Chapter 20 the kinetic theory of gases
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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 20 The kinetic Theory of Gases

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Chapter 20 the kinetic theory of gases

Chapter 20The kinetic Theory of Gases


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

20-2 Avogadro’s Number


20 3 ideal gases

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

The gas constant R

The Boltzmann constant k

20-3 Ideal Gases


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.

Work Done by an Ideal Gas at Constant Temperature


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

Work Done at Constant Volume and at Constant Pressure

Sample Problem 20-1


Chapter 20 the kinetic theory of gases

Sample Problem 20-2


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

20-4 Pressure , Temperature , and RMS Speed


Chapter 20 the kinetic theory of gases

With

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


Sample problem 20 3

(a)

(b)

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

Sample Problem 20-3

20-5 Translational Kinetic Energy


Chapter 20 the kinetic theory of gases

Something unexpected:

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.


20 6 mean free path

The expression for the mean free path

20-6 Mean Free Path


Sample problem 20 4

(a)

(b)

Sample Problem 20-4


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, v1to v2is:

20-7 The Distribution of Molecular Speeds


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 :

Average,RMS,and Most Probable Speeds


Sample problem 20 5

The most probable speed is

Sample Problem 20-5


Sample problem 20 6

(a)

(b)

(c)

Sample Problem 20-6


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.

20-8 The Molar Specific Heats of an Ideal Gas


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

Molar Specific Heat at Constant Volume


Chapter 20 the kinetic theory of gases

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.


Molar specific heat at constant pressure

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

Molar Specific Heat at Constant Pressure


Sample problem 20 7

(a)

(b)

(c)

or

Sample Problem 20-7


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) .

20-9 Degrees of Freedom and Molar Specific Heats


Sample problem 20 8

Sample Problem 20-8

20-10 A Hint of Quantum Theory


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

20-11 The Adiabatic Expansion of an Ideal Gas


Chapter 20 the kinetic theory of gases

Proof of Eq. 20-53

The first law of thermodynamics can then be written as


Chapter 20 the kinetic theory of gases

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


Sample problem 20 9

(a)

(b)

Sample Problem 20-9


Review summary

REVIEW & SUMMARY

Avogadro’s Number

The number of moles n is

Ideal Gas


Chapter 20 the kinetic theory of gases

The Boltzmann constant k

Work in an Isothermal Volume Change

Pressure,Temperature,and Molecular Speed


Chapter 20 the kinetic theory of gases

Temperature and Kinetic Energy

Mean Free Path

Maxwell Speed Distribution


Chapter 20 the kinetic theory of gases

Molar Specific Heats


Chapter 20 the kinetic theory of gases

Degrees of Freedom and Cv

Adiabatic Process


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