atm.. Calculate the purity of the outgoing Ar in percentage.Ellingham Diagram补充习题参考答案（魏）1.ΔS m =19.1J/mol.K, ΔG m = -5740 J/mol, ΔF m = -5740 J/molIsothermally expands to a vacuum: w = 0, ΔH m =0 , ΔU m = 0,ΔS m =19.1J/mol.K, ΔG m = -5740 J/mol, ΔF m = -5740 J/mol2. 3.68 × 10-3 atm3、Pa x x Br H C Cl H C 406.0;594.05556==Pa p Pa p Br H C Cl H C 26838;744445556==4.5、 JG J G J G a a ex mix id mix mix B A R B R A 5302)5(;6912)4(;1610)3(;788.1;62.1)2(;894.0;81.0)1()()(=∆-=∆-=∆====γγ 6. a endothermic one; b. Yes; c J J EMn E Fe 704;1584==μμd ;/9363mol J G m m ix -=∆e Pa p Pa p Fe Mn 4;1198==7. J S n P b 4578-=ω; 418.0=Sn a Pure Substance as Standard Statepq（b ）I 、II 、IIIIII:AA AA x RT T p RT T T ln )(ln)()(**+=+=μμμk A8. a) Mg boils and which makes o S ∆more negative, so the slope changes for larger; b) Firstly, we should avoid using metallic material for this purpose since the melting points of metals are mostly too low. Ceramic materials, usually composed of oxides and having high melting points can be chosen The material should not be reduced by pure silicon at 1600ºC. By examing Ellingham diagram, crucibles (坩埚) made of Al 2O 3 .c ) -890kJ /molO2;d ) -170kJ /molFeO; e) -30kJ; f) Pa 2110－; g)721063.0/⨯=pco p CO 9、⑨ 650ºC ，1220 ºC and 1520 ºC ; ⑩ 1480 ºC ;⑪ When the temperature is equal to or higher that 710 ºC ; ⑫ 2/100molO kJ G o -=∆ ⑬ 900 ºC; ⑭0,102/112,1010'25'2=∆=-=∆=--G Pa P molO kJ G Pa P O O , Pa p e O 10')(210-= ⑮ 510-=K ;⑯ 1220ºC10、a) -489120+197.06TlnT J/mol; b) 2.89×10-54 ; c)J G 749429=∆; Ni is stable under this condition,and NiO is not stable; d) Pa p e o 58')(21046.3⨯= e) from the calculation, we found that at 1000ºC, Pa p e o 58')(21046.3⨯=. So at 1000ºC, when theoxygen pressure is less than 3.46×1058Pa, Ni is stable and can not be oxidized, and NiO will be reduced to Ni under this condition. 11. a)mol kJ G o /2.23=∆;b)43.42=⎪⎭⎫ ⎝⎛e CO CO p p . This is the minimumCO/CO2 ratio required to reduce pure FeO to Fe at 1600ºC. c)2.142=⎪⎭⎫ ⎝⎛eCO CO p p . This is the minimum CO/CO2 ratio required to reduce FeO in a slag( 炉渣) to Fe in a metallic iron melt under the given conditions at 1600ºC.12.%100)1015.3%10⨯⨯-＝（Ar。

热力学复习题及答案

热力学复习题及答案1. 热力学的定义是什么？答：热力学是研究能量转化和能量传递规律的一个物理学分支。

2. 什么是热力学系统？答：热力学系统是指被选定的一部分物质或空间，用于研究热力学性质和过程的对象或范围。

3. 请简要解释热力学过程中的熵变。

答：热力学过程中的熵变指系统熵的变化，代表了系统无序度的改变。

熵增加表示系统的无序度增加，熵减少表示系统的无序度减少。

4. 热力学第一定律是什么？答：热力学第一定律，也称能量守恒定律，表示能量不会被创造或破坏，只能从一种形式转化为另一种形式，能量的总量保持不变。

5. 温度和热量有什么区别？答：温度是物体分子运动的程度，用来衡量热力学系统的热平衡状态。

热量是能量的传递形式，表示因温度差而引起的能量传递。

6. 请解释等温过程和绝热过程。

答：等温过程是指系统与外界保持恒定温度的热力学过程。

绝热过程是指系统与外界无能量交换的热力学过程。

7. 热力学循环是什么？答：热力学循环是指能量转化过程中系统从一个状态经过一系列过程最终回到原来状态的过程。

8. 请解释热力学可能性原理。

答：热力学可能性原理，也称热力学第二定律，表示任何孤立系统都不可能完全转化热能为有效的功。

9. 热力学第三定律是什么？答：热力学第三定律，也称绝对温标定律，指出在绝对零度（0K）下，所有物质的熵可以达到最低值，即熵的极限为零。

10. 请解释吉布斯自由能。

答：吉布斯自由能，简称G，是热力学系统在等温等压条件下的可用能量。

它在化学平衡时取最小值，可用于预测化学反应的方向。

[工学]南昌大学材料热力学答案

The problems of the first law1.1 a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25℃ and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327℃. The molar heat of fusion of the lead is 4.8kJ/mol. The molar heat capacity C P of lead may be taken as 29.3J/(mol K)Solution: )/(363102.20721]108.4)25327(3.29[2121)(23322s m V v n n WQ nMv mv W H T C n Q Q Q absorb melting p melt increase absorb =⨯=⨯+-⨯===∆+∆=+=-1.2 what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at the rate of 20 m/minSolution )/(24560208.975)/(12160602410467000//)(104670001868.4102500sin 3S J t h mg P S J t Q t W PJ Q gincrea Burning Burning =⨯⨯=∆==⨯⨯====⨯⨯=1.3 One cubic decimeter (1 dm 3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20℃.(a) what is the total area of the droplets?(b) Calculate the minimum work required to produce the droplets. Assume that the droplets are rest (have zerovelocity)Water have a surface tension of 72.75 dyn/cm at 20℃ (NOTES: the term surface energy (ene/cm 2) is also used for surface tension dyn/cm)Solution)(6.436)106103(1075.72)(106)105.0(4)105.0(34)101(232523263631J S W m nS S Single total =⨯-⨯⨯⨯=∆=⨯=⨯⨯⨯⨯⨯⨯⨯⨯==-+----σππ1.4 Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25℃, the pressure is 10 atm. Assume that helium is an ideal gas.(a) when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm), what will be thetemperature of the first gas to hit the specimen?(b) As the helium flows, the pressure in the tank drops. What will be the temperature of the helium entering thequench chamber when the pressure in the tank has fallen to 1 atm?Solution: )(180118298)(1185.229810101325501010101325)5500(1)()(118)101(298)()(0334.0/00K T T T K RR nC W T b K T P P T T Adiabatica p CR P=-=∆-==⨯⨯⨯⨯⨯⨯⨯-⨯==∆=⨯==--1.5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T 0. The valve on the tank is oðened and the surrounding gas is allowed to flow suickly into t(e tank until the pressure insi`e the tank is equals the pressure outside. Assume that no heat flow takes place. What is the0final tempeture kf t èe gaS in the tank? The heat cap!city mf the gas, C p and C v each íay be(assumed to be c/nsuant over thå temperature rang!spanNed by the døperiment. You answer may be meft in terms of C p and S v hint: one way to approach the xroblem is to define the system as the gas ends up in the tank.solution 0/000/00)0()(T P P T T P PT T Adiabatic PPC R C R ≈-==1.6 Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO 2 and CH 4 (gas)[This heat of reaction is also called the low calorific power of methane] convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atm NOTE: this value is a good approximation for the low calorific powder of natural gasDATA: )()()(224g O H g CO g CH FOR80.5705.9489.17]/[0298---•∆mol g Kcal Hsolution)1000/(9.2610252103048.01101076.191)/(76.191)89.1780.57205.94()2(22333332982982224422SCF Btu mol g Kcal H H H H H OH CO O CH CH O H CO =⨯⨯⨯⨯⨯=•=∆+⨯---=∆-∆+∆-=∆+=+- 1.7Methane is delivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O 2 and 79% N 2)(a) Assuming complete combustion, what is the composition of the flue gas (the gas following combustion)? (b) What is the temperature of the gas, assuming no heat loss?(c) The furnace processes 2000kg of glass hourly, and its heat losses to the surroundings average 400000 kJ/h.calculate the fuel consumption at STP (in m 3/h) assuming that for gas H 1600-H 298=1200KJ/KG(d) A heat exchanger is installed to transfer some of the sensible heat of the flue gas to the combustion air.Calculate the decrease in fuel consumption if the combustion air is heated to 800K DATA STP means T=298K, P=1atm22224O N O H CO CH for2.82.89.117.1316)/(C mol cal C P •Solution)(210448.1125.9100076.191298)/(25.9)]87.012.72(2.843.179.1171.87.13[01.0)(%87.0%%12.72%%43.17%2%%71.8)11.1(221791.1231%22)(0,,222222224K T T T C mol cal X C C b O N CO O H CO O H CO O CH a i i p p p =⨯⨯+=∆+=•=+⨯+⨯+⨯=======-⨯+⨯⨯+=+=+∑)/(1644)0224.011868.448.11)8001600(48.1125.9189570(102800000)/(189570)298800)](48.1187.8)48.1125.9[(100076.191)()/(87.848.11/]211002.22.816[)()/(3214)0224.011868.448.11)2981600(48.1125.9100076.191(102800000)/(280000040000020001200)(33min ,,,,298,,33min h m V mol g cal dTn C n C H H C mol cal X C C d h m V h KJ P C gConsu i i r p i i p p i i p r p g Consu =⨯⨯-⨯-⨯=•=-⨯-⨯-⨯=--∆=∆•=⨯⨯+===⨯⨯-⨯-⨯⨯==+⨯=⎰∑∑∑1.8 In an investigation of the thermodynamic properties of a-manganese, the following heat contents were determined:H 700-H 298=12113 J/(g atom) H 1000-H 298=22803 J/(g atom)Find a suitable equation for H T -H 298 and also for C P as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given tempeture rang.Solution )298(0055.0)298(62.35011.062.35011.062.3522803)2981000(2)2981000(12113)298700(2)298700(]2[2229822222982---=∆-=-===-+-=-+-+=+==∆⎰⎰T T H TC b a ba ba T baT bTdT a dT C H T P T P1.9 A fuel gas containing 40% CO, 10% CO 2, and the rest N 2 (by volume) is burnt completely with air in a furnace. The incoming and ongoing temperatures of the gases in the furnace are 773K and 1250K,respectively. Calculate (a) the maximum flame temperature and (b) heat supplied to the furnace per cu. ft of exhaust gasmolJ Hmol J H CO f CO f /393296/1104580,298,0,298,2-=∆-=∆)/(10184.403.29)/(1067.11010.492.19)/(1037.81020.935.44)/(1042.01097.345.283,253,253,253,222molK J T C molK J T T C molK J T T C molK J T T C N P O P CO P CO P -------⨯+=⨯-⨯+=⨯-⨯+=⨯-⨯+= Solution?0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)()/(1019.01058.528.33722.0278.0)/(1067.01038.477.281.065.005.02.0)()/(282838110458393296%2.72%8.27%10%65%5%20)4/(1122298127332981523733253253298,,,,298,253,,,,,253,,,,,,,0,298,0,298,298,22222222222222==+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆⨯-⨯+=+==⨯-⨯+=+++===-=∆-∆=∆========+-----------⎰⎰⎰∑∑⎰∑∑∑∑T T T T T T T dTT T dTT T dTn C n C n H H molK J T T C C n C C molK J T T C C C C n C C a mol J n Hn H H N CO production O N CO CO reation then O N air mole need fuel mole when CO O CO T TT i i r p i i p p i i N P CO P i i p p r p O P N P CO P CO P i i p p r p i pf i rf idTT T Q dT T T Q b T T T T T T T dTT T dTT T dT n C n C n H H T TT i i r p i i p p i i 9.0)1019.01058.528.33(2.02828389.0)1019.01058.528.33(2.0282838)(0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)(253125029812502982531250298125029829812125029815231250253253298,,,,298,⨯⨯-⨯++⨯-=⨯⨯-⨯++⨯-===+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆-----------⎰⎰⎰⎰⎰∑∑⎰1.10 (a) for the reaction2221CO O CO →+,what is the enthalpy of reaction (0H ∆) at 298 K ?(b) a fuel gas, with composition 50% CO, 50% N 2 is burned using the stoichiometric amount of air. What is the composition of the flue gas?(c) If the fuel gas and the air enter there burner at 298 K, what is the highest temperature the flame may attain(adiabatic flame temperature)? DATA :standard heats of formationfH ∆ at 298 K)/(393000)/(1100002mol J CO mol J CO -=-=Heat capacities [J/(mol K)] to be used for this problem N 2=33, O 2=33, CO=34, CO 2=57Solution )(21100)298)(39889.0(222.02830000)/(3975.03325.057)/(33111.034222.033666.033)(%,75%%,251.111002.22%%1.11%%,6.66%%,2.222.0/25.015.0%)()/(283000393000110000)(,0,,,,,,22220,298,0,298,0K T T dT C n H H K mol J X C C K mol J X C C C N CO product O N CO fuel b mol J n H n H H a P p p i P r i P r i P p i P p i P f i r f ==-⨯-⨯=-∆=∆•=⨯+⨯==•=⨯+⨯+⨯====-====+==+-=∆-∆=∆⎰∑∑∑∑1.11 a particular blast furnace gas has the following composition by (volume): N 2=60%, H 2=4, CO=12%, CO 2=24%(a) if the gas at 298K is burned with the stochiometric amount of dry air at 298 K, what is the composition of the flue gas? What is the adiabatic flame temperature?(b) repeat the calculation for 30% excess combustion air at 298K(C)what is the adiabatic flame temperature when the blast furnace gas is preheated to 700K (the dry air is at 298K) (d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will thE dlaMe temperature be affected?DaTA(k J?mol)2CO CO FOR513.393523.110)/(--∆mol kJ H f2222,)(O N g O H CO CO FOR ?? 34505733]/[K mol J C P •SolutionOH O H CO O CO a 222222121)(→+→+ 416.0)(104.0)(:22==N n O n Air6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 32.0)(08.0)(:22==N n O n Air 92.0)(04.0)(36.0)(:222===N n O H n CO n Flue)(98.1108)(8108.53106308.43)/(8.533492.05004.05736.092.004.036.06308.43)08.241(04.0)523.11051.393(12.03,,222222K T K T K J C C C n CKJH H H N O H CO ii r P O H H CO CO ==⨯=∆=⨯+⨯+⨯=++==-⨯+-⨯=∆+∆=∆∑--(b)repeat the calculation for 30% excess0combustion air at 298K6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel024.0)(016.1)(04.0)(36.0)(:2222====O n N n O H n CO n Flue December 13, 2020(C)what is the adiabatic flame temperature when the blasp furnace gas is preheated to 700K (the dry air is at 298K)6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 32.0)(08.0)(:22==N n O n Air 92.0)(04.0)(36.0)(:222===N n O H n CO n Flue)(6.1401)(6.11038.5310373.59)/(8.533492.05004.05736.096.004.036.0373.59)346.02804.05724.03312.0()298700()08.241(04.0)523.11051.393(12.03,,298700222222K T K T K J C C C n CKJH H H H N O H CO ii r P fuel O H H CO CO ==⨯=∆=⨯+⨯+⨯=++==⨯+⨯+⨯+⨯⨯-+-⨯+-⨯=∆+∆+∆=∆∑---(d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will the flame temperature be affected?)(8.1051)(8.75388.57106308.43)/(88.5734024.034016.15004.05736.0024.0016.104.036.06308.43)08.241(04.0)523.11051.393(12.03,,2222222K T K T K J C C C C n CKJH H H O N O H CO ii r P O H H CO CO ==⨯=∆=⨯+⨯+⨯+⨯=+++==-⨯+-⨯=∆+∆=∆∑--6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 008.04.01576015)(32.0)(08.0)(:222=-===O H n N n O n Air 92.0)(048.0)(36.0)(:222===N n O H n CO n Flue)(1103)(8052.54106308.43)/(2.543492.050048.05736.092.0048.036.06308.43)08.241(04.0)523.11051.393(12.03,,222222K T K T K J C C C n CKJH H H N O H CO ii r P OH H CO CO ==⨯=∆=⨯+⨯+⨯=++==-⨯+-⨯=∆+∆=∆∑--1.12 A bath of molten copper is super cooled to 5℃ below its true melting point. Nucleation of solid copper then takes place, and the solidification proceeds under adiabatic conditions. What percentage of the bath solidifies? DATA: Heat of fusion for copper is 3100 cal/mol at 1803℃(the melting point of copper) C P,L =7.5(cal/mol ℃), C P,S =5.41+(1.5*10-3T )(cal/mol ℃) Solution)/(310355.75.0)17981803(105.1541.5310002231798,1798,17981803,18031798,1803,mol cal HH dT C dT C H LS SL L P S P L S =⨯-⨯-⨯+⨯+==+++-⎰⎰1.13 Cuprous oxide (Cu 2O) is being reduced by hydrogen in a furnace at 1000K, (a)write the chemical reaction for the reduced one mole of Cu 2O(b)how much heat is release or absorbed per mole reacted? Given the quantity of heat and state whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction)DATA: heat of formation of 1000K in cal/mol Cu 2O=-41900 H 2O=-59210 solution)/(173104190059210222mol cal H OH Cu H O Cu =-=∆+=+,exothermic reaction1.14(a) what is the enthalpy of pure, liquid aluminum at 1000K?(b) an electric resistance furnace is used to melt pure aluminum at the rate of 100kg/h. the furnace is fed with solid aluminum at 298K. The liquid aluminum leaves the furnace at 1000K. what is the minimum electric powder rating (kW) of furnace.DATA : For aluminum : atomic weight=27g/mol, C p,s =26(J/molK), C p,L =29(J/molK), Melting point=932K, Heat of fusion=10700J/mol Solution)(28.0)(7.2793600110002727184)/(2718410700)9321000(29)298932(261000932,932298,1000,kW W P mol J H dT C dT C H SLL P S P l ==⨯⨯==+-⨯+-⨯=++=⎰⎰1.15 A waste material (dross from the melting of aluminum) is found to contain 1 wt% metallic aluminum. The rest may be assumed to aluminum oxide. The aluminum is finely divided and dispersed in the aluminum oxide; that is the two material are thermally connected.If the waster material is stored at 298K. what is the maximum temperature to which it may rise if all the metallic aluminum is oxidized by air/ the entire mass may be assumed to rise to the same temperature. Data : atomic weight Al=27g/mol, O=16g/mol, C p,s,Al =26(J/molK), C p,s, Al2O3=104J/mol, heat formation of Al 2O 3=-1676000J/molSolution;)(600)(3021041029927275.116122711676000K T K T T ==∆∆⨯⨯++⨯⨯=⨯⨯1.16 Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356K) is sprayed on a cooling surface, where it solidified and cools to 400K. The copper is supplied to the apparatus at the rate of one kilogram per minute. Cooling water is available at 20℃, and is not allowed to raise above 80℃. What is the minimum flow rate of water in the apparatus, in cubic meters per minute? DATA; for water: C p =4.184J/g k, Density=1g/cm 3; for copper: molecular weight=63.54g/mol C p =7cal/mol k, heat of fusion=3120 cal/molSolution:min)/(10573.2)2080(1min /min54.631000)]4001356(73120[min /33m V VQQ WaterCopper -⨯=-=⨯⨯-⨯+=1.17 water flowing through an insulated pipe at the rate of 5L/min is to be heated from 20℃ to 60℃ b an electrical resistance heater. Calculate the minimum power rating of the resistance heater in watts. Specify the system and basis for you calculation. DA TA; For water C p =4.184J/g k, Density=1g/cm 3 Solution:)(139476010005)2060(184.4W W =⨯⨯-⨯=1.18 The heat of evaporation of water at 100℃ and 1 atm is 2261J/mol (a) what percentage of that energy is used as work done by the vapor?(b)if the density of water vapor at 100℃ and 1 atm is 0.597kg/m 3 what is the internal energy change for the evaporation of water?Solution:)/(375971822613101%6.71822613101%)/(31010224.0273373101325mol J Q W U mol J V P =⨯+-=+=∆=⨯==⨯⨯=∆1.19 water is the minimum amount of steam (at 100℃ and 1 atm pressure) required to melt a kilogram of ice (at 0℃)? Use data for problem 1.20 Solution)(125,3341000)10018.42261(g m m =⨯=⨯+1.20 in certain parts of the world pressurized water from beneath the surface of the earth is available as a source of thermal energy. To make steam, the geothermal water at 180℃ is passed through a flash evaporator that operates at 1atm pressure. Two streams come out of the evaporator, liquid water and water vapor. How much water vapor is formed per kilogram of geothermal water? Is the process reversible? Assume that water is incompressible. The vapor pressure of water at 180℃ is 1.0021 Mpa( about 10 atm) Data: C P,L =4.18J/(g k), C P ,v =2.00J/(g k), △H V =2261J/g, △H m =334 J/g Solution:leirreversib g x x x )(138),1000(8018.4)8018.48022261(=-⨯⨯=⨯-⨯+The problems of the second law2.1 The solar energy flux is about 4J cm 2/min. in no focusing collector the surface temperature can reach a value of about 900℃. If we operate a heat engine using the collector as the heat source and a low temperature reservoir at 25℃, calculate the area of collector needed if the heat engine is to produce 1 horse power. Assume the engine operates at maximum efficiency.Solution)(25.6)(7466010427390)2590(24m S W tWP StQ T T T W H H L H ===⨯⨯+-=-=2.2 A refrigerator is operated by 0.25 hp motor. If the interior of the box is to be maintained at -20℃ ganister a maximum exterior temperature of 35℃, what the maximum heat leak (in watts) into the box that can be tolerated if the motor runs continuously? Assume the coefficient of performance is 75% of the value for a reversible engine.Solution:)(64374625.02035202734375.0W P P T T T P Q T T T W L LL LH HHLH =⨯⨯+-⨯=-=-=2.3 suppose an electrical motor supplies the work to operate a Carnot refrigerator. The interior of the refrigerator is at 0℃. Liquid water is taken in at 0℃ and converted to ice at 0℃. To convert 1 g of ice to 1 g liquid. △H=334J/g is required. If the temperature outside the box is 20℃, what mass of ice can be produced in one minute by a 0.25 hp motor running continuously? Assume that the refrigerator is perfectly insulated and that the efficiencies involved have their largest possible value.Solution:)(4576033474625.020273g m M m P P T T T P L LLLH ===⨯⨯=-=2.4 under 1 atm pressure, helium boils at 4.126K. The heat of vaporization is 84 J/mol what size motor (in hp) is needed to run a refrigerator that must condense 2 mol of gaseous helium at 4.126k to liquid at the same temperature in one minute? Assume that the ambient temperature is 300K and that the coefficient of performance of the refrigerator is 50% of the maximum possible.Solution:)(52.0)(393'60284216.4216.4300'5.0%50hp W P P T T T P P Q T T T W L L L H LLLH ==⨯⨯-=-==-=2.5 if a fossil fuel power plant operating between 540 and 50℃ provides the electrical power to run a heat pump that works between 25 and 5℃, what is the amount of heat pumped into the house per unit amount of heat extracted from the power plant boiler.(a) assume that the efficiencies are equal to the theoretical maximum values(b) assume the power plant efficiency is 70% of maximum and that coefficient of performance of the heat pumpis 10% of maximum(c) if a furnace can use 80% of the energy in fossil foe to heat the house would it be more economical in terms ofoverall fissile fuel consumption to use a heat pump or a furnace ? do the calculations for cases a and b solution:1,2,2,1,212,2,2,2,21,1,1,1,198.82527352527354050540)(H H H H H H L H H H L H P P P P P P P T T T P P T T T P a =+-=+-=-=-= .,)(6286.0)(1,2,not is b ok is a c PP b H H =2.6 calculate △U and △S when 0.5 mole of liquid water at 273 K is mixed with 0.5 mol of liquid water at 373 K and the system is allowed to reach equilibrium in an adiabatic enclosure. Assume that C p is 77J /(mol K) from 273K to 373K Solution:)/(933.0)273323ln(5.0)373323ln(5.0)ln()ln()(02211K J C C T T C n T T C n S J U P P E P E P =+=+=∆=∆2.7 A modern coal burning power plant operates with a steam out let from the boiler at 540℃ and a condensate temperature of 30℃.(a) what is the maximum electrical work that can be produced by the plant per joule of heat provided to theboiler?(b) How many metric tons (1000kg) of coal per hour is required if the plant out put is to be 500MW (megawatts).Assume the maximum efficiency for the plant. The heat of combustion of coal is 29.0 MJ/k g(c) Electricity is used to heat a home at 25℃ when the out door temperature is 10℃ by passing a currentthrough resistors. What is the maximum amount of heat that can be added to the home per kilowatt-hour of electrical energy supplied?Solution:)(3.69)(6937136005000.29)()(89.013054030540)(ton kg m T T T mb J Q T T T W a LH LH H L H ==⨯=-=+-=-= )(9.191102525273)(J Q Q T T T W c H HHLH =-+=-=2.8 an electrical resistor is immersed in water at the boiling temperature of water (100℃) the electrical energy input into the resistor is at the rate of one kilowatt(a) calculate the rate of evaporation of the water in grams per second if the water container is insulated that is noheat is allowed to flow to or from the water except for that provided by the resistor(b) at what rate could water could be evaporated if electrical energy were supplied at the rate of 1 kw to a heatpump operating between 25 and 100℃data for water enthalpy of evaporation is 40000 J/mol at 100℃; molecular weight is 18g/mol; density is 1g/cm 3solution:)(23.2,2510027310010004000018)()(45.0,10004000018)(g m m b g m ma =-+===2.9 some aluminum parts are being quenched (cooled rapidly ) from 480℃ to -20℃ by immersing them in abrine , which is maintained at -20℃ by a refrigerator. The aluminum is being fed into the brine at a rate of one kilogram per minute. The refrigerator operates in an environment at 30℃; that is the refrigerator may reject heat at 30℃. what is them minus power rating in kilowatts, of motor required to operate the refrigerator?Data for aluminum heat capacity is 28J/mol K; Molecular weight 27g/mol Solution:)(5.102)(102474202732030)20480(28271000kW W P P T T T P P L L L L H W L ==---=-=--⨯=2.10 an electric power generating plant has a rated output of 100MW. The boiler of the plant operates at 300℃. The condenser operates at 40℃(a) at what rate (joules per hour) must heat be supplied to the boiler?(b) The condenser is cooled by water, which may under go a temperature rise of no more than 10℃. Whatvolume of cooling water in cubic meters per hour, is require to operate the plant?(c) The boiler tempeture is to be raised to 540℃,but the condensed temperature and electric output will remainthe same. Will the cooling water requirement be increased, decreased, or remain the same?Data heat capacity 4.184, density 1g/cm 3 Solution: )(109.7)(102.21040300273300)(1188J t P Q W P T T T P a H H L H H H ⨯==⨯=-+=-= )(1003.1184.41010)(103.4)(34611m V Q V J Q b LL ⨯==⨯⨯⨯⨯= noW P T T T P c L H H H )(10626.11040540273540)(88⨯=-+=-= 2.11 (a) Heat engines convert heat that is available at different temperature to work. They have been several proposals to generate electricity y using a heat engine that operate on the temperature differences available at different depths in the oceans. Assume that surface water is at 20℃, that water at a great depth is at 4℃, and that both may be considered to be infinite in extent. How many joules of electrical energy may be generated for each joule of energy absorbed from surface water? (b) the hydroelectric generation of electricity use the drop height of water as the energy source. in a particular region the level of river drops from 100m above sea level to 70m above the sea level . what fraction of the potential energy change between those two levels may be converted into electrical energy? how much electrical energy ,in kilowatt-hours, may be generated per cubic meter of water that undergoes such a drop? Solution: )/(1006.136001000)()(055.0127320420)(6h kW h mg P b J Q T T T W a H H L H ⨯=⨯∆==+-=-=2.12 a sports facility has both an ice rink and a swimming pool. to keep the ice frozen during the summer requires the removal form the rink of 105 KJ of thermal energy per hour. It has been suggested that this task be performed by a thermodynamic machine, which would be use the swimming pool as the high temperature reservoir. The ice in the rink is to be maintain at a temperature of –15℃, and the swimming pool operates at 20℃, (a) what is the theoretical minimum power, in kilowatts, required to run the machine? (b) how much heat , in joule per hour , would be supplied t the pool by this machine?Solution: )(1014.1101527320273)()(77.33600/10152731520)(555kJ Q b kW P T T T P a H L L L H ⨯=-+==-+=-=2.13solution:)/(81.6810ln 314.877.45277.6282.4)/(152940)()/(67.4977.45277.6282.4)()/(152940)(22)(2molK cal S mol cal H d molK cal S c mol cal H b AlNN Al a -=+-⨯-⨯=∆=∆-=-⨯-⨯=∆=∆=+ 2.14 solution:)/(2257412000)27340273ln 184.4273336263273ln1.2()(400,010,K J dT T C T H dT T C m S WATER P m m ICE P =+++=+∆+=∆⎰⎰-2.15)(70428)(2896100077773002J W J Q T T T W L L L H ==-=-= 2.16)(4.3719))2.4300(314.85.13.83(3002.4300)(7.58663.832.42.4300J Q T T T W J Q T T T W H H L H L L L H =-⨯+-=-==-=-=2.17 yes d Q c K J P P nR S b J pdV n W Q OU T a )(0)()/(1.1910ln 314.81ln)()(570410ln 298314.810)(0==⨯⨯==∆=⨯⨯=-=-==∆=∆⎰ 2.18)(1222335273020********g m m m T T T L L H =-=-=⨯ Property Relations 1. At -5︒C, the vapor pressure of ice is 3.012mmHg and that of supercooled liquid water is 3.163mmHg. The latent heat of fusion of ice is 5.85kJ/mol at -5︒C. Calculate ∆G and ∆S per mole for the transition of from water to ice at -5︒C. (3.2, 94) Solution: mol J P P RT G waterO H iceO H /9.1089523.0ln 268314.8163.3012.3ln )5273(314.8ln ,,22-=⨯⨯=-⨯==∆mol J H /1085.53⨯=∆)/(23.22268)9.108(5850K mol J T G H S S T H G ⋅=--=∆-∆=∆∴∆-∆=∆ 2. (1) A container of liquid lead is to be used as a calorimeter to determine the heat of mixing of two metals, A andB. It has been determined by experiment that the “heat capacity ” of the bath is 100cal/︒C at 300︒C. With the bath originally at 300︒C, the following experiments are performed;(2) A mechanical mixture of 1g of A and 1g of B is dropped into the calorimeter. A and B were originally at 25︒C. When the two have dissolved, the temperature of the bath is found to have increased 0.20︒C. 2. Two grams of a 50:50(wt.%) A-B alloy at 25︒C is dropped similarly into the calorimeter. The temperature decreases 0.40︒C. (a) What is the heat of mixing of the 50:50 A-B alloy (per gram of alloy)? (b) To what temperature does it apply ? (3.5, 94)Solution: mol J K cal C bath P /418/100,==(a) g cal T C Q bath P /102/2.01002/,=⨯=∆=This is the heat of mixing.(b) The heat capacity of C P, alloy : )/(072.06.27424.0100)254.0300(2,,K g cal TC C bath P alloy P ⋅=⨯⨯=--⨯∆⨯=Assuming that the calorimeter can be applied to the maximum of T ︒C, the for mixing to form 1 gram of alloy:10)'300(,1+-=T C Q bath P , )'(,2T T C Q alloy P -⋅=, 21Q Q =)'(10)'300(,,T T C T C alloy P bath P -=+-3. The equilibrium freezing point of water is 0︒C. At that temperature the latent heat of fusion of ice (the heat required to melt the ice) is 6063J/mol. (a) What is the entropy of fusion of ice at 0︒C ? (b) What is the change of Gibbs free energy for ice →water at 0︒C?(c) What is the heat of fusion of ice at -5︒C ? C P(ice) = 0.5 cal/(g. ︒C); C P(water) = 1.0 cal/(g. ︒C). (d) Repeat parts a and b at -5︒C. (3.6, p94)Solution: (a) At 0︒C, ∆G =0, ∴ T m ∆S = ∆H)./(09.222736030K mol J T H S m ==∆=∆(b) At 0︒C, ∆G =0© )./(62.37)./(1818.45.0)./(5.0,K mol J K mol J K g cal C ice P =⨯⨯==)./(24.75)./(1818.40.1)./(0.1,K mol J K mol J K g cal C water P =⨯⨯==a reversible process can be designed as follows to do the calculation:。

热力学复习题答案

热力学复习题答案1. 热力学第一定律表述了能量守恒的原理，其数学表达式为：\[ \Delta U = Q - W \]其中，\( \Delta U \) 表示内能的变化，\( Q \) 表示系统吸收的热量，\( W \) 表示系统对外做的功。

2. 热力学第二定律指出，热量不能自发地从低温物体传到高温物体，其数学表达式为：\[ \Delta S \geq \frac{Q}{T} \]这里，\( \Delta S \) 表示熵变，\( Q \) 表示热量，\( T \) 表示温度。

3. 理想气体的状态方程为：\[ PV = nRT \]其中，\( P \) 表示压强，\( V \) 表示体积，\( n \) 表示摩尔数，\( R \) 表示理想气体常数，\( T \) 表示温度。

4. 卡诺循环的效率公式为：\[ \eta = 1 - \frac{T_c}{T_h} \]这里，\( \eta \) 表示效率，\( T_c \) 表示冷源温度，\( T_h \)表示热源温度。

5. 热力学第三定律表述了绝对零度不可达到的原理，即：\[ \lim_{T \to 0} S = 0 \]其中，\( S \) 表示熵，\( T \) 表示温度。

6. 熵变可以通过以下公式计算：\[ \Delta S = \int \frac{\delta Q}{T} \]这里，\( \Delta S \) 表示熵变，\( \delta Q \) 表示微小的热量变化，\( T \) 表示温度。

7. 吉布斯自由能的变化可以用来判断反应的自发性，其表达式为：\[ \Delta G = \Delta H - T\Delta S \]其中，\( \Delta G \) 表示吉布斯自由能的变化，\( \Delta H \) 表示焓变，\( T \) 表示温度，\( \Delta S \) 表示熵变。

8. 热力学中的麦克斯韦关系可以通过以下公式表示：\[ \left( \frac{\partial S}{\partial V} \right)_T =\left( \frac{\partial P}{\partial T} \right)_V \]这里，\( S \) 表示熵，\( V \) 表示体积，\( P \) 表示压强，\( T \) 表示温度。

“材料热力学”补充习题参考答案

“材料热力学”补充习题参考答案教材各章习题参考答案 (魏)3.2 ΔG = -108.9 J/mol; ΔS = -21.42 J/(mol.K) 3.6 (a )22.09/(.)S J mol K ?=；(b) At 0?C, ?G =0;(c) ?H = 5841.9 J;(d) ?S =21.39J /(mol.K)，?G = 109.38 J/mol4.1 (a ) 2898.28J/mol; ( b ) No; ( c ) 345 J/mol; ( d ) 14939 atm; ( e )4921 J/mol 4.2 ( a ) 272.8K; ( b ) Pa P 610345?≈? ; ( c ) 249.46K4.3 1202K4.4 P=5.73?10-6 atm 4.5 0.16P 4.708.10430685ln +-=TP4.8 ( a ) 1180K; ( b ) 695.3K; ( c ) 114.4kJ/mol; ( d ) 7123 J/mol; ( e )4.2J/mol4.9 In the initial state: 4.06 mol %; in the final state:5.3 mol% 4.10 ( a )348 kJ; ( b ) 2.3×10-3Pa ;( c ) “ solution not possible ”; (d ) “solution not possible ”5.1atmp H 0005.0=5.2、atmp o 1221007.1-?=If the error in enthalpy is 500cal, the uncertainty in the pressure calculated is 28.6%, and if the error in enthalpy is -500cal, the uncertainty is -22.1%5.3、(a) T =462K; (b) T = 420K 5.4 (a)atmP O 2621014.1-?=, (b) P O2 =2.28?10-10 atm., (c) The equilibriumoxygen pressure remains the same when the total pressure increases, which means a higher purity level of N 2 .5.5 (a) 略； (b) Pa atm P H 8.181013056.1800019.0)('2=?==; (c) 21.5L Ar is needed to be bubbled into the melt.5.6（a ）0.880.900.920.940.960.981.00 1.02 1.04 1.06 1.087.27.47.67.88.08.28.48.6l n K a1/T , 10-31/K=-=?ooG kJ H1000;50- 66.6kJ(b) Ja = 3 < Ka, the reaction will proceed from left to right, and theatmosphere will not oxidize Ni. 5.7 略5.8. (a) P SiO = 8.1?10-8 (atm) (b) ?H o = 639500J; ?So =334.9J/K(c ) PO2 =10-30 atm 5.9 5.10．JH o72250=?，the reaction is an endothermic one.5.11. (a),166528J Ho=?the reaction is an endothermic one.;(b) At 1168K, the equilibrium pressure of CO2 equals one atmosphere. 5.12 (a) 略， (b) MgCO P P =; (c) T = 2037 K5.13 (a) 略； (b) 13109.2?=K ; (c) ppm 186.05.14 (a) 略； (b) kJ H 52.267=?; (c) K T 1592=5.15 (a) )(106.13atm -?≈; (b) )(1028.210)(2atm P g O H -?=5.16 (a)97.9=K ; (b) atm x 14.4=; (c) if the temperature is increased,the fraction of water reacted will increase since the equilibria constant increases with increasing temperature.6.2 （a ）1.287V;(b) When the water impure, the voltage will go higher; (c)1.219V 6.4 (a) 145.3kJ;(b) The maximum work that could be derived is 702.36kJ; (c) In this case, the maximum work that could be derived is 696.56kJ.)(106.08)(atm Pg u -?=6.5 (a) -6252J/mol; (b) 370.0)(=II Cda ; (c) )(42.3mmHg P Cd =;6.67.87?10-4 V 6.7 (a))(22g Cl Mg MgCl+=(b)Pa P Cl 21'1086.82-?=;(c) 2.485V6.8 (a) PaP O 11'2105.5-?=;(b) Anode: e Ni Ni 2+→Cathode: -→+2222/1Oe O ;(c) 0.757V; (d) 0.261V6.10 (a) )(509.3V E o=;(b) 0.074kJ;(c) 4.1?106J;(d) Y es. In this case, the open circuit voltage is 3.648V;(e) In this case, to keep the temperature constant, 3.92?106J heatshould be removed from the battery per hour. 6.11(a)TGCOAl C O Al o26.3211008.12/322/36232-?=+=+Δ(b) The minimum voltage at which the electrolysis may be carriedout at 1250K is 1.172V .7.1 0.117 atm 7.5 ( a ) ,82.52.52.5BA BA BB T PV V V x x x x x ??=+=-- ?,102.5 2.5 2.5A B A A B A T PV V V x x x x x ??=+=-- ?( b) B A Mx x V5.2=7.72)1(736.0ln Sn Snx --=γ7.8 The maximum solubility of MgF2 in liquid MgCl at 900?Cis 19mol% .7.9 ( a ) 1121K; ( b ) 1. 8 cal/K 9.69.8 Solution:(a) 90 mol%B is the composition of the first solid to form;10 mol % is the composition of the last liquid drop.(b) solid (60 mol%B is the composition) is about 77% ; liquid(15 mol%B is the composition) is 23%9.9 (a) 2900℃, α(12%) (b) 2300℃, liq(95%) (c) 8.2%α(compositionis 24% )+91.8%β(85%)补充习题参考答案（魏）1.ΔS m =19.1J/mol.K, ΔG m = -5740 J/mol, ΔF m = -5740 J/molIsothermally expan ds to a vacuum: w = 0, ΔH m =0 , ΔU m =0,ΔS m =19.1J/mol.K, ΔG m = -5740 J/mol, ΔF m = -5740 J/mol2. 3.68 × 10-3 atm3、x x Br H C Cl H C 406.0;594.05556==Pa p Pa p Br H C Cl H C 26838;744445556==4.5、JGJ GJ G a a exmix idmix mix B A R B R A 5302)5(;6912)4(;1610)3(;788.1;62.1)2(;894.0;81.0)1()()(=?-=?-=?====γγ6. a endothermic one; b. Y es; c JJ EMn EFe 704;1584==μμd;/9363mol J G m mix -=?ePap Pa p Fe Mn 4;1198==S n P b4578-=ω;418.0=Sn a8. a) Mg boils and which makes oS ?more negative, so the slope changes for larger; b) Firstly, we should avoid using metallic material for this purpose since the melting points of metals are mostly too low. Ceramic materials, usually composed of oxides and having high melting points can be chosenThe material should not be reduced by pure silicon at 1600oC. By examing Ellingham diagram, crucibles (坩埚) made of Al 2O 3 .c ) -890kJ /molO2;d ) -170kJ /molFeO; e) -30kJ; f) Pa2110－;g)721063.0/?=pco p COPure Substance as Standard Statepq（b ）I 、II 、IIIIII:AA x RT T p RT T T ln )(ln)()(**+=+=μμμk A9、① 650oC ，1220 oC and 1520 oC ; ② 1480 oC ;③ When the temperature is equal to or higher that 710 oC ;④ 2/100molO kJ G o-=?⑤ 900 oC; ⑥,102/112,1010'25'2=?=-=?=--G Pa PmolO kJ G Pa P O O ,Pap e O 10')(210-=⑦ 510-=K;⑧ 1220oC10、a) -489120+197.06TlnT J/mol; b) 2.89×10-54 ; c)JG 749429=?; Ni is stable under thiscondition, and NiO is not stable; d)p e o 58')(21046.3?= e) fromthe calculation, we found that at 1000oC,Pap e o 58')(21046.3?=. Soat 1000oC, when the oxygen pressure is less than 3.46×1058Pa, Ni is stable and can not be oxidized, and NiO will be reduced to Ni under this condition. 11. a)molkJ G o/2.23=?; b)43.42=eCO CO p p . This is theminimum CO/CO2 ratio required to reduce pure FeO to Fe at 1600oC. c)2.142=eCO CO p p . This is the minimum CO/CO2ratio required to reduce FeO in a slag( 炉渣) to Fe in a metallic iron melt under the given conditions at 1600oC.12.%10?-Ar .3 15 % 100 ) 10。

材料热力学与动力学复习题答案word版本

材料热力学与动力学复习题答案、常压时纯Al 的密度为p =2.7g/crR ,熔点T m =660.28C ，熔化时体积增加5%。

用理查得规那么和克-克方程估计一下，当压力增加1Gpa 时其熔点大约是多少?由克-克方程dPdT温度变化对AH m 影响较小，可以忽略,代入得dP dTH R Tm R Tm1 dTT VTVV T对积分 p pdpRTm Tm T1 dT TpT VTm整理 PR Tm , _T1 TmT R TmRTII 1Tm VVAl 的摩尔体积 V m =m/p =10cm=1 xi0-5m 3Al 体积增加 A V=5%Vn=0.05 X 0_5m 3Tp VR97105 10 60.14K& 314Tm =Tm+ T =660.28+273.15+60.14=993.57K二、热力学平衡包含哪些内容，如何判断热力学平衡。

内容：〔1〕热平衡，体系的各局部温度相等；〔2〕质平衡：体系与环境所含有的质量不变；〔3〕力平衡：体系各局部所受的力平衡，即在不考虑重力的前提下，体系内部各处所受的压力相等；〔4〕化学平衡：体系的组成不随时间而改变。

热力学平衡的判据：〔1〕熵判据：由熵的定义知dS 』不可逆对于孤立体系，有 Q 0，T 可逆因此有dS 0不可逆，由于可逆过程由无限多个平衡态组成，因此对于孤立体可逆系有dS 0不可逆，对于封闭体系，可将体系和环境一并作为整个孤立体系来考虑熵的变化，即S 总S 体系S 环境0自务平衡解：由理查德规那么 SmHm TmHm RTm(2) 自由能判据假设当体系不作非体积功时，在等温等容下，有自发过程d F T ,V 0平衡状态上式说明，体系在等温等容不作非体积功时，任其自然，自发变化总是向自由能减小的方向进行，直至自由能减小到最低值，体系到达平衡为止。

(3) 自由焓判据假设当体系不作非体积功时，在等温等压下，有自发过程0平衡状态所以体系在等温等容不作非体积功时，任其自然，自发变化总是向自由能减小的方向进行，直至自由能减小到最低值，体系到达平衡为止三、试比拟理想熔体模型与规那么熔体模型的异同点。

热力学习题及答案解析

热力学习题及答案解析热力学是物理学中的一个重要分支，研究热量和能量转化的规律。

在学习热力学的过程中，经常会遇到一些题目，下面我将针对几个常见的热力学学习题目进行解析。

1. 热力学第一定律是什么？请用自己的话解释。

热力学第一定律，也被称为能量守恒定律，它表明能量在系统中的转化是守恒的。

简单来说，能量既不能被创造也不能被消灭，只能从一种形式转化为另一种形式。

这个定律可以用数学公式表示为：ΔU = Q - W，其中ΔU表示系统内能的变化，Q表示系统吸收的热量，W表示系统对外做的功。

2. 一个物体从20°C加热到80°C，热量变化是多少？要计算这个问题，我们需要使用热容量的概念。

热容量表示单位温度变化时物体吸收或释放的热量。

对于一个物体，它的热容量可以表示为C = m × c，其中m表示物体的质量，c表示物体的比热容。

假设这个物体的质量为1kg，比热容为4.18J/g°C。

那么它的热容量就是C =1kg × 4.18J/g°C = 4.18J/°C。

根据热力学第一定律，热量的变化等于系统内能的变化，即Q = ΔU。

由于这个物体只发生温度变化，内能的变化可以表示为ΔU = C × ΔT，其中ΔT表示温度的变化。

根据题目给出的信息，温度变化为80°C - 20°C = 60°C。

将这些数值代入公式，我们可以得到热量变化为Q = ΔU = C × ΔT = 4.18J/°C × 60°C = 250.8J。

所以，这个物体的热量变化为250.8J。

3. 一个气体在等温过程中吸收了300J的热量，对外做了100J的功，求系统内能的变化。

在等温过程中，温度保持不变，因此根据热力学第一定律，系统内能的变化等于吸收的热量减去对外做的功，即ΔU = Q - W。

根据题目给出的信息，吸收的热量Q = 300J，对外做的功W = 100J。

南昌大学材料热力学答案

The problems of the first law1.1 a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25℃ and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327℃. The molar heat of fusion of the lead is 4.8kJ/mol. The molar heat capacity C P of lead may be taken as 29.3J/(mol K)Solution: )/(363102.20721]108.4)25327(3.29[2121)(23322s m V v n n WQ nMv mv W H T C n Q Q Q absorb melting p melt increase absorb =⨯=⨯+-⨯===∆+∆=+=-1.2 what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at the rate of 20 m/minSolution )/(24560208.975)/(12160602410467000//)(104670001868.4102500sin 3S J t h mg P S J t Q t W PJ Q gincrea Burning Burning =⨯⨯=∆==⨯⨯====⨯⨯=1.3 One cubic decimeter (1 dm 3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20℃.(a) what is the total area of the droplets?(b) Calculate the minimum work required to produce the droplets. Assume that the droplets are rest (have zerovelocity)Water have a surface tension of 72.75 dyn/cm at 20℃ (NOTES: the term surface energy (ene/cm 2) is also used for surface tension dyn/cm)Solution)(6.436)106103(1075.72)(106)105.0(4)105.0(34)101(232523263631J S W m nS S Single total =⨯-⨯⨯⨯=∆=⨯=⨯⨯⨯⨯⨯⨯⨯⨯==-+----σππ1.4 Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25℃, the pressure is 10 atm. Assume that helium is an ideal gas.(a) when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm), what will be thetemperature of the first gas to hit the specimen?(b) As the helium flows, the pressure in the tank drops. What will be the temperature of the helium entering thequench chamber when the pressure in the tank has fallen to 1 atm?Solution: )(180118298)(1185.229810101325501010101325)5500(1)()(118)101(298)()(0334.0/00K T T T K RR nC W T b K T P P T T Adiabatica p CR P=-=∆-==⨯⨯⨯⨯⨯⨯⨯-⨯==∆=⨯==--1.5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T 0. The valve on the tank is oðened and the surrounding gas is allowed to flow suickly into t(e tank until the pressure insi`e the tank is equals the pressure outside. Assume that no heat flow takes place. What is the0final tempeture kf t èe gaS in the tank? The heat cap!city mf the gas, C p and C v each íay be(assumed to be c/nsuant over thå temperature rang!spanNed by the døperiment. You answer may be meft in terms of C p and S vM hint: one way to approach the xroblem is to define the system as the gas ends up in the tank. hint: one way to approach the xroblem is to define the system as the gas ends up in the tank.solution 0/000/00)()(T P P T T P PT T Adiabatic PPC R C R ≈-==1.6 Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO 2 and CH 4 (gas)[This heat of reaction is also called the low calorific power of methane] convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atm NOTE: this value is a good approximation for the low calorific powder of natural gasDATA: )()()(224g O H g CO g CH FOR80.5705.9489.17]/[0298---∙∆mol g Kcal Hsolution)1000/(9.2610252103048.01101076.191)/(76.191)89.1780.57205.94()2(22333332982982224422SCF Btu mol g Kcal H H H H H OH CO O CH CH O H CO =⨯⨯⨯⨯⨯=∙=∆+⨯---=∆-∆+∆-=∆+=+- 1.7Methane is delivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O 2 and 79% N 2)(a) Assuming complete combustion, what is the composition of the flue gas (the gas following combustion)? (b) What is the temperature of the gas, assuming no heat loss?(c) The furnace processes 2000kg of glass hourly, and its heat losses to the surroundings average 400000 kJ/h.calculate the fuel consumption at STP (in m 3/h) assuming that for gas H 1600-H 298=1200KJ/KG(d) A heat exchanger is installed to transfer some of the sensible heat of the flue gas to the combustion air.Calculate the decrease in fuel consumption if the combustion air is heated to 800K DATA STP means T=298K, P=1atm22224O N O H CO CH for2.82.89.117.1316)/(C mol cal C P ∙Solution)(210448.1125.9100076.191298)/(25.9)]87.012.72(2.843.179.1171.87.13[01.0)(%87.0%%12.72%%43.17%2%%71.8)11.1(221791.1231%22)(0,,222222224K T T T C mol cal X C C b O N CO O H CO O H CO O CH a i i p p p =⨯⨯+=∆+=∙=+⨯+⨯+⨯=======-⨯+⨯⨯+=+=+∑)/(1644)0224.011868.448.11)8001600(48.1125.9189570(102800000)/(189570)298800)](48.1187.8)48.1125.9[(100076.191)()/(87.848.11/]211002.22.816[)()/(3214)0224.011868.448.11)2981600(48.1125.9100076.191(102800000)/(280000040000020001200)(33min ,,,,298,,33min h m V mol g cal dTn C n C H H C mol cal X C C d h m V h KJ P C gConsu i i r p i i p p i i p r p g Consu =⨯⨯-⨯-⨯=∙=-⨯-⨯-⨯=--∆=∆∙=⨯⨯+===⨯⨯-⨯-⨯⨯==+⨯=⎰∑∑∑1.8 In an investigation of the thermodynamic properties of a-manganese, the following heat contents were determined:H 700-H 298=12113 J/(g atom) H 1000-H 298=22803 J/(g atom)Find a suitable equation for H T -H 298 and also for C P as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given tempeture rang.Solution )298(0055.0)298(62.35011.062.35011.062.3522803)2981000(2)2981000(12113)298700(2)298700(]2[2229822222982---=∆-=-===-+-=-+-+=+==∆⎰⎰T T H TC b a ba ba T baT bTdT a dT C H T P T P1.9 A fuel gas containing 40% CO, 10% CO 2, and the rest N 2 (by volume) is burnt completely with air in a furnace. The incoming and ongoing temperatures of the gases in the furnace are 773K and 1250K,respectively. Calculate (a) the maximum flame temperature and (b) heat supplied to the furnace per cu. ft of exhaust gasmolJ Hmol J H CO f CO f /393296/1104580,298,0,298,2-=∆-=∆)/(10184.403.29)/(1067.11010.492.19)/(1037.81020.935.44)/(1042.01097.345.283,253,253,253,222molK J T C molK J T T C molK J T T C molK J T T C N P O P CO P CO P -------⨯+=⨯-⨯+=⨯-⨯+=⨯-⨯+= Solution?0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)()/(1019.01058.528.33722.0278.0)/(1067.01038.477.281.065.005.02.0)()/(282838110458393296%2.72%8.27%10%65%5%20)4/(1122298127332981523733253253298,,,,298,253,,,,,253,,,,,,,0,298,0,298,298,22222222222222==+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆⨯-⨯+=+==⨯-⨯+=+++===-=∆-∆=∆========+-----------⎰⎰⎰∑∑⎰∑∑∑∑T T T T T T T dTT T dTT T dTn C n C n H H molK J T T C C n C C molK J T T C C C C n C C a mol J n Hn H H N CO production O N CO CO reation then O N air mole need fuel mole when CO O CO T TT i i r p i i p p i i N P CO P i i p p r p O P N P CO P CO P i i p p r p i pf i rf idTT T Q dT T T Q b T T T T T T T dTT T dTT T dT n C n C n H H T TT i i r p i i p p i i 9.0)1019.01058.528.33(2.02828389.0)1019.01058.528.33(2.0282838)(0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)(253125029812502982531250298125029829812125029815231250253253298,,,,298,⨯⨯-⨯++⨯-=⨯⨯-⨯++⨯-===+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆-----------⎰⎰⎰⎰⎰∑∑⎰1.10 (a) for the reaction2221CO O CO →+,what is the enthalpy of reaction (0H ∆) at 298 K ?(b) a fuel gas, with composition 50% CO, 50% N 2 is burned using the stoichiometric amount of air. What is the composition of the flue gas?(c) If the fuel gas and the air enter there burner at 298 K, what is the highest temperature the flame may attain(adiabatic flame temperature)? DATA :standard heats of formationfH ∆ at 298 K)/(393000)/(1100002mol J CO mol J CO -=-=Heat capacities [J/(mol K)] to be used for this problem N 2=33, O 2=33, CO=34, CO 2=57Solution )(21100)298)(39889.0(222.02830000)/(3975.03325.057)/(33111.034222.033666.033)(%,75%%,251.111002.22%%1.11%%,6.66%%,2.222.0/25.015.0%)()/(283000393000110000)(,0,,,,,,22220,298,0,298,0K T T dT C n H H K mol J X C C K mol J X C C C N CO product O N CO fuel b mol J n H n H H a P p p i P r i P r i P p i P p i P f i r f ==-⨯-⨯=-∆=∆∙=⨯+⨯==∙=⨯+⨯+⨯====-====+==+-=∆-∆=∆⎰∑∑∑∑1.11 a particular blast furnace gas has the following composition by (volume): N 2=60%, H 2=4, CO=12%, CO 2=24%(a) if the gas at 298K is burned with the stochiometric amount of dry air at 298 K, what is the composition of the flue gas? What is the adiabatic flame temperature?(b) repeat the calculation for 30% excess combustion air at 298K(C)what is the adiabatic flame temperature when the blast furnace gas is preheated to 700K (the dry air is at 298K) (d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will thE dlaMe temperature be affected?DaTA(k J?mol)2CO CO FOR513.393523.110)/(--∆m o l kJ H f2222,)(O N g O H CO CO FOR?? 34505733]/[K mol J C P ∙SolutionOH O H CO O CO a 222222121)(→+→+ 416.0)(104.0)(:22==N n O n Air6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 32.0)(08.0)(:22==N n O n Air 92.0)(04.0)(36.0)(:222===N n O H n CO n Flue)(98.1108)(8108.53106308.43)/(8.533492.05004.05736.092.004.036.06308.43)08.241(04.0)523.11051.393(12.03,,222222K T K T K J C C C n CKJH H H N O H CO ii r P O H H CO CO ==⨯=∆=⨯+⨯+⨯=++==-⨯+-⨯=∆+∆=∆∑--(b)repeat the calculation for 30% excess0combustion air at 298K6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel416.0)(104.0)(:22==N n O n Air 024.0)(016.1)(04.0)(36.0)(:2222====O n N n O H n CO n Flue July 16, 2019(C)what is the adiabatic flame temperature when the blasp furnace gas is preheated to 700K (the dry air is at 298K)6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 32.0)(08.0)(:22==N n O n Air 92.0)(04.0)(36.0)(:222===N n O H n CO n Flue)(6.1401)(6.11038.5310373.59)/(8.533492.05004.05736.096.004.036.0373.59)346.02804.05724.03312.0()298700()08.241(04.0)523.11051.393(12.03,,298700222222K T K T K J C C C n CKJH H H H N O H CO ii r P fuel O H H CO CO ==⨯=∆=⨯+⨯+⨯=++==⨯+⨯+⨯+⨯⨯-+-⨯+-⨯=∆+∆+∆=∆∑---(d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will the flame temperature be affected?)(8.1051)(8.75388.57106308.43)/(88.5734024.034016.15004.05736.0024.0016.104.036.06308.43)08.241(04.0)523.11051.393(12.03,,2222222K T K T K J C C C C n CKJH H H O N O H CO ii r P O H H CO CO ==⨯=∆=⨯+⨯+⨯+⨯=+++==-⨯+-⨯=∆+∆=∆∑--6.0)(04.0)(24.0)(12.0)(:222====N n H n CO n CO n Fuel 008.04.01576015)(32.0)(08.0)(:222=-===O H n N n O n Air 92.0)(048.0)(36.0)(:222===N n O H n CO n Flue)(1103)(8052.54106308.43)/(2.543492.050048.05736.092.0048.036.06308.43)08.241(04.0)523.11051.393(12.03,,222222K T K T K J C C C n CKJH H H N O H CO ii r P OH H CO CO ==⨯=∆=⨯+⨯+⨯=++==-⨯+-⨯=∆+∆=∆∑--1.12 A bath of molten copper is super cooled to 5℃ below its true melting point. Nucleation of solid copper then takes place, and the solidification proceeds under adiabatic conditions. What percentage of the bath solidifies? DATA: Heat of fusion for copper is 3100 cal/mol at 1803℃(the melting point of copper) C P,L =7.5(cal/mol ℃), C P,S =5.41+(1.5*10-3T )(cal/mol ℃) Solution)/(310355.75.0)17981803(105.1541.5310002231798,1798,17981803,18031798,1803,mol cal HH dT C dT C H LS SL L P S P L S =⨯-⨯-⨯+⨯+==+++-⎰⎰1.13 Cuprous oxide (Cu 2O) is being reduced by hydrogen in a furnace at 1000K, (a)write the chemical reaction for the reduced one mole of Cu 2O(b)how much heat is release or absorbed per mole reacted? Given the quantity of heat and state whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction)DATA: heat of formation of 1000K in cal/mol Cu 2O=-41900 H 2O=-59210 solution)/(173104190059210222mol cal H OH Cu H O Cu =-=∆+=+,exothermic reaction1.14(a) what is the enthalpy of pure, liquid aluminum at 1000K?(b) an electric resistance furnace is used to melt pure aluminum at the rate of 100kg/h. the furnace is fed with solid aluminum at 298K. The liquid aluminum leaves the furnace at 1000K. what is the minimum electric powder rating (kW) of furnace.DATA : For aluminum : atomic weight=27g/mol, C p,s =26(J/molK), C p,L =29(J/molK), Melting point=932K, Heat of fusion=10700J/mol Solution)(28.0)(7.2793600110002727184)/(2718410700)9321000(29)298932(261000932,932298,1000,kW W P mol J H dT C dT C H SLL P S P l ==⨯⨯==+-⨯+-⨯=++=⎰⎰1.15 A waste material (dross from the melting of aluminum) is found to contain 1 wt% metallic aluminum. The rest may be assumed to aluminum oxide. The aluminum is finely divided and dispersed in the aluminum oxide; that is the two material are thermally connected.If the waster material is stored at 298K. what is the maximum temperature to which it may rise if all the metallic aluminum is oxidized by air/ the entire mass may be assumed to rise to the same temperature. Data : atomic weight Al=27g/mol, O=16g/mol, C p,s,Al =26(J/molK), C p,s, Al2O3=104J/mol, heat formation of Al 2O 3=-1676000J/molSolution;)(600)(3021041029927275.116122711676000K T K T T ==∆∆⨯⨯++⨯⨯=⨯⨯1.16 Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356K) is sprayed on a cooling surface, where it solidified and cools to 400K. The copper is supplied to the apparatus at the rate of one kilogram per minute. Cooling water is available at 20℃, and is not allowed to raise above 80℃. What is the minimum flow rate of water in the apparatus, in cubic meters per minute? DATA; for water: C p =4.184J/g k, Density=1g/cm 3; for copper: molecular weight=63.54g/mol C p =7cal/mol k, heat of fusion=3120 cal/molSolution:min)/(10573.2)2080(1min /min54.631000)]4001356(73120[min /33m V VQQ WaterCopper -⨯=-=⨯⨯-⨯+=1.17 water flowing through an insulated pipe at the rate of 5L/min is to be heated from 20℃ to 60℃ b an electrical resistance heater. Calculate the minimum power rating of the resistance heater in watts. Specify the system and basis for you calculation. DA TA; For water C p =4.184J/g k, Density=1g/cm 3 Solution:)(139476010005)2060(184.4W W =⨯⨯-⨯=1.18 The heat of evaporation of water at 100℃ and 1 atm is 2261J/mol (a) what percentage of that energy is used as work done by the vapor?(b)if the density of water vapor at 100℃ and 1 atm is 0.597kg/m 3 what is the internal energy change for the evaporation of water?Solution:)/(375971822613101%6.71822613101%)/(31010224.0273373101325mol J Q W U mol J V P =⨯+-=+=∆=⨯==⨯⨯=∆1.19 water is the minimum amount of steam (at 100℃ and 1 atm pressure) required to melt a kilogram of ice (at 0℃)? Use data for problem 1.20 Solution)(125,3341000)10018.42261(g m m =⨯=⨯+1.20 in certain parts of the world pressurized water from beneath the surface of the earth is available as a source of thermal energy. To make steam, the geothermal water at 180℃ is passed through a flash evaporator that operates at 1atm pressure. Two streams come out of the evaporator, liquid water and water vapor. How much water vapor is formed per kilogram of geothermal water? Is the process reversible? Assume that water is incompressible. The vapor pressure of water at 180℃ is 1.0021 Mpa( about 10 atm) Data: C P,L =4.18J/(g k), C P ,v =2.00J/(g k), △H V =2261J/g, △H m =334 J/g Solution:leirreversib g x x x )(138),1000(8018.4)8018.48022261(=-⨯⨯=⨯-⨯+The problems of the second law2.1 The solar energy flux is about 4J cm 2/min. in no focusing collector the surface temperature can reach a value of about 900℃. If we operate a heat engine using the collector as the heat source and a low temperature reservoir at 25℃, calculate the area of collector needed if the heat engine is to produce 1 horse power. Assume the engine operates at maximum efficiency.Solution)(25.6)(7466010427390)2590(24m S W tWP StQ T T T W H H L H ===⨯⨯+-=-=2.2 A refrigerator is operated by 0.25 hp motor. If the interior of the box is to be maintained at -20℃ ganister a maximum exterior temperature of 35℃, what the maximum heat leak (in watts) into the box that can be tolerated if the motor runs continuously? Assume the coefficient of performance is 75% of the value for a reversible engine.Solution:)(64374625.02035202734375.0W P P T T T P Q T T T W L LL LH HHLH =⨯⨯+-⨯=-=-=2.3 suppose an electrical motor supplies the work to operate a Carnot refrigerator. The interior of the refrigerator is at 0℃. Liquid water is taken in at 0℃ and converted to ice at 0℃. To convert 1 g of ice to 1 g liquid. △H=334J/g is required. If the temperature outside the box is 20℃, what mass of ice can be produced in one minute by a 0.25 hp motor running continuously? Assume that the refrigerator is perfectly insulated and that the efficiencies involved have their largest possible value.Solution:)(4576033474625.020273g m M m P P T T T P L LLLH ===⨯⨯=-=2.4 under 1 atm pressure, helium boils at 4.126K. The heat of vaporization is 84 J/mol what size motor (in hp) is needed to run a refrigerator that must condense 2 mol of gaseous helium at 4.126k to liquid at the same temperature in one minute? Assume that the ambient temperature is 300K and that the coefficient of performance of the refrigerator is 50% of the maximum possible.Solution:)(52.0)(393'60284216.4216.4300'5.0%50hp W P P T T T P P Q T T T W L L L H LLLH ==⨯⨯-=-==-=2.5 if a fossil fuel power plant operating between 540 and 50℃ provides the electrical power to run a heat pump that works between 25 and 5℃, what is the amount of heat pumped into the house per unit amount of heat extracted from the power plant boiler.(a) assume that the efficiencies are equal to the theoretical maximum values(b) assume the power plant efficiency is 70% of maximum and that coefficient of performance of the heat pumpis 10% of maximum(c) if a furnace can use 80% of the energy in fossil foe to heat the house would it be more economical in terms ofoverall fissile fuel consumption to use a heat pump or a furnace ? do the calculations for cases a and b solution:1,2,2,1,212,2,2,2,21,1,1,1,198.82527352527354050540)(H H H H H H L H H H L H P P P P P P P T T T P P T T T P a =+-=+-=-=-= .,)(6286.0)(1,2,not is b ok is a c PP b H H =2.6 calculate △U and △S when 0.5 mole of liquid water at 273 K is mixed with 0.5 mol of liquid water at 373 K and the system is allowed to reach equilibrium in an adiabatic enclosure. Assume that C p is 77J /(mol K) from 273K to 373K Solution:)/(933.0)273323ln(5.0)373323ln(5.0)ln()ln()(02211K J C C T T C n T T C n S J U P P E P E P =+=+=∆=∆2.7 A modern coal burning power plant operates with a steam out let from the boiler at 540℃ and a condensate temperature of 30℃.(a) what is the maximum electrical work that can be produced by the plant per joule of heat provided to theboiler?(b) How many metric tons (1000kg) of coal per hour is required if the plant out put is to be 500MW (megawatts).Assume the maximum efficiency for the plant. The heat of combustion of coal is 29.0 MJ/k g(c) Electricity is used to heat a home at 25℃ when the out door temperature is 10℃ by passing a currentthrough resistors. What is the maximum amount of heat that can be added to the home per kilowatt-hour of electrical energy supplied?Solution:)(3.69)(6937136005000.29)()(89.013054030540)(ton kg m T T T mb J Q T T T W a LH LH H L H ==⨯=-=+-=-=)(9.191102525273)(J Q Q T T T W c H HHLH =-+=-=2.8 an electrical resistor is immersed in water at the boiling temperature of water (100℃) the electrical energy input into the resistor is at the rate of one kilowatt(a) calculate the rate of evaporation of the water in grams per second if the water container is insulated that is noheat is allowed to flow to or from the water except for that provided by the resistor(b) at what rate could water could be evaporated if electrical energy were supplied at the rate of 1 kw to a heatpump operating between 25 and 100℃data for water enthalpy of evaporation is 40000 J/mol at 100℃; molecular weight is 18g/mol; density is 1g/cm 3solution:)(23.2,2510027310010004000018)()(45.0,10004000018)(g m m b g m ma =-+===2.9 some aluminum parts are being quenched (cooled rapidly ) from 480℃ to -20℃ by immersing them in abrine , which is maintained at -20℃ by a refrigerator. The aluminum is being fed into the brine at a rate of one kilogram per minute. The refrigerator operates in an environment at 30℃; that is the refrigerator may reject heat at 30℃. what is them minus power rating in kilowatts, of motor required to operate the refrigerator?Data for aluminum heat capacity is 28J/mol K; Molecular weight 27g/mol Solution:)(5.102)(102474202732030)20480(28271000kW W P P T T T P P L L L L H W L ==---=-=--⨯=2.10 an electric power generating plant has a rated output of 100MW. The boiler of the plant operates at 300℃. The condenser operates at 40℃(a) at what rate (joules per hour) must heat be supplied to the boiler?(b) The condenser is cooled by water, which may under go a temperature rise of no more than 10℃. Whatvolume of cooling water in cubic meters per hour, is require to operate the plant?(c) The boiler tempeture is to be raised to 540℃,but the condensed temperature and electric output will remainthe same. Will the cooling water requirement be increased, decreased, or remain the same?Data heat capacity 4.184, density 1g/cm 3 Solution: )(109.7)(102.21040300273300)(1188J t P Q W P T T T P a H H L H H H ⨯==⨯=-+=-= )(1003.1184.41010)(103.4)(34611m V Q V J Q b LL ⨯==⨯⨯⨯⨯= noW P T T T P c L H H H )(10626.11040540273540)(88⨯=-+=-= 2.11 (a) Heat engines convert heat that is available at different temperature to work. They have been several proposals to generate electricity y using a heat engine that operate on the temperature differences available at different depths in the oceans. Assume that surface water is at 20℃, that water at a great depth is at 4℃, and that both may be considered to be infinite in extent. How many joules of electrical energy may be generated for each joule of energy absorbed from surface water? (b) the hydroelectric generation of electricity use the drop height of water as the energy source. in a particular region the level of river drops from 100m above sea level to 70m above the sea level . what fraction of the potential energy change between those two levels may be converted into electrical energy? how much electrical energy ,in kilowatt-hours, may be generated per cubic meter of water that undergoes such a drop? Solution: )/(1006.136001000)()(055.0127320420)(6h kW h mg P b J Q T T T W a H H L H ⨯=⨯∆==+-=-=2.12 a sports facility has both an ice rink and a swimming pool. to keep the ice frozen during the summer requires the removal form the rink of 105 KJ of thermal energy per hour. It has been suggested that this task be performed by a thermodynamic machine, which would be use the swimming pool as the high temperature reservoir. The ice in the rink is to be maintain at a temperature of –15℃, and the swimming pool operates at 20℃, (a) what is the theoretical minimum power, in kilowatts, required to run the machine? (b) how much heat , in joule per hour , would be supplied t the pool by this machine?Solution: )(1014.1101527320273)()(77.33600/10152731520)(555kJ Q b kW P T T T P a H L L L H ⨯=-+==-+=-=2.13solution:)/(81.6810ln 314.877.45277.6282.4)/(152940)()/(67.4977.45277.6282.4)()/(152940)(22)(2molK cal S mol cal H d molK cal S c mol cal H b AlNN Al a -=+-⨯-⨯=∆=∆-=-⨯-⨯=∆=∆=+ 2.14 solution:)/(2257412000)27340273ln 184.4273336263273ln1.2()(400,010,K J dT T C T H dT T C m S WATER P m m ICE P =+++=+∆+=∆⎰⎰-2.15)(70428)(2896100077773002J W J Q T T T W L L L H ==-=-= 2.16)(4.3719))2.4300(314.85.13.83(3002.4300)(7.58663.832.42.4300J Q T T T W J Q T T T W H H L H L L L H =-⨯+-=-==-=-=2.17 yes d Q c K J P P nR S b J pdV n W Q OU T a )(0)()/(1.1910ln 314.81ln)()(570410ln 298314.810)(0==⨯⨯==∆=⨯⨯=-=-==∆=∆⎰ 2.18)(1222335273020********g m m m T T T L L H =-=-=⨯ Property Relations 1. At -5︒C, the vapor pressure of ice is 3.012mmHg and that of supercooled liquid water is 3.163mmHg. The latent heat of fusion of ice is 5.85kJ/mol at -5︒C. Calculate ∆G and ∆S per mole for the transition of from water to ice at -5︒C. (3.2, 94) Solution: mol J P P RT G waterO H iceO H /9.1089523.0ln 268314.8163.3012.3ln )5273(314.8ln ,,22-=⨯⨯=-⨯==∆mol J H /1085.53⨯=∆)/(23.22268)9.108(5850K mol J T G H S S T H G ⋅=--=∆-∆=∆∴∆-∆=∆ 2. (1) A container of liquid lead is to be used as a calorimeter to determine the heat of mixing of two metals, A andB. It has been determined by experiment that the “heat capacity ” of the bath is 100cal/︒C at 300︒C. With the bath originally at 300︒C, the following experiments are performed;(2) A mechanical mixture of 1g of A and 1g of B is dropped into the calorimeter. A and B were originally at 25︒C. When the two have dissolved, the temperature of the bath is found to have increased 0.20︒C. 2. Two grams of a 50:50(wt.%) A-B alloy at 25︒C is dropped similarly into the calorimeter. The temperature decreases 0.40︒C. (a) What is the heat of mixing of the 50:50 A-B alloy (per gram of alloy)? (b) To what temperature does it apply ? (3.5, 94)Solution: mol J K cal C bath P /418/100,==(a) g cal T C Q bath P /102/2.01002/,=⨯=∆=This is the heat of mixing.(b) The heat capacity of C P, alloy : )/(072.06.27424.0100)254.0300(2,,K g cal TC C bath P alloy P ⋅=⨯⨯=--⨯∆⨯=Assuming that the calorimeter can be applied to the maximum of T ︒C, the for mixing to form 1 gram of alloy:10)'300(,1+-=T C Q bath P , )'(,2T T C Q alloy P -⋅=, 21Q Q =)'(10)'300(,,T T C T C alloy P bath P -=+-3. The equilibrium freezing point of water is 0︒C. At that temperature the latent heat of fusion of ice (the heat required to melt the ice) is 6063J/mol. (a) What is the entropy of fusion of ice at 0︒C ? (b) What is the change of Gibbs free energy for ice →water at 0︒C?(c) What is the heat of fusion of ice at -5︒C ? C P(ice) = 0.5 cal/(g. ︒C); C P(water) = 1.0 cal/(g. ︒C). (d) Repeat parts a and b at -5︒C. (3.6, p94)Solution: (a) At 0︒C, ∆G =0, ∴ T m ∆S = ∆H)./(09.222736030K mol J T H S m ==∆=∆(b) At 0︒C, ∆G =0© )./(62.37)./(1818.45.0)./(5.0,K mol J K mol J K g cal C ice P =⨯⨯==)./(24.75)./(1818.40.1)./(0.1,K mol J K mol J K g cal C water P =⨯⨯==a reversible process can be designed as follows to do the calculation:。

南昌大学材料科学基础复习题与部分答案-2012

单项选择题：第 1 章原子结构与键合1. 高分子材料中的 C-H 化学键属于。

（A ）氢键（B ）离子键（ C ）共价键2. 属于物理键的是。

（ A ）共价键（B ）范德华力（ C ）离子键3. 化学键中通过共用电子对形成的是。

（ A ）共价键（B ）离子键（ C ）金属键第 2章固体结构4. 以下不具有多晶型性的金属是。

（A ）铜（B ）锰（C ）铁5. fcc 、bcc 、hcp 三种单晶材料中，形变时各向异性行为最显著的是。

（ A ）fcc （B ）bcc （C ）hcp6. 与过渡金属最容易形成间隙化合物的元素是。

（A ）氮（B ）碳（C ）硼7. 面心立方晶体的孪晶面是。

（ A ）{112} （B ）{110} （ C ） {111} 8. 以下属于正常价化合物的是（。

（ A ）Mg 2（ B ）5 C ） 3PbCu Sn Fe C第 3章晶体缺陷9. 在晶体中形成空位的同时又产生间隙原子，这样的缺陷称为。

（ A ）肖特基缺陷（B ）弗仑克尔缺陷（C ）线缺陷10. 原子迁移到间隙中形成空位 -间隙对的点缺陷称为。

（ A ）肖脱基缺陷（B ） Frank 缺陷（C ）堆垛层错11. 刃型位错的滑移方向与位错线之间的几何关系是？（A ）垂直（B ）平行（C ）交叉 12. 能进行攀移的位错必然是。

（ A ）刃型位错（B ）螺型位错（C ）混合位错13. 以下材料中既存在晶界、又存在相界的是（ A ）孪晶铜（B ）中碳钢（C ）亚共晶铝硅合金 14. 大角度晶界具有 ____________个自由度。

（A ）3 （B ）4 （C ）5 第 4 章固体中原子及分子的运动15. 菲克第一定律描述了稳态扩散的特征，即浓度不随变化。

（A ）距离（B ）时间（C ）温度 16. 在置换型固溶体中，原子扩散的方式一般为。

（ A ）原子互换机制（ B ）间隙机制（C ）空位机制17. 固体中原子和分子迁移运动的各种机制中，得到实验充分验证的是（ A ）间隙机制（B ）空位机制（C ）交换机制18. 原子扩散的驱动力是。

材料热力学习题解答

《材料热力学》复习思考题解答3. 在1560℃时，C 在液态铁中的活度系数和偏摩尔超额焓由下列式表示： 2l n 0.37711.7c C C X X γ=-++25.415.017.25E C C C H X X =++(K Cal) 其标准态为纯石墨，计算1560℃时液相与石墨平衡的相线的斜率。

解：以石墨为标准态时，C 在液态铁中的化学位为：l n (1)LC CC R T a μμ=+ 石墨当液相与石墨平衡时，L C Cμμ=石墨。

即ln 0C α=。

又ln ln ln C C C X αγ=+ln ln 0(2)C C X γ∴+=由(2)式得：平衡时0.2067C X =两边取微分得：(ln )(ln )1[](1/)[]0(1/)C C C X T C C C C d T dX dX T X X γγ∂∂++=∂∂ (ln )[](1/)ln ln 1(1/)[()]1()CC X EC C C C C T C TC C CdX H X T d T R X X X X γγγ∂-∂∴==⋅∂∂-++∂∂2(5.415.017.25) 4.1810000.20678.311(723.4)278.6C C CC X X X X ++⨯⨯=-⋅++=- 2C dX T dT=-CdX 又d(1/T)5221278.68.310(1560273)C dX dT T -∴=-==⨯+C dX d(1/T) 1()K - 4. 在1000K 时，A-B 二元溶液中，当0.01B X =时，0.1B a =。

在盛有大量A 的量热计中加入少量的B 组元时，测得吸热7000Cal/mol ，假定2ln ln B A B X γγ=。

求1500K 时，当0.02B X =时，B 组元的活度。

解：在1000K 时，当0.01B X =时，0.1B a =0.1100.01B γ∴== 又022ln ln10ln 2.3490.99B B A X γγ=== 又ln [](1/)ii P H R T γ∂∆=∂15001500010001000l n (1/)BBH d d T Rγ∆∴=⎰⎰1500100011[ln ][ln ]()15001000B B B H R γγ∆∴=+-7000 4.18112.349()8.31150010001.175⨯=+-= 202l n (l n )0.981.175B A B X γγ∴==⨯ 1.128= l n 3.09B γ∴= 3.090.020.0B B B a X γ==⨯=7. 若A-B 二元合金系在液、固态两组元均能无限互溶，且均为理想溶液。

南昌大学工程材料学学期期末考试试题(A)及详解答案

工程材料学学期期末考试试题(A)及详解答案共5 页第1 页5. 杠杆定律只适用于两相区。

( )6. 金属晶体中，原子排列最紧密的晶面间的距离最小，结合力大，所以这些晶面间难以发生滑移。

( )7. 共析转变时温度不变，且三相的成分也是确定的。

( )8. 热加工与冷加工的主要区别在于是否对变形金属加热。

( )9. 过共析钢为消除网状渗碳体应进行正火处理。

( ) 10. 可锻铸铁能够进行锻造。

（）四、简答题（每小题5分,共20分）1．在图1中分别画出纯铁的)011(、)111(晶面和]011[、]111[晶向。

并指出在室温下对纯铁进行拉伸试验时，滑移将沿以上的哪个晶面及晶向进行？图12．为什么钳工锯 T10，T12 等钢料时比锯 10，20 钢费力，锯条容易磨钝？3．奥氏体不锈钢的晶间腐蚀是怎样产生的？如何防止？4．低碳钢渗碳表面化学热处理的温度范围是多少？温度选择的主要理由是什么？五、请用直线将下列材料牌号与典型应用零件及热处理工艺连接起来。

（每小题2分,共10分）材料牌号应用零件热处理工艺HT250 弹簧调质+氮化Cr12MoV 飞机起落架固溶+时效7A04（LC9）机车曲轴自然时效（退火）65Mn 冷冲模淬火+中温回火38CrMoAl 机床床身淬火+低温回火六、某工厂仓库积压了许多退火状态的碳钢，由于钢材混杂，不知道钢的化学成分，现找出其中一根，经金相分析后，发现其组织为珠光体+铁素体，其中铁素体占80% ，回答以下问题：（每小题4分,共12分）①求该钢的含碳量；②计算该钢组织中各相组分的相对百分含量；10．硅（Si），锰（Mn）；磷（P），硫（S）。

11．回火索氏体（或S回），索氏体（或S）。

12．20CrMnT，T10。

13．强化铁素体；提高淬透性。

14．灰口铸铁；最低抗拉强度300MPa，珠光体。

15．硬铝合金，α+β型钛合金三、判断题：(每小题1分,共10分)1．×， 2．√， 3．×， 4．×， 5．√， 6．×， 7．√， 8．×， 9．√， 10．×。

材料热力学习题答案

The problems of the first law1. a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25℃ and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327℃. The molar heat of fusion of the lead is 4.8kJ/mol. The molar heat capacity C P of lead may be taken as 29.3J/(mol K) (1.1)Solution: )/(5.112.20721]108.4)25327(3.29[2121)(2322s m V v n n WQ nMv mv W H T C n Q Q Q absorb melting p melt increase absorb ==⨯+-⨯===∆+∆=+=2. what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at eh rate of 20 m/min (1.2)Solution )/(24560208.975)/(12160602410467000//)(104670001868.4102500sin 3S J t h mg P S J t Q t W P J Q gincrea Burning Burning =⨯⨯=∆==⨯⨯====⨯⨯=3 One cubic decimeter (1 dm 3) of water is broken into droplets having a diameter of onemicrometer (1 um) at 20℃. (1.3)(a) what is the total area of the droplets?(b) Calculate the minimum work required to produce the droplets. Assume that the dropletsare rest (have zero velocity)Water have a surface tension of 72.75 dyn/cm at 20℃ (NOTES: the term surface energy (ene/cm 2) is also used for surface tension dyn/cm)Solution)(25.218)106103(1075.72)(103)101(4)101(34)101(232523263631J S W m nS S Single total =⨯-⨯⨯⨯=∆=⨯=⨯⨯⨯⨯⨯⨯⨯⨯==-+----σππ4.Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25℃, the pressure is 10 atm. Assume that helium is an ideal gas.(a) when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm),what will be the temperature of the first gas to hit the specimen?(b) As the helium flows, the pressure in the tank drops. What will be the temperature of thehelium entering the quench chamber when the pressure in the tank has fallen to 1 atm? (1.4)Solution: )(180118298)(1185.229810101325501010101325)5500(1)()(118)101(298)()(0334.0/00K T T T K RR nC W T b K T P PT T Adiabatic a p C R P=-=∆-==⨯⨯⨯⨯⨯⨯⨯-⨯==∆=⨯==--5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T 0. The valve on the tank is opened and the surrounding gas is allowed to flow quickly into the tank until the pressure inside the tank is equals the pressure outside. Assume that no heat flow takes place. What is the final tempeture of the gas in the tank? The heat capacity of the gas, C p and C v each may be assumed to be constant over the temperature rang spanned by the experiment. You answer may be left in terms of C p and C vhint: one way to approach the problem is to define the system as the gas ends up in the tank. (1.5)solution 0/000/00)()(T P P T T P PT T Adiabatic PPC R C R ≈-==6. Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO 2 and CH 4 (gas)[This heat of reaction is also called the low calorific power of methane] convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atmNOTE: this value is a good approximation for the low calorific powder of natural gas (1.6)DA TA:)()()(224g O H g CO g CH FOR80.5705.9489.17]/[0298---∙∆mol g Kcal Hsolution)1000/(9.2610252103048.01101076.191)/(76.191)89.1780.57205.94()2(22333332982982224422SCF Btu mol g Kcal H H H H H OH CO O CH CH O H CO =⨯⨯⨯⨯⨯=∙=∆+⨯---=∆-∆+∆-=∆+=+-7. Methane is delivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O 2 and 79% N 2) (1.7)(a) Assuming complete combustion, what is the composition of the flue gas (the gasfollowing combustion)?(b) What is the temperature of the gas, assuming no heat loss?(c) The furnace processes 2000kg of glass hourly, and its heat losses to the surroundingsaverage 400000 kJ/h. calculate the fuel consumption at STP (in m 3/h) assuming that for gas H 1600-H 298=1200KJ/KG(d) A heat exchanger is installed to transfer some of the sensible heat of the flue gas to thecombustion air. Calculate the decrease in fuel consumption if the combustion air is heated to 800KDA TA STP means T=298K, P=1atm22224O N O H CO CH for 2.82.89.117.1316)/(C mol cal C P ∙Solution)(210448.1125.9100076.191298)/(25.9)]87.012.72(2.843.179.1171.87.13[01.0)(%87.0%%12.72%%43.17%2%%71.8)11.1(221791.1231%22)(0,,222222224K T T T C mol cal X C C b O N CO O H CO O H CO O CH a i i p p p =⨯⨯+=∆+=∙=+⨯+⨯+⨯=======-⨯+⨯⨯+=+=+∑)/(1644)0224.011868.448.11)8001600(48.1125.9189570(102800000)/(189570)298800)](48.1187.8)48.1125.9[(100076.191)()/(87.848.11/]211002.22.816[)()/(3214)0224.011868.448.11)2981600(48.1125.9100076.191(102800000)/(280000040000020001200)(33min ,,,,298,,33min h m V mol g cal dTn C n C H H C mol cal X C C d h m V h KJ P C gConsu i i r p i i p p i i p r p g Consu =⨯⨯-⨯-⨯=∙=-⨯-⨯-⨯=--∆=∆∙=⨯⨯+===⨯⨯-⨯-⨯⨯==+⨯=⎰∑∑∑8.In an investigation of the thermodynamic properties of a-manganese, the following heat contents were determined: H 700-H 298=12113 J/(g atom) H 1000-H 298=22803 J/(g atom)Find a suitable equation for H T -H 298 and also for C P as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given tempeture rang. (1.8)Solution )298(0055.0)298(62.35011.062.35011.062.3522803)2981000(2)2981000(12113)298700(2)298700(]2[2229822222982---=∆-=-===-+-=-+-+=+==∆⎰⎰T T H TC b a ba ba T baT bTdT a dT C H TP T P9.A fuel gas containing 40% CO, 10% CO 2, and the rest N 2 (by volume) is burnt completely with air in a furnace. The incoming and ongoing temperatures of the gases in the furnace are 773K and 1250K,respectively. Calculate (a) the maximum flame temperature and (b) heat supplied to the furnace per cu. ft of exhaust gas (1.9)molJ Hmol J H CO f CO f /393296/1104580,298,0,298,2-=∆-=∆)/(10184.403.29)/(1067.11010.492.19)/(1037.81020.935.44)/(1042.01097.345.283,253,253,253,222molK J T C molK J T T C molK J T T C molK J T T C N P O P CO P CO P -------⨯+=⨯-⨯+=⨯-⨯+=⨯-⨯+=Solution?0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)()/(1019.01058.528.33722.0278.0)/(1067.01038.477.281.065.005.02.0)()/(282838110458393296%2.72%8.27%10%65%5%20)4/(1122298127332981523733253253298,,,,298,253,,,,,253,,,,,,,0,298,0,298,298,22222222222222==+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆⨯-⨯+=+==⨯-⨯+=+++===-=∆-∆=∆========+-----------⎰⎰⎰∑∑⎰∑∑∑∑T T T T T T T dT T T dTT T dT n C n C n H H molK J T T C C n C C molK J T T C C C C n C C a mol J n Hn H H N CO production O N CO CO reation then O N air mole need fuel mole when CO O CO T TT i i r p i i p p i i N P CO P i i p p r p O P N P CO P CO P i i p p r p i pf i rf idTT T Q dT T T Q b T T T T T T T dT T T dTT T dT n C n C n H H T TT i i r p i i p p i i 9.0)1019.01058.528.33(2.02828389.0)1019.01058.528.33(2.0282838)(0)499.0321.018.1()1067.01019.277.28(28.282831067.01038.477.289.0)1019.01058.528.33(2.0282838)(253125029812502982531250298125029829812125029815231250253253298,,,,298,⨯⨯-⨯++⨯-=⨯⨯-⨯++⨯-===+--⨯+⨯++⨯=⨯-⨯++⨯⨯-⨯+-⨯=--∆=∆-----------⎰⎰⎰⎰⎰∑∑⎰10. (a) for the reaction 2221CO O CO →+,what is the enthalpy of reaction (0H ∆) at 298 K ?(b) a fuel gas, with composition 50% CO, 50% N 2 is burned using the stoichiometric amount of air. What is the composition of the flue gas?(c) If the fuel gas and the air enter there burner at 298 K, what is the highest temperaturethe flame may attain (adiabatic flame temperature)? DA TA :standard heats of formation f H ∆ at 298 K (1.10))/(393000)/(1100002mol J CO mol J CO -=-=Heat capacities [J/(mol K)] to be used for this problem N 2=33, O 2=33, CO=34, CO 2=57 Solution)(21100)298)(39889.0(222.02830000)/(3975.03325.057)/(33111.034222.033666.033)(%,75%%,251.111002.22%%1.11%%,6.66%%,2.222.0/25.015.0%)()/(283000393000110000)(,0,,,,,,22220,298,0,298,0K T T dT C n H H K mol J X C C K mol J X C C C N CO product O N CO fuel b mol J n H n H H a P p p i P r i P r i P p i P p i P f i r f ==-⨯-⨯=-∆=∆∙=⨯+⨯==∙=⨯+⨯+⨯====-====+==+-=∆-∆=∆⎰∑∑∑∑11.a particular blast furnace gas has the following composition by (volume): N 2=60%, H 2=4, CO=12%, CO 2=24%(a) if the gas at 298K is burned with the stochiometric amount of dry air at 298 K, what is the composition of the flue gas? What is the adiabatic flame temperature? (b) repeat the calculation for 30% excess combustion air at 298K(C)what is the adiabatic flame temperature when the blast furnace gas is preheated to 700K (the dry air is at 298K)(d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will the flame temperature be affected? DA TA(k J/mol) （1.11）2CO CO FOR513.393523.110)/(--∆m o lkJ H f 2222,)(O N g O H CO CO FOR34505733]/[K mol J C P ∙Solution)(1052)(75438286370])295.03450(241604[026.0])335.03457(110523393513[079.0])([%8.66%%,8.6%%,6.2%%,8.15%%,9.72.0/83.110012%)()(1122)(82538313430])295.03450(241604[029.0])335.03457(110523393513[086.0])([%7.65%%,7.5%%,9.2%%,1.17%%,6.82.0/810012%2121)(,,,,,,,02222,,,,,,,0222222222K T K T T n C T T X C dT n C n C H x H N O H CO CO b K T K T T n C T T X C dT n C n C H x H N O H CO CO OH O H CO O CO a i i r P ii P i i r P i i p P i i i i r P ii P i i r P i i p P i i ===∆=∆-∆-⨯--+∆-⨯---=+--∆=∆=====⨯+====∆=∆-∆-⨯--+∆-⨯---=+--∆=∆=====+=→+→+∑∑∑⎰∑∑∑∑∑⎰∑∑)(1419),(11213842594034286.0)402(2.39714.0])295.03450(241604[029.0])335.03457(110523393513[086.0)3(K T K T T T T T H ===∆=∆⨯--∆⨯-∆-⨯--+∆-⨯---=∆12．A bath of molten copper is super cooled to 5℃ below its true melting point. Nucleation of solid copper then takes place, and the solidification proceeds under adiabatic conditions. What percentage of the bath solidifies?DATA: Heat of fusion for copper is 3100 cal/mol at 1803℃(the melting point of copper) C P,L =7.5(cal/mol ℃), C P,S =5.41+(1.5*10-3T )(cal/mol ℃) （1.12） Solution)/(310355.75.0)17981803(105.1541.5310002231798,1798,17981803,18031798,1803,mol cal H H dT C dT C HL S SL L P S P LS =⨯-⨯-⨯+⨯+==+++-⎰⎰13．Cuprous oxide (Cu 2O) is being reduced by hydrogen in a furnace at 1000K, (a)write the chemical reaction for the reduced one mole of Cu 2O(b)how much heat is release or absorbed per mole reacted? Given the quantity of heat and state whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction) DATA: heat of formation of 1000K in cal/mol Cu 2O=-41900 H 2O=-59210 （1.13） solution)/(173104190059210222mol cal H OH Cu H O Cu =-=∆+=+,exothermic reaction14. (a) what is the enthalpy of pure, liquid aluminum at 1000K?(b) an electric resistance furnace is used to melt pure aluminum at the rate of 100kg/h. the furnace is fed with solid aluminum at 298K. The liquid aluminum leaves the furnace at 1000K. what is the minimum electric powder rating (kW) of furnace.DATA : For aluminum : atomic weight=27g/mol, C p,s =26(J/molK), C p,L =29(J/molK), Melting point=932K, Heat of fusion=10700J/mol (1.14)Solution )(28.0)(7.2793600110002727184)/(2718410700)9321000(29)298932(261000932,932298,1000,kW W P mol J H dT C dT C H SLL P S P l ==⨯⨯==+-⨯+-⨯=++=⎰⎰15 A waste material (dross from the melting of aluminum) is found to contain 1 wt% metallic aluminum. The rest may be assumed to aluminum oxide. The aluminum is finely divided and dispersed in the aluminum oxide; that is the two material are thermally connected.If the waster material is stored at 298K. what is the maximum temperature to which it may rise if all the metallic aluminum is oxidized by air/ the entire mass may be assumed to rise to the same temperature. Data : atomic weight Al=27g/mol, O=16g/mol, C p,s,Al =26(J/molK), C p,s,Al2O3=104J/mol, heat formation of Al 2O 3=-1676000J/mol(1.15)Solution;)(600)(3021041029927275.116122711676000K T K T T ==∆∆⨯⨯++⨯⨯=⨯⨯16 Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356K) is sprayed on a cooling surface, where it solidified and cools to 400K. The copper is supplied to the apparatus at the rate of one kilogram per minute. Cooling water is available at 20℃, and is not allowed to raise above 80℃. What is the minimum flow rate of water in the apparatus, in cubic meters per minute? DATA; for water: C p =4.184J/g k, Density=1g/cm 3; for copper: molecular weight=63.54g/mol C p =7cal/mol k, heat of fusion=3120 cal/mol (1.16)Solution:min)/(10573.2)2080(1min /min54.631000)]4001356(73120[min /33m V VQ Q Water Copper -⨯=-=⨯⨯-⨯+=17 water flowing through an insulated pipe at the rate of 5L/min is to be heated from 20℃ to 60℃ b an electrical resistance heater. Calculate the minimum power rating of the resistance heater in watts. Specify the system and basis for you calculation. DATA; For water C p =4.184J/g k, Density=1g/cm 3 (1.17) Solution: )(139476010005)2060(184.4W W =⨯⨯-⨯=18 The heat of evaporation of water at 100℃ and 1 atm is 2261J/mol (a) what percentage of that energy is used as work done by the vapor?(b)if the density of water vapor at 100℃ and 1 atm is 0.597kg/m 3 what is the internal energy change for the evaporation of water? (1.18)Solution: )/(375971822613101%6.71822613101%)/(31010224.0273373101325mol J Q W U mol J V P =⨯+-=+=∆=⨯==⨯⨯=∆19 water is the minimum amount of steam (at 100℃ and 1 atm pressure) required to melt a kilogram of ice (at 0℃)? Use data for problem 1.20 (1.19) Solution )(125,3341000)10018.42261(g m m =⨯=⨯+20 in certain parts of the world pressurized water from beneath the surface of the earth is available as a source of thermal energy. To make steam, the geothermal water at 180℃ is passed through a flash evaporator that operates at 1atm pressure. Two streams come out of the evaporator, liquid water and water vapor. How much water vapor is formed per kilogram of geothermal water? Is the process reversible? Assume that water is incompressible. The vapor pressure of water at 180℃ is 1.0021 Mpa( about 10 atm) Data: C P,L =4.18J/(g k), C P,v =2.00J/(g k), △H V =2261J/g, △H m =334 J/g (1.20) Solution:leirreversib g x x x )(138),1000(8018.4)8018.48022261(=-⨯⨯=⨯-⨯+The problems of the second law1 The solar energy flux is about 4J cm 2/min. in no focusing collector the surface temperature can reach a value of about 900℃. If we operate a heat engine using the collector as the heat source and a low temperature reservoir at 25℃, calculate the area of collector needed if the heat engine is to produce 1 horse power. Assume the engine operates at maximum efficiency. (2.1)Solution )(664.0)(74660104273900)25900(24m S W tWP StQ T T T W H H L H ===⨯⨯+-=-=2 A refrigerator is operated by 0.25 hp motor. If the interior of the box is to be maintained at -20℃ ganister a maximum exterior temperature of 35℃, what the maximum heat leak (in watts) into the box that can be tolerated if the motor runs continuously? Assume the coefficient of performance is 75% of the value for a reversible engine. (2.2)Solution:)(114474625.02035202733475.0%75W P P T T T P Q T T T W L LLLH HHLH =⨯⨯+-⨯=-=-=3 suppose an electrical motor supplies the work to operate a Carnot refrigerator. The interior of the refrigerator is at 0℃. Liquid water is taken in at 0℃ and converted to ice at 0℃. To convert 1 g of ice to 1 g liquid. △H=334J/g is required. If the temperature outside the box is 20℃, what mass of ice can be produced in one minute by a 0.25 hp motor runningcontinuously? Assume that the refrigerator is perfectly insulated and that the efficiencies involved have their largest possible value. (2.3)Solution: )(4576033474625.020273g m M m P P T T T P L LLLH ===⨯⨯=-=4 under 1 atm pressure, helium boils at 4.126K. The heat of vaporization is 84 J/mol what size motor (in hp) is needed to run a refrigerator that must condense 2 mol of gaseous helium at 4.126k to liquid at the same temperature in one minute? Assume that the ambient temperature is 300K and that the coefficient of performance of the refrigerator is 50% of the maximum possible. (2.4)Solution: )(52.0)(393'60284216.4216.4300'5.0%50hp W P P T T T P P Q T T T W L L L H LLLH ==⨯⨯-=-==-= 5 if a fossil fuel power plant operating between 540 and 50℃ provides the electrical powerto run a heat pump that works between 25 and 5℃, what is the amount of heat pumped into the house per unit amount of heat extracted from the power plant boiler. (a) assume that the efficiencies are equal to the theoretical maximum values(b) assume the power plant efficiency is 70% of maximum and that coefficient ofperformance of the heat pump is 10% of maximum(c) if a furnace can use 80% of the energy in fossil foe to heat the house would it be moreeconomical in terms of overall fissile fuel consumption to use a heat pump or a furnace ? do the calculations for cases a and b (2.5)solution:1,2,2,1,212,2,2,2,21,1,1,1,198.82527352527354050540)(H H H H H H L H H H L H P P P P P P P T T T P P T T T P a =+-=+-=-=-=.,)(6286.0)(1,2,not is b ok is a c P P b H H =6 calculate △U and △S when 0.5 mole of liquid water at 273 K is mixed with 0.5 mol of liquid water at 373 K and the system is allowed to reach equilibrium in an adiabaticenclosure. Assume that C p is 77J /(mol K) from 273K to 373K (2.6) Solution:)/(933.0)273323ln(5.0)373323ln(5.0)ln()ln()(02211K J C C T T C n T T C n S J U P P E P E P =+=+=∆=∆ 7 A modern coal burning power plant operates with a steam out let from the boiler at 540℃and a condensate temperature of 30℃.(a) what is the maximum electrical work that can be produced by the plant per joule of heatprovided to the boiler?(b) How many metric tons (1000kg) of coal per hour is required if the plant out put is to be500MW (megawatts). Assume the maximum efficiency for the plant. The heat of combustion of coal is 29.0 MJ/k g(c) Electricity is used to heat a home at 25℃ when the out door temperature is 10℃ bypassing a current through resistors. What is the maximum amount of heat that can be added to the home per kilowatt-hour of electrical energy supplied? (2.7)Solution:)(3.69)(6937136005000.29)()(89.013054030540)(ton kg m T T T mb J Q T T T W a LH LH H L H ==⨯=-=+-=-=)(9.191102525273)(J Q Q T T T W c H HHLH =-+=-=8 an electrical resistor is immersed in water at the boiling temperature of water (100℃) the electrical energy input into the resistor is at the rate of one kilowatt(a) calculate the rate of evaporation of the water in grams per second if the water containeris insulated that is no heat is allowed to flow to or from the water except for that provided by the resistor(b) at what rate could water could be evaporated if electrical energy were supplied at therate of 1 kw to a heat pump operating between 25 and 100℃data for water enthalpy of evaporation is 40000 J/mol at 100℃; molecular weight is 18g/mol; density is 1g/cm 3 (2.8)solution:)(23.2,2510027310010004000018)()(45.0,10004000018)(g m m b g m ma =-+===9 some aluminum parts are being quenched (cooled rapidly ) from 480℃ to -20℃ byimmersing them in a brine , which is maintained at -20℃ by a refrigerator. The aluminum is being fed into the brine at a rate of one kilogram per minute. The refrigerator operates in an environment at 30℃; that is the refrigerator may reject heat at 30℃. what is them minuspower rating in kilowatts, of motor required to operate the refrigerator? Data for aluminum heat capacity is 28J/mol K; Molecular weight 27g/mol (2.9)Solution:)(5.102)(102474202732030)20480(28271000kW W P P T T T P P L L L L H W L ==---=-=--⨯=10 an electric power generating plant has a rated output of 100MW. The boiler of the plantoperates at 300℃. The condenser operates at 40℃(a) at what rate (joules per hour) must heat be supplied to the boiler?(b) The condenser is cooled by water, which may under go a temperature rise of no morethan 10℃. What volume of cooling water in cubic meters per hour, is require to operate the plant?(c) The boiler tempeture is to be raised to 540℃,but the condensed temperature and electricoutput will remain the same. Will the cooling water requirement be increased, decreased, or remain the same?Data heat capacity 4.184, density 1g/cm 3 (2.10)Solution: )(109.7)(102.21040300273300)(1188J t P Q W P T T T P a H H L H H H ⨯==⨯=-+=-=)(1003.1184.41010)(103.4)(34611m V Q V J Q b L L ⨯==⨯⨯⨯⨯=noW P T T T P c L H H H )(10626.11040540273540)(88⨯=-+=-=11 (a) Heat engines convert heat that is available at different temperature to work. Theyhave been several proposals to generate electricity y using a heat engine that operate on the temperature differences available at different depths in the oceans. Assume that surface water is at 20℃, that water at a great depth is at 4℃, and that both may be considered to be infinite in extent. How many joules of electrical energy may be generated for each joule of energy absorbed from surface water? (b) the hydroelectric generation of electricity use the drop height of water as the energy source. in a particular region the level of river drops from 100m above sea level to 70m above the sea level . what fraction of the potential energy change between those two levels may be converted into electrical energy? how much electrical energy ,in kilowatt-hours, may be generated per cubic meter of water that undergoes such a drop? (2.11)Solution:)/(1006.136001000)()(055.0127320420)(6h kW hmg P b J Q T T T W a H H L H ⨯=⨯∆==+-=-=12 a sports facility has both an ice rink and a swimming pool. to keep the ice frozen during the summer requires the removal form the rink of 105 KJ of thermal energy per hour. It has been suggested that this task be performed by a thermodynamic machine, which would be use the swimming pool as the high temperature reservoir. The ice in the rink is to be maintain at a temperature of –15℃, and the swimming pool operates at 20℃, (a) what is the theoretical minimum power, in kilowatts, required to run the machine? (b) how much heat , in joule per hour , would be supplied t the pool by this machine? (2.12)Solution:)(1014.1101527320273)()(77.33600/10152731520)(555kJ Q b kW P T T T P a H L L L H ⨯=-+==-+=-=13solution:)/(81.6810ln 314.877.45277.6282.4)/(152940)()/(67.4977.45277.6282.4)()/(152940)(22)(2molK cal S mol cal H d molK cal S c mol cal H b AlNN Al a -=+-⨯-⨯=∆=∆-=-⨯-⨯=∆=∆=+14solution:)/(2257412000)27340273ln 184.4273336263273ln1.2()(40,010,K J dT T C T H dT T C m S WATER P m mICE P =+++=+∆+=∆⎰⎰- 15)(70428)(2896100077773002J W J Q T T T W L L L H ==-=-=16)(4.3719))2.4300(314.85.13.83(3002.4300)(7.58663.832.42.4300J Q T T T W J Q T T T W H H L H L L L H =-⨯+-=-==-=-=17yesd Q c K J PPnR S b J pdV n W Q OU T a )(0)()/(1.1910ln 314.81ln )()(570410ln 298314.810)(0==⨯⨯==∆=⨯⨯=-=-==∆=∆⎰18)(122233527302033560500g m m m T T T L L H =-=-=⨯教材各章习题参考答案 (魏)3.2 ΔG = -108.9 J/mol; ΔS = -21.42 J/(mol.K)3.6 (a ) 22.09/(.)S J mol K ∆=；(b) At 0︒C, ∆G =0; (c) ∆H = 5841.9 J;(d) ∆S =21.39J /(mol.K)，∆G = 109.38 J/mol4.1 (a ) 2898.28J/mol; ( b ) No; ( c ) 345 J/mol; ( d ) 14939 atm; ( e )4921 J/mol4.2 ( a ) 272.8K; ( b ) Pa P 610345⨯≈∆ ; ( c ) 249.46K 4.3 1202K4.4 P=5.73⨯10-6 atm 4.5 0.16P4.7 08.10430685ln +-=TP 4.8 ( a ) 1180K; ( b ) 695.3K; ( c ) 114.4kJ/mol; ( d ) 7123 J/mol; ( e )4.2J/mol4.9 In the initial state: 4.06 mol %; in the final state:5.3 mol% 4.10 ( a )348 kJ; ( b ) 2.3×10-3Pa ;( c ) “ solution not possible ”; (d ) “solution not possible ”5.1 atm p H 0005.0= 5.2、atmp o 1221007.1-⨯=If the error in enthalpy is 500cal, the uncertainty in the pressure calculated is 28.6%, and if the error in enthalpy is -500cal, the uncertainty is -22.1%5.3、(a) T =462K; (b) T = 420K5.4 (a) atm P O 2621014.1-⨯=, (b) P O2 =2.28⨯10-10 atm., (c) The equilibriumoxygen pressure remains the same when the total pressure increases, which means a higher purity level of N 2 .5.5 (a) 略； (b) Pa atm P H 8.181013056.1800019.0)('2=⨯==; (c) 21.5L Ar isneeded to be bubbled into the melt.5.6（a ）l n K a1/T, 10-31/K=∆-=∆o o G kJ H 1000;50- 66.6kJ(b) Ja = 3 < Ka, the reaction will proceed from left to right, and theatmosphere will not oxidize Ni. 5.7 略5.8. (a) P SiO = 8.1⨯10-8 (atm) (b) ∆H o = 639500J; ∆So =334.9J/K (c ) PO2 =10-30 atm 5.9 5.10．J H o72250=∆，the reaction is an endothermic one.5.11. (a),166528J H o =∆ the reaction is an endothermic one.; (b) At 1168K, the equilibrium pressure of CO2 equals one atmosphere.)(106.08)(atm Pg u -⨯=5.12 (a) 略， (b) Mg CO P P =; (c) T = 2037 K 5.13 (a) 略； (b) 13109.2⨯=K ; (c) ppm 186.0 5.14 (a) 略； (b) kJ H 52.267=∆; (c) K T 1592= 5.15 (a) )(106.13atm -⨯≈; (b) )(1028.210)(2atm P g O H -⨯=5.16 (a) 97.9=K ; (b) atm x 14.4=; (c) if the temperature is increased, the fraction of water reacted will increase since the equilibria constant increases with increasing temperature.6.2 （a ）1.287V;(b) When the water impure, the voltage will go higher; (c) 1.219V 6.4 (a) 145.3kJ;(b) The maximum work that could be derived is 702.36kJ; (c) In this case, the maximum work that could be derived is696.56kJ.6.5 (a) -6252J/mol; (b) 370.0)(=II Cd a ; (c) )(42.3mmHg P Cd =; 6.67.87⨯10-4 V 6.7 (a))(22g Cl Mg MgCl +=(b) Pa P Cl 21'1086.82-⨯=;(c) 2.485V6.8 (a) Pa P O 11'2105.5-⨯=;(b) Anode: e Ni Ni 2+→Cathode: -→+2222/1O e O ;(c) 0.757V; (d) 0.261V6.10 (a) )(509.3V E o=;(b) 0.074kJ;(c) 4.1⨯106J;(d) Yes. In this case, the open circuit voltage is 3.648V;(e) In this case, to keep the temperature constant, 3.92⨯106J heatshould be removed from the battery per hour. 6.11(a) TG CO Al C O Al o 26.3211008.12/322/36232-⨯=+=+Δ(b) The minimum voltage at which the electrolysis may be carriedout at 1250K is 1.172V .7.1 0.117 atm 7.5 ( a ) ,82.5 2.5 2.5B A BA BB T PV V V x x x x x ⎛⎫∂=+=--⎪∂⎝⎭ ,102.5 2.5 2.5A B A A B A T PV V V x x x x x ⎛⎫∂=+=-- ⎪∂⎝⎭( b) B A M x x V 5.2=7.7 2)1(736.0ln Sn Sn x --=γ7.8 The maximum solubility of MgF2 in liquid MgCl at 900︒C is 19。

热力学习题与答案（原件）讲解

材料热力学习题1、阐述焓H 、内能U 、自由能F 以及吉布斯自由能G 之间的关系，并推导麦克斯韦方程之一：T P PST V )()(∂∂-=∂∂。

答： H=U+PV F=U-TS G=H-TS U=Q+W dU=δQ+δWdS=δQ/T, δW=-PdV dU=TdS-PdVdH=dU+PdV+VdP=TdS+VdP dG=VdP-SdTdG 是全微分，因此有：TP P TP ST V ，PT G T P G ，T V P G T P T G P S T G P T P G )()()()()()(2222∂∂-=∂∂∂∂∂=∂∂∂∂∂=∂∂∂∂=∂∂∂∂∂-=∂∂∂∂=∂∂∂因此有又而2、论述：试绘出由吉布斯自由能—成分曲线建立匀晶相图的过程示意图，并加以说明。

（假设两固相具有相同的晶体结构）。

由吉布斯自由能曲线建立匀晶相图如上所示，在高温T 1时，对于所有成分，液相的自由能都是最低；在温度T 2时，α和L 两相的自由能曲线有公切线，切点成分为x1和x2，由温度T 2线和两个切点成分在相图上可以确定一个液相线点和一个固相线点。

根据不同温度下自由能成分曲线，可以确定多个液相线点和固相线点，这些点连接起来就成为了液相线和固相线。

在低温T 3，固相α的自由能总是比液相L 的低，因此意味着此时相图上进入了固相区间。

3、论述：通过吉布斯自由能成分曲线阐述脱溶分解中由母相析出第二相的过程。

第二相析出：从过饱和固溶体α中(x0)析出另一种结构的β相(xβ)，母相的浓度变为xα. 即：α→β+ α1α→β+ α1 的相变驱动力ΔGm的计算为ΔGm=Gm(D)-Gm(C)，即图b中的CD段。

图b中EF是指在母相中出现较大为xβ的成分起伏时，由母相α析出第二相的驱动力。

4、根据Boltzman方程S=kLnW，计算高熵合金FeCoNiCuCrAl和FeCoNiCuCrAlTi0.1（即FeCoNiCuCrAl各为1mol，Ti为0.1mol）的摩尔组态熵。

材料热力学习题解答第1一2章

（3）ΔU=ΔH=0
V W = -Q = -nRT ln 2 = - ×8.314×273×ln2 = -5619(J) V1
（4）Q=0; W=ΔU,即-pe(V2-V1)=nCV,m(T2-T1), -0.5p2V2= nCV,m(T2-T1) ; -0.5nRT2= nCV,m(T2-T1)-0.5×8.314×T2=2.5×8.314×(T2-273) ; T2=227.5K
W =Байду номын сангаасΔU = nCV, m (T2 - T1 ) = ΔH = nCp, m (T2 - T1 ) =
100 ×2.5×8.314×(227.5- 273)= -3378(J) 28
100 ×3.5×8.314×(227.5- 273)= -4729(J) 28
13、在244K温度下，1.00mol单原子气体（1）从1.01MPa、244K等温可逆膨胀到 505kPa,(2) 从1.01MPa、244K绝热可逆膨胀到505kPa，求两过程中的Q、W、ΔU 及ΔH，并作p-V图表示上述气体所进行的两个过程。解：（1）ΔU=ΔH=0
5、2.00mol的水蒸气在100℃、101325Pa下变为水，求Q、W、ΔU及ΔH。已知水的气化热为2258J/g。
解：Q Q p H -n vapH m -2 22581810-3 -81.29(kJ) W -pe V p e Vg nRT -2 8.314 37310-3 6.20(kJ) U Q W -81.29 6.20 -75.09(kJ)
4、在101kPa下，气体由10.0dm3膨胀到16.0dm3，吸收了1255J的热，求ΔU、 ΔH、W。
2H Q p 1255J 3U Q W 1255- 606 649J 1W -pe V -101103 (16- 10)10 - 3 -606(J) 解：

热力学复习题答案

热力学复习题答案热力学是物理学中研究能量转换和物质状态变化规律的科学。

在复习热力学时，理解一些基本概念和原理是至关重要的。

以下是一些热力学复习题的答案，供参考。

1. 热力学第一定律：热力学第一定律是能量守恒定律在热力学过程中的表述。

它表明，系统吸收的热量与对外做的功和系统内能的增加量相等。

即：\[ \Delta Q = \Delta U + W \]其中，\(\Delta Q\) 表示系统吸收或放出的热量，\(\Delta U\)表示系统内能的变化，\(W\) 表示系统对外做的功。

2. 热力学第二定律：热力学第二定律指出，不可能从单一热源吸热使之完全变为功而不产生其他影响。

它揭示了自然过程的不可逆性。

3. 熵：熵是表示系统无序程度的物理量。

熵增加意味着系统无序程度增加。

熵的变化可以通过以下公式计算：\[ \Delta S = \frac{Q_{\text{可逆}}}{T} \]其中，\(\Delta S\) 表示熵的变化，\(Q_{\text{可逆}}\) 表示在可逆过程中系统吸收或放出的热量，\(T\) 是绝对温度。

4. 理想气体状态方程：理想气体状态方程是描述理想气体状态的方程，其形式为：\[ PV = nRT \]其中，\(P\) 表示压强，\(V\) 表示体积，\(n\) 表示物质的量，\(R\) 是理想气体常数，\(T\) 是绝对温度。

5. 卡诺循环：卡诺循环是一种理想化的热机循环，它由两个等温过程和两个绝热过程组成。

卡诺循环的效率是所有循环中最高的，其效率由以下公式给出：\[ \eta = 1 - \frac{T_C}{T_H} \]其中，\(\eta\) 是卡诺循环的效率，\(T_C\) 是冷源的绝对温度，\(T_H\) 是热源的绝对温度。

6. 热力学第三定律：热力学第三定律指出，当系统的温度趋近于绝对零度时，系统的熵趋近于一个常数。

这意味着在绝对零度下，所有完美晶体的熵为零。

7. 吉布斯自由能：吉布斯自由能是描述在恒定温度和压力下，系统能够对外做的最大非体积功的能力。

南昌大学2014上半年材料热力学重点题(附氧势图)

solution:)/(81.6810ln 314.877.45277.6282.4)/(152940)()/(67.4977.45277.6282.4)()/(152940)(22)(2m olK cal S m ol cal H d m olK cal S c m ol cal H b AlNN Al a -=+-⨯-⨯=∆=∆-=-⨯-⨯=∆=∆=+Solution ：)/(173104190059210222mol cal H OH Cu H O Cu =-=∆+=+,exothermic reactionFor the reaction :)()(212g H g H → 035.33121314.823212,)(,-=⨯-⨯=-=∆H P g H P p C C CJC H dT C H H P oP oo 2128241702035.3217990)2982000(29820002982982000=⨯-=-⨯∆+∆=∆+∆=∆⎰JC H dT C H H P oP oo 2128241702035.3217990)2982000(29820002982982000=⨯-=-⨯∆+∆=∆+∆=∆⎰J C S dT C S S P oP oo 57.432982000ln035.335.492982000ln29820002982982000=⨯-=⨯∆+∆=∆+∆=∆⎰J S T H G 12568457.432000212824020000200002000=⨯-=∆-∆=∆56.72000314.8125684ln125684lnln lnln )(2/1)(2/1)(2/12/1)(20002222=⨯=→==-=-=∆g H H g H H g H H H g H o P P P P RT P P RT P P RT K RT GatmP P P P P H g H H g H g H 0005.0562.71ln1,1)(2)(2)(2=→=≈=+Solution: (a) When the equilibrium is reached,0P ln 21ln 2=∆=+∆=∆O o o RT G J RT G G －RT T P O 21)06.1539850(18.4ln 2+-⨯=T = 500︒C = 773KatmP P O O 26221014.169.36773314.821)77306.1539850(18.4ln -⨯=-=⨯⨯⨯+-⨯=(a) at T=300︒C=573K,Although the equilibrium P O2 is very low, kinetically the reaction isnot favoured and reaction speed is very slow. So 300︒C is not suitable atAt T=800︒C=1073K, lnP O2 =-22.2, P O2 =2.28⨯10-10 atm. At 800︒C, if the equilibrium is reached, nitrogen can be of high purity level. However, at this high temperature , particles of Cu will weld together to reduce effective work surface. So it is not suitable to use this high temperature in purification either.(c ) The equilibrium oxygen pressure remains the same when the total pressure increases, which means a higher purity level of N 2 .Solution: N 2 =2N, H 2 = 2H[]21221,N N a P K N = ， [],21221,H H a P K H =For N2 dissolving :For H2 dissolving ：2/1'2'2/12)(][][H HP H P H =（a ）For dissolving N2, P N2 = 1 atm, [N]=35cm 3/100g melt,melt g cm P N P N N N 100/75.24)5.0(35][)(][32/12/122/1'2=⨯==‘similarly: [H]’ =24.75cm 3/100g melttotal gas : [H]'＋[N]' = 49.5 cm 3/100g melt (b) [H]' =24.75 cm 3/100g melt (c ) [H]'＋[N]' =2/1'2'2/12)(][][N N P N P N = [N](0.33)1/2 /1+[H](0.33)1/2/1=20.10+20.10 = 40.2cm 3/100g meltSolution ：（1）0.2H∆ （2）G∆=max W （3）56KJ.696}{0.21P P P P RTlnG KTlnk G G 23O OH CH CO 20H 2322=+∆=+∆=∆）（）（）（）（θθSolution:(a)molJF Z -6252EG =-=∆θθ(b)0.370a ln RT G Cd==∆ (c))(3.42P PPCdmmHg ==θSolution:(b)PaP P g Cl g Cl 21)()(10*86.8-RT ln G 125.4T -605000G 22-==∆=∆θθ(c)-2.485VZF-GE =∆=答案更正为：Temperat ure Phase CompositionFraction1300 Liquid 60 61.5α8 38.5β99 0 1000+ Liquid 70 50.8α9 49.2β98 0 1000- Liquid _ 0α7 63.7β98 36.3Solution: )/(363102.20721]108.4)25327(3.29[2121)(23322s m V v n n WQ nMv m v W H T C n Q Q Q absorb melting p melt increase absorb =⨯=⨯+-⨯===∆+∆=+=-Solution )/(24560208.975)/(12160602410467000//)(104670001868.4102500sin 3S J t h m g P S J t Q t W P J Q g increa Burning Burning =⨯⨯=∆==⨯⨯====⨯⨯=Solution ：)(6.436)106103(1075.72)(106)105.0(4)105.0(34)101(232523263631J S W m nS S Single total =⨯-⨯⨯⨯=∆=⨯=⨯⨯⨯⨯⨯⨯⨯⨯==-+----σππSolution)(25.6)(7466010427390)2590(24m S W tWP StQ T T T W H H L H ===⨯⨯+-=-=Solution:)(64374625.02035202734375.0W P P T T T P Q T T T W L LLLH HHLH =⨯⨯+-⨯=-=-=solution:1,2,2,1,212,2,2,2,21,1,1,1,198.82527352527354050540)(H H H H H H L H H H L H P P P P P P P T T T P P T T T P a =+-=+-=-=-=.,)(6286.0)(1,2,not is b ok is a c P P b H H =Solution:molJ P P RT G waterO H ice O H /9.1089523.0ln 268314.8163.3012.3ln)5273(314.8ln,,22-=⨯⨯=-⨯==∆mol J H /1085.53⨯=∆)/(23.22268)9.108(5850K mol J T G H S ST H G ⋅=--=∆-∆=∆∴∆-∆=∆Solution: (a) At 0︒C, ∆G =0, ∴ T m ∆S = ∆H)./(09.222736030K mol J T H S m ==∆=∆ (b) At 0︒C, ∆G =0 ©)./(62.37)./(1818.45.0)./(5.0,K mol J K mol J K g cal C ice P =⨯⨯==./(1818.40.1)./(0.1,Kmol J K g cal C water P ⨯⨯==a reversible process can be designed as follows to do the calculation:molJ HdT C C dTC H dT C H H H Hwater P ice p water p ice p fu/9.584160305)24.7562.37()(273268,,268273,273268,)3()2()1(=+⨯-=∆+-=+∆+=∆+∆+∆=∆⎰⎰⎰（d ）)./(39.2109.22268273ln )24.7562.37()(3273268,,268273,273268,)3()2()1()4(K m ol J SdT TC C dTTC S dT TC S S S water P ice p waterp icep =+⨯-=∆+-=+∆+=∆+∆+∆=∆⎰⎰⎰38.10939.212689.5841)4()4()4(=⨯-=∆-∆=∆S T H GIce, 0︒Cwater, 0︒Cwater, -5︒Cice, -5︒C（1）（2）（3）（4）Solution: (a)diam ondgr aphite C C =mol kJ H H H ographite f o diam ond f /1897,,=∆-∆=∆)./(36.338.274.5,,K molJ S S S o graphite f o diam ond f -=+-=∆-∆=∆molJ S T H G /28.2898)36.3(2981897=-⨯-=∆-∆=∆(b) No, diamond is not thermodynamically stable relative to graphite at 298K. (c )molJ P V G diamand /29.34101309951.310126=⨯⨯⨯=∆=∆-(c ) Assuming N atm , ∆G = 0, reversible processes as following can be designed to realize this,（4）graphite, 298K, N atmdiamond, 298K, N atm)(14939028.2898194.028.28981013051.3101225.2101228.289810130)1)(V V ()(V 28.2898V 66)3()2()1()4(atm N N N N P P G G G G diamond graphite diamond graphite ==+-=+⨯⎪⎪⎭⎫ ⎝⎛⨯-⨯-=+⨯--=∆-++∆∆∆∆∆--＝＋＋＝,0,0''=∆=∆=∆⎰⎰dT TC dT C C T Tp T T p pmol J H H /1897298900=∆=∆K mol J S S ./36.3298900-=∆=∆molJ S T H G /492136.39001897=⨯+=∆-∆=∆Solution: (a) Ag 2O = 1/2O 2 + 2Ag30514/7300,==∆-=∆mol cal H H o AgO f o K m ol J S S S S O Ag O Ag o ./044.661.2949212.102212298,2298,2298,=-⨯+⨯=∆-∆+∆=∆TS T S T H G o o o o 044.663051430514-=∆-=∆-∆=∆when Ag2O begins to decompose,ln 044.66305140ln 2=+-=+∆=∆O o P RT T ie J RT G G(a) i n pure oxygen at 1 atm, RTlnP O2 = 030514-66.044T = 0 T = 462K(b) i n air at P total = =1 atm , P O2 =0.21ie. 30514- 66.044T + RTln0.21 = 0 T = 386KSolution: (a))1(ln Td R H K d o a ∆-= Plot T K a /1~ln0.880.900.920.940.960.981.001.02 1.04 1.06 1.087.27.47.67.88.08.28.48.6lnK a =2.01+6003(1/T)l n K a1/T, 10-3KduishuLinear Fit of Data1_Kduishu.J R H RH dT K d o oa 4990960036003ln -=⨯-=∆→=∆-=At T=1000K, lnK a =8.01, K a = 3010kJ J K RT G a o 6.666660001.81000314.8ln 1000==⨯⨯-=-=∆(b)aaa o K J K J RT J RT K RT J RT G G <===+-=+∆=∆3%5%15lnln ln lnSo the atmosphere will oxidize Ni.Solution:(-3)10^*3.680.32*0.00005*320PNa==BrH C B Cl H C X AA 5656A *::A P P =325.101)1(P P 325.101P P B *A *B *A *=-=++A A B A X X X Xk P aP k P a P X X B A B A 71.2659.74404.00.5956====Solution:(1)894.0814.0396.3033.37*30.396kPa 50.66*0.6P )()()(=====R B R A R A A a a a同理得(2)788.162.12222)(='=''=+⨯'=B AAA R A r r r r a 同理得(3)JmixG G mix mixG a RT a RT G mix R B R A 16102ln ln )()(-=∆∆=∆+=∆(4)m olJm ixG G m ix m ixGX RT X RT G m ix id ididBA id 69152ln ln -=∆∆=∆+=∆(5)J mixG mixG mixG id ex 5305=∆-∆=∆c.molJWXmolJWXX W X WX FeMn E MnFeE Mn BA M E 87.71846.16176.094.4492a 22=======μμ时， d.m olJX X X X RT X X RT M EMn Mn Fe Fe MEi i M 9370G )ln ln (G )ln (mixG -=∆++=∆+=∆∑ e.Solution:The standard Gibbs free energy change for reaction I: a.[]298.53TlnT244560-G ⨯+=∆θ b.5422711031074.1ln G --⨯=⨯==∆K K KRT 同理可得θ c.JJ RT G 5107ln G ⨯=+∆=∆θ ; Ni is stable under this condition,and NiO is not stable;d.Paatm P J RT G O 5853103.3103.3ln G 2⨯=⨯=+∆=∆θe 。

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