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# Chapter 20 The kinetic Theory of Gases - PowerPoint PPT Presentation

Chapter 20 The kinetic Theory of Gases. 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. 20-2 Avogadro’s Number. At low enough densities,all real gases tend to obey the relation.

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### Chapter 20The kinetic Theory of Gases

One mole is the number of atoms in a 12 g sample of carbon – 12.

The number of moles n is

The gas constant R

The Boltzmann constant k

### 20-3 Ideal Gases

On a p-v diagram,an relationisotherm is a curve that connects point that have the same temperature.

### Work Done by an Ideal Gas at Constant Temperature

If the pressure of the gas is constant

### Work Done at Constant Volume and at Constant Pressure

Sample Problem 20-1

The average rate at which momentum is delivered to the shaded wall by this single molecule is

The pressure is

### 20-4 Pressure , Temperature , and RMS Speed

With axis:

Combining Eq.20-21 with the ideal gas law leads to

(a) axis:

(b)

Its average translational kinetic energy over the time that we watch it is

### Sample Problem 20-3

20-5 Translational Kinetic Energy

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.

(a) axis:

(b)

### Sample Problem 20-4

The value of this total area is unity

The fraction (frac) of molecules with speed in an interval of,say, v1to v2is:

### 20-7 The Distribution of Molecular Speeds

The average of the square of the speed is

The root – mean – square speed is :

(a) axis:

(b)

(c)

### Sample Problem 20-6

Internal Energy E axis:int

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.

### 20-8 The Molar Specific Heats of an Ideal Gas

is a constant called the molar specific heat at constant volume.

W=0

### Molar Specific Heat at Constant Volume

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.

(a) pressure.

(b)

(c)

or

### Sample Problem 20-7

The equipartition of energy pressure.

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) .

### Sample Problem 20-8 pressure.

20-10 A Hint of Quantum Theory

The relation between the pressure and the volume during such an adiabatic process is

the ratio of the molar specific heats for

### 20-11 The Adiabatic Expansion of an Ideal Gas

Proof of Eq. 20-53 an adiabatic process is

The first law of thermodynamics can then be written as

From the ideal gas law,we have an adiabatic process is

Free Expansions

The initial and final points on a p-v diagram must be on the same isotherm,and instead of Eq.20-56

(b)

### REVIEW & SUMMARY an adiabatic process is

The number of moles n is

Ideal Gas

The Boltzmann constant k an adiabatic process is

Work in an Isothermal Volume Change

Pressure,Temperature,and Molecular Speed

Temperature and Kinetic Energy an adiabatic process is

Mean Free Path

Maxwell Speed Distribution

Molar Specific Heats an adiabatic process is

Degrees of Freedom and Cv an adiabatic process is