1. Chapter 20 The kinetic Theory of Gases

2. 20-2 Avogadro’s Number
The mole is one of the seven SI base units and is defined as follows:
One mole is the number of atoms in a 12 g sample of carbon – 12.
The number of moles n is

3. 20-3 Ideal Gases
At low enough densities,all real gases tend to obey the relation
The gas constant R
The Boltzmann constant k

4. Work Done by an Ideal Gas at Constant Temperature
On a p-v diagram,an isotherm is a curve that connects point that have the same temperature.

5. Work Done at Constant Volume and at Constant Pressure
If the volume of the gas is constant
If the pressure of the gas is constant
Sample Problem 20-1

6. Sample Problem 20-2

7. 20-4 Pressure , Temperature , and RMS Speed
The only change in the particle’s momentum is along the x axis:
The average rate at which momentum is delivered to the shaded wall by this single molecule is
The pressure is

8. With
Combining Eq with the ideal gas law leads to

9. 20-5 Translational Kinetic Energy
Sample Problem 20-3
(a)
(b)
20-5 Translational Kinetic Energy
Its average translational kinetic energy over the time that we watch it is

10. At a given temperature T, all ideal gas molecules – no matter what their mass – have the same average translational kinetic energy ,namely , kT .When we measure the temperature of a gas ,we are also measuring the average translational kinetic energy of its molecules.
Something unexpected:

11. 20-6 Mean Free Path
The expression for the mean free path

12. Sample Problem 20-4
(a)
(b)

13. 20-7 The Distribution of Molecular Speeds
Maxwell’s speed distribution law is
The value of this total area is unity
The fraction (frac) of molecules with speed in an interval of,say, v1 to v2 is:

14. Average,RMS,and Most Probable Speeds
The average speed is:
The average of the square of the speed is
The root – mean – square speed is :

15. The most probable speed is
Sample Problem 20-5

16. Sample Problem 20-6
(a)
(b)
(c)

17. 20-8 The Molar Specific Heats of an Ideal Gas
Internal Energy Eint
The internal energy Eint of the sample is
The internal energy Eint of an ideal gas is a function of the gas temperature only;it does not depend on any other variable.

18. Molar Specific Heat at Constant Volume
The heat Q is related to the temperature change by
is a constant called the molar specific heat at constant volume.
W=0

19. The internal energy of any ideal gas by substituting Cv for
A change in the internal energy Eint of a confined ideal gas depends on the change in the gas temperature only;it does not depend on what type of process process the change in the temperature.

20. Molar Specific Heat at Constant Pressure
is a constant called the molar specific heat at constant pressure.

21. Sample Problem 20-7
(a)
(b)
(c) or

22. 20-9 Degrees of Freedom and Molar Specific Heats
The equipartition of energy
Every kind of molecule has a certain number f of degrees of freedom, which are independent ways in which the molecule can store energy.Each such degree of freedom has associated with it—on average —an energy of per molecule (or per mole) .

23. Sample Problem 20-8
20-10 A Hint of Quantum Theory

24. 20-11 The Adiabatic Expansion of an Ideal Gas
The relation between the pressure and the volume during such an adiabatic process is
the ratio of the molar specific heats for

25. Proof of Eq
The first law of thermodynamics can then be written as

26. Free Expansions From the ideal gas law,we have
The initial and final points on a p-v diagram must be on the same isotherm,and instead of Eq.20-56

27. Sample Problem 20-9
(a)
(b)

28. REVIEW & SUMMARY
Avogadro’s Number
The number of moles n is
Ideal Gas

29. Work in an Isothermal Volume Change
The Boltzmann constant k
Work in an Isothermal Volume Change
Pressure,Temperature,and Molecular Speed

30. Temperature and Kinetic Energy
Mean Free Path
Maxwell Speed Distribution

31. Molar Specific Heats

32. Degrees of Freedom and Cv
Adiabatic Process