Thermodynamics and Statistical Mechanics Kinetic Theory of Gases

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Thermodynamics and Statistical Mechanics Kinetic Theory of Gases Thermo & Stat Mech Spring 2006

Thermodynamics and Statistical Mechanics Kinetic Theory of Gases Thermo & Stat Mech Spring 2006 Class 14 1

Mixing of Two Ideal Gases Change of Gibbs Function An expression is needed for

Mixing of Two Ideal Gases Change of Gibbs Function An expression is needed for the specific Gibbs function. Thermo & Stat Mech - Spring 2006 Class 14 2

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 3

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 3

Specific Entropy Thermo & Stat Mech - Spring 2006 Class 14 4

Specific Entropy Thermo & Stat Mech - Spring 2006 Class 14 4

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 5

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 5

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 6

Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14 6

Mixing of Two Ideal Gases Thermo & Stat Mech - Spring 2006 Class 14

Mixing of Two Ideal Gases Thermo & Stat Mech - Spring 2006 Class 14 7

For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14 8

For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14 8

For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14 9

For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14 9

For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14 10

For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14 10

For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14 11

For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14 11

Basic Assumptions 1. A macroscopic volume contains a large number of molecules. 2. The

Basic Assumptions 1. A macroscopic volume contains a large number of molecules. 2. The separation of molecules is large compared to molecular dimensions. 3. No forces exist between molecules except those associated with collisions 4. The collisions are elastic. Thermo & Stat Mech - Spring 2006 Class 14 12

Basic Assumptions When no external forces are applied: 5. The molecules are uniformly distributed

Basic Assumptions When no external forces are applied: 5. The molecules are uniformly distributed within a container. 6. The directions of the velocities of the molecules are uniformly distributed. The fraction of molecules with speeds in the range v to v + dv is: f (v) dv Thermo & Stat Mech - Spring 2006 Class 14 13

Molecular Speeds f (v) is the probability density. Thermo & Stat Mech - Spring

Molecular Speeds f (v) is the probability density. Thermo & Stat Mech - Spring 2006 Class 14 14

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 15

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 15

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 16

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 16

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 17

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 17

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 18

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 18

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 19

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 19

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 20

Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14 20

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 21

Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14 21

Ideal Gas Law Thermo & Stat Mech - Spring 2006 Class 14 22

Ideal Gas Law Thermo & Stat Mech - Spring 2006 Class 14 22

Molecular Kinetic Energy Thermo & Stat Mech - Spring 2006 Class 14 23

Molecular Kinetic Energy Thermo & Stat Mech - Spring 2006 Class 14 23

Equipartition of Energy Thermo & Stat Mech - Spring 2006 Class 14 24

Equipartition of Energy Thermo & Stat Mech - Spring 2006 Class 14 24

Internal Energy Thermo & Stat Mech - Spring 2006 Class 14 25

Internal Energy Thermo & Stat Mech - Spring 2006 Class 14 25

Heat Capacities Thermo & Stat Mech - Spring 2006 Class 14 26

Heat Capacities Thermo & Stat Mech - Spring 2006 Class 14 26

Maxwell Velocity Distribution Consider a gas at equilibrium. The number of molecules in any

Maxwell Velocity Distribution Consider a gas at equilibrium. The number of molecules in any range of velocity does not change. Collisions cause individual molecules to change velocity, but the distribution does not change. For every collision that changes the distribution, there must be one that changes it back. Thermo & Stat Mech - Spring 2006 Class 14 27

Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14 28

Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14 28

Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14 29

Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14 29

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 30

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 30

Evaluation of Constants Thermo & Stat Mech - Spring 2006 Class 14 31

Evaluation of Constants Thermo & Stat Mech - Spring 2006 Class 14 31

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 32

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 32

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 33

Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14 33

Some Molecular Speeds Thermo & Stat Mech - Spring 2006 Class 14 34

Some Molecular Speeds Thermo & Stat Mech - Spring 2006 Class 14 34