principles of Physics--24thermal 1

dN n= is the same everywhere. dV
v =v =v
2 x 2 y
2 2 x 2 y
2 z
2 z
v =v =v
2 x 2 y
2 z
v =v +v +v
1 2 = v 3
(3) Molecular interpretation of the pressure of an ideal gas Why does the pressure of gas exist? A large number of gas molecules collide with the wall of container. The ideal gas (V, N, m) is in equilibrium state. ni ---- The number of molecules v of velocity υi per unit volume
wall
ni vix dAdt
The impulse is :
υi
υixdt
v
dA
x
ni vix dAdt (2mvix )
The total impulse exerted by the molecules which collide with dA in the interval dt are :
（1）分子间距 >> 分子大小 ） （2）每个分子可看作是弹性小球； ）每个分子可看作是弹性小球； （3）除碰撞瞬间外，忽略分子间的相互作用及 ）除碰撞瞬间外， 重力的影响； 重力的影响； （4）分子的运动遵循经典力学规律 ）分子的运动遵循经典力学规律.
② Equation of state of ideal gas
(2) The statistic assumptions of a lot of ideal gas molecules ① The distribution of molecules with respect to the position is uniform. ② The distribution of molecules’ velocity with respect to the direction is uniform.
③ The third law of thermodynamics Absolute zero can not be achieved.
6. Equation of state of ideal gas Ideal gas condition Equilibrium state ① Ideal gas model: a collection of atoms or molecules that move randomly, exert no long-range forces on one another, and occupy a negligible fraction of the volume of their container.
11. 12. 13. 14. 15. 16. 17.
18.
19.
Avogadro 阿伏加德罗 Boltzmann 玻尔兹曼 liquefaction 液化 solidification 凝固 mole 摩尔 molar mass 摩尔质量 the average translational kinetic energy: 平均平动动能 root-mean-square (rms) speed: 方均根 速率 the most probable speed: 最概然速率 (最可几速率 最可几速率) 最可几速率
R −23 kB = = 1.38 × 10 J / K NA
PV = Nk BT
P = nk BT
P=
ρ
M
RT
N ---- total number of molecules. n ---- number of molecules per unit volume.
Example 1: The room temperature changes from 150C to 270C. The pressure does not change. What percent does the number of the molecules in the room decrease? Solution:
TC ( 0C )
TC = T − 273.15
Triple point of water (water, water vapor and ice can coexist in equilibrium.): 273.16K • The Fahrenheit scale
TF ( 0 F )
9 TF = TC + 32 5
2 2 dI = ∑ 2mvix ni vix dAdt = ∑ 2mvix ni dAdt = ∑ mni vix dAdt vix f0 vix f0
Biblioteka Baidu
The force:
dI dF = dt
dF dI 2 2 P= = = ∑ mni vix = m∑ ni vix dA dtdA
v
2 x
The pressure:
5. temperature: Macro: Degree of hot or cold Micro: Degree of molecule’s thermal motion
① The zeroth law of thermodynamics (law of equilibrium): If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Two objects in thermal equilibrium with each other are at the same temperature.
T 12 n1 − n2 1 =1− = = 4 00 P = nkT, ∴ n1 T2 300
Example 2: The density of the ideal gas of temperature 270C and pressure 10-2 atm is ρ=11.3g/m3. Find the molar mass. Solution:
ni = Ni /V N = ∑ Ni
n = ∑ ni
The change in momentum of the molecule in the x direction is :
∆pxi = −mvxi − mvxi = −2mvxi
The number of molecules with the r velocity vi which collide with dA in the interval dt:
Chapter 16 Temperature and the kinetic Theory of Gases §1. Concepts (P548-555, 562-564) §2. The kinetic theory of gases (P564-570) §3. Theorem of equipartition of energy (P605-608) §4. Distribution of molecular speeds (P570-572) §5. the mean free path of gas molecules
② temperature scale: • The Celsius temperature scale
Ice point 0oC
boiling point 100oC • The Kelvin temperature scale (absolute temperature) T SI unit : Kelvin
§1 Concepts
1. Macroscopic quantity and Microscopic quantity: Macro: pressure P, volume V, temperature T, internal energy Micro: mass m, velocity v, position r , momentum, energy of a particle 2. Equilibrium state: P, V, T do not change. dynamic equilibrium 3. Thermal Equilibrium : is the situation in which two objects in thermal contact cease to have any exchange of energy. 4. quasi-static process: A quasi-static process is one that proceeds slowly enough to allow the system always in a state of thermal equilibrium. Equilibrium state ----- point on the P-V graph Quasi-static process ----- curve on the P-V graph
ν ---- the number of moles
m PV = ν RT = RT M
R ---- the universal gas constant R=8.315 J/mol·K
NA ---- Avogadro’s number NA=6.022×1023/mol
kB ---- Boltzmann’s constant
∴M =
ρRT
P
= 27.9g / mol
§2. The kinetic theory of gases 1. Molecular interpretation of the pressure of an ideal gas (1) Microscopic model of an ideal gas ① The number of molecules in the gas is large, and the average separation between them is large compared with their dimensions. ② The molecules obey Newton’s laws of motion, but as a whole they move randomly. ③ The molecules interact only by short-range forces during elastic collisions. ④ The molecules makes elastic collisions with the walls. ⑤ The gas under consideration is a pure substance; that is, all molecules are identical.
Chapter 16 Temperature and the kinetic Theory of Gases
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
gaseous adj. 气体的, 气态的 气体的 piston n. 活塞 thermodynamics 热力学 thermometer n. 温度计 体温计 温度计, insulated adj. 隔热的，绝缘的 隔热的， capillary n. 毛细管，毛细血管 毛细管， mercury n. 水银，汞 水银， Celsius adj. 摄氏的 Kelvin 开尔文 dilute adj. 淡的 弱的 稀释的 淡的, 弱的,
=
∑
niv n
2 ix
So :
1 2 1 2 2 2 P = nmv = nmv = n( mv ) = nε t 3 3 2 3