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## PowerPoint Slideshow about ' Chapter 20 The kinetic Theory of Gases' - rico

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### 20-2 Avogadro’s Number

### 20-3 Ideal Gases

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

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

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

### Sample Problem 20-3

### 20-7 The Distribution of Molecular Speeds

### Average,RMS,and Most Probable Speeds

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

### Molar Specific Heat at Constant Volume

### 20-9 Degrees of Freedom and Molar Specific Heats

### Sample Problem 20-8

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

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

At low enough densities,all real gases tend to obey the relation

The gas constant R

The Boltzmann constant k

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

If the volume of the gas is constant

If the pressure of the gas is constant

Sample Problem 20-1

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

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

(b)

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

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.

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, v1to v2is:

The average of the square of the speed is

The root – mean – square speed is :

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.

The heat Q is related to the temperature change by

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

W=0

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.

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) .

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

The first law of thermodynamics can then be written as

From the ideal gas law,we have

Free Expansions

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

Adiabatic Process

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