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Chapter 20 The kinetic Theory of Gases

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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  1. Chapter 20The kinetic Theory of Gases

  2. 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

  3. At low enough densities,all real gases tend to obey the relation The gas constant R The Boltzmann constant k 20-3 Ideal Gases

  4. 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

  5. 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

  6. Sample Problem 20-2

  7. 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

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

  9. (a) (b) Its average translational kinetic energy over the time that we watch it is Sample Problem 20-3 20-5 Translational Kinetic Energy

  10. 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.

  11. The expression for the mean free path 20-6 Mean Free Path

  12. (a) (b) Sample Problem 20-4

  13. 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

  14. 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

  15. The most probable speed is Sample Problem 20-5

  16. (a) (b) (c) Sample Problem 20-6

  17. 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

  18. 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

  19. 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.

  20. is a constant called the molar specific heat at constant pressure. Molar Specific Heat at Constant Pressure

  21. (a) (b) (c) or Sample Problem 20-7

  22. 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

  23. Sample Problem 20-8 20-10 A Hint of Quantum Theory

  24. 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

  25. Proof of Eq. 20-53 The first law of thermodynamics can then be written as

  26. 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

  27. (a) (b) Sample Problem 20-9

  28. REVIEW & SUMMARY Avogadro’s Number The number of moles n is Ideal Gas

  29. The Boltzmann constant k Work in an Isothermal Volume Change Pressure,Temperature,and Molecular Speed

  30. Temperature and Kinetic Energy Mean Free Path Maxwell Speed Distribution

  31. Molar Specific Heats

  32. Degrees of Freedom and Cv Adiabatic Process

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