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Chapter 20 The kinetic Theory of GasesPowerPoint Presentation

Chapter 20 The kinetic Theory of Gases

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### Chapter 20The kinetic Theory of Gases

### 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

### 20-6 Mean Free Path

### 20-7 The Distribution of Molecular Speeds

### Average,RMS,and Most Probable Speeds

### Sample Problem 20-5

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

### Molar Specific Heat at Constant Volume

### Molar Specific Heat at Constant Pressure

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

### Sample Problem 20-8 pressure.

### 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 relationisotherm is a curve that connects point that have the same temperature.

If the volume of the gas is constant relation

If the pressure of the gas is constant

Sample Problem 20-1

Sample Problem 20-2 relation

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

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

20-5 Translational Kinetic Energy

Something unexpected: axis:

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.

The expression for the mean free path axis:

Maxwell’s speed distribution law is axis:

The value of this total area is unity

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

The average speed is: axis:

The average of the square of the speed is

The root – mean – square speed is :

The most probable speed is axis:

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.

The heat Q is related to the temperature change by axis:

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

W=0

The internal energy of any ideal gas by substituting Cv for axis:

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.

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

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) .

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

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

The Boltzmann constant k an adiabatic process is

Work in an Isothermal Volume Change

Pressure,Temperature,and Molecular Speed

Molar Specific Heats an adiabatic process is

Degrees of Freedom and Cv an adiabatic process is

Adiabatic Process

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