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Lecture 14 Chapter 19 Ideal Gas Law and Kinetic Theory of Gases Chapter 20 Entropy and the Second Law of Thermodynamic

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**1. **Lecture 14 Chapter 19 Ideal Gas Law and Kinetic Theory of Gases Chapter 20 Entropy and the Second Law of Thermodynamics

**4. **Thermal effects using liquid nitrogen again. For air in the balloon at room temp At room temp we have pV=nRT and T=273K then dip it liquid nitrogen p’V’=nRT with T= 78K, p’V’ should be smaller by a factor of 273/78=3.5 compared to pV So why does the balloon get a lot smaller?

**5. **Avogadro’s Number

**6. **Avogadro’s Number

**7. **Ideal Gases

**8. **Ideal Gas Law in terms of Boltzman Constant

**9. **Work done by an ideal gas

**10. **pV diagram

**11. **What is the work done by an ideal gas when the temperature is constant?

**12. **What is the work done by an ideal gas when the temperature is constant?

**14. **Sample problem 19-2

**15. **What’s Next

**16. **Kinetic theory model of a gas: Find p due to one molecule first and then sum them up Assume elastic collisions between walls and molecules and neglect collisions between molecules.
Only want the x component of the momentum since the change in y is parallel to surface and does not contribute to the pressure.Assume elastic collisions between walls and molecules and neglect collisions between molecules.
Only want the x component of the momentum since the change in y is parallel to surface and does not contribute to the pressure.

**17. **Assume elastic collisions between walls and molecules and neglect collisions between molecules.
Only want the x component of the momentum since the change in y is parallel to surface and does not contribute to the pressure.Assume elastic collisions between walls and molecules and neglect collisions between molecules.
Only want the x component of the momentum since the change in y is parallel to surface and does not contribute to the pressure.

**18. **What is the root mean square of the velocity of the Molecules? Since we have trillions of molecules moving randomly in all directions the square of the speed in any direction is equal. So we can equate the squares of the components and multiply by 3 to get the magnitude. Actually we use the root-mean-square of the speed.Since we have trillions of molecules moving randomly in all directions the square of the speed in any direction is equal. So we can equate the squares of the components and multiply by 3 to get the magnitude. Actually we use the root-mean-square of the speed.

**19. **Average Molecular speeds at 300 K This is the average speed. Some molecules are going much faster and some slower. On the sun T= 2*106 K and hydrogen is
82 times faster than at vroom temperature. Molecules would break up at such collisions.This is the average speed. Some molecules are going much faster and some slower. On the sun T= 2*106 K and hydrogen is
82 times faster than at vroom temperature. Molecules would break up at such collisions.

**20. **Average Kinetic Energy of the Molecule When you measure the temperature of the gas, you are measuring the translational energy.When you measure the temperature of the gas, you are measuring the translational energy.

**21. **Mean Free Path

**23. **What is v, the speed of a molecule in an ideal gas?

**24. **Maxwell’s speed distribution law: Explains boiling. It is the faster moving molecules in the tail of the distribution that escape from the surface of a water.
It is also the protons in the tail in the sun that have high enough energy to overcome the Coulomb barrier to cause nuclear fusion.It is the faster moving molecules in the tail of the distribution that escape from the surface of a water.
It is also the protons in the tail in the sun that have high enough energy to overcome the Coulomb barrier to cause nuclear fusion.

**25. **Want to relate ?Eint to the kinetic energy of the atoms of the gas.

**26. **From the heat we can calculate the specific heat for various processes. For example,

**27. **Lets calculate the specific heat, CV of an ideal gas at constant volume

**28. **Calculate CV

**29. **Cv for different gases

**30. **Specific Heat at Constant Pressure These predictions for the specific heats agree well with experiment as long as gases are nearly ideal.These predictions for the specific heats agree well with experiment as long as gases are nearly ideal.

**31. **Adiabatic Expansion of an Ideal Gas: Q = 0

**32. **Adiabatic Expansion of an Ideal Gas: Q = 0

**33. **Adiabatic Expansion of an Ideal Gas: Q = 0

**34. **PROBLEM 20-58E

**35. **Problem 20-61P

**38. **(b) Find the pressure and volume at points 2 and 3. The pressure at point 1 is 1 atm = 1.013 x 105 Pa.

**39. **Equipartition Theroem DegreDegre

**40. **Specific heats including rotational motion

**41. **CV for a diatomic gas as a function of T Note how each plateau is quantized. Quantum mechanics is required to explain why the vibrational modes are froizen out at lower temperatures.Note how each plateau is quantized. Quantum mechanics is required to explain why the vibrational modes are froizen out at lower temperatures.

**42. **What is Entropy S? Two equivalent definitions It is a measure of a system’s energy gained or lost as heat per unit temperature.
It is also a measure of the ways the atoms can be arranged to make up the system. It is said to be a measure of the disorder of a system.

**43. **A system tends to move in the direction where entropy increases For an irreversible process the entropy always increases. ?S > 0
For a reversible process it can be 0 or increase.

**44. **Heat Flow Direction
Why does heat flow from hot to cold instead of vice versa? Because the entropy increases.
What is this property that controls direction?

**45. **The statistical nature of entropy Black beans on the right
White beans on the left
Add some energy by shaking them up and they mix
They never will go back together even though energy of conservation is not violated.
Again what controls the direction?

**46. **However, the above formula can only be used to calculate the entropy change if the process is reversible..

**49. **Isothermal expansion of a gas

**50. **Example: Four moles of an ideal gas undergo a reversible isothermal expansion from volume V1 to volume V2 = 2V1 at temperature T = 400K.

**52. **For an ideal gas in any reversible process where the temperature and volume may change, the entropy change is given by the following:

**53. **Summary

**54. **Statistical View of Entropy

**55. **An insulated box containing 6 molecules

**56. **N=6

**58. **This shows the number of microstates available for each configuration

**59. **Statistical View of Entropy

**60. **Use Stirling formula

**61. **2nd Law of Thermodynamics

**62. **Grading for Phys 631

**63. **Classes 2007-2008

**64. **Reminders

**65. **The Breaking Broomstick Demo

**66. **Breaking Broomstick Demo

**67. **Broomstick Breaking Cont.

**68. **Apparatus