[工学]南昌大学材料热力学答案

The problems of the first law

1.1 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: )

/(363102.2072

1

]108.4)25327(3.29[2

1

21)

(2332

2s m V v n n W

Q 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/min

Solution )

/(24560

208.975)/(12160

602410467000

//)

(104670001868.4102500sin 3S J t h mg P S J t Q t W P

J Q g

increa 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 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

)

(6.436)106103(1075.72)

(106)105.0(4)105.0(3

4

)101(23252326363

1J S W m nS S Single total =⨯-⨯⨯⨯=∆=⨯=⨯⨯⨯⨯⨯⨯⨯⨯=

=-+----σππ

1.4 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 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 the helium entering the

quench chamber when the pressure in the tank has fallen to 1 atm?

Solution: )

(180118298)

(1185.2298

10101325501010101325)5500(1)

()

(118)10

1

(298)()

(03

3

4.0/0

0K T T T K R

R nC W T b K T P P T T Adiabatic

a p C

R 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 0/0

00/0

0)0(

)(T P P T T P P

T T Adiabatic P

P

C 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 gas

DATA: )

()()(224g O H g CO g CH FOR

80

.5705

.9489.17]/[0298---•∆mol g Kcal H

solution

)1000/(9.2610252103048.01

101076.191)/(76.191)89.1780.57205.94()2(223

33

33298

2982224422SCF Btu mol g Kcal H H H H H O

H CO O CH CH O H CO =⨯⨯⨯⨯⨯=•=∆+⨯---=∆-∆+∆-=∆+=+- 1.7

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)

(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=1atm