Review from Last Lecture

1. Review from Last Lecture • State Equation of Ideal Gas • Kinetic Theory • Boltzmann’s Constant • Avagadro’s Constant • Ideal Gas Constant • Distributions • Mean • Boltzmann Distribution • Maxwell-Boltzmann Velocity Distribution

2. Velocity Distribution • Different velocities

3. Review from Last Lecture • Thermodynamics • The study of changes to the state of a system • State variables: Pressure, Volume, Temperature • Heat (Q) and work (W) are both measures of energy flowing into and out of the system • 1st Law of Thermodynamics • Types of State Changes • Isochoric (volume constant) • Isobaric (pressure constant) • Isothermal (temperature constant) • Adiabatic (no heat flow)

4. Isochoric Processes • In an isochoric process, no work is done because the volume doesn’t change

5. Specific Heat (Constant Volume) • Define a specific heat as heat required to raise temperature of one mole by one degree (K):

6. Isobaric Processes • In an isobaric process, the work is easy to calculate because the pressure doesn’t change

7. Specific Heat (Constant Pressure) • We define a new specific heat for changes at constant pressure • Some of the heat flowing into the system is used to do work so

8. Isothermal Processes • If the temperature is constant, the internal energy is also constant

9. Adiabatic Processes • In an adiabatic process, there is no heat flow • Use the state equation

10. Adiabatic Processes

11. Adiabatic Processes • Another derivation

12. The 2nd Law of Thermodynamics This conserves energy! Tc Th  Q • Why do we need a second law? • The 1st Law allows heat to flow from cold to hot (it doesn’t actually distinguish between work and heat)

13. The 2nd Law of Thermodynamics • Two ways of stating 2nd Law • Kelvin-Planck: It is impossible to construct an engine that converts a given amount of heat into an equivalent amount of work • Clausius It is impossible to transfer heat from a lower temperature to a higher temperature without doing work • Actually these are identical

14. Another State Variable? • State variables depend one on the “state” of the gas • This really means that in moving from one state to another the change in a state variable depends only on the beginning and ending states • Temperature (energy) is a state variable but work and heat (changes in energy) are not Can integrate this Can’t integrate these (because T is independent of V)

15. Another State Variable? • But we can transform the heat into a state variable • Just divide out the temperature • This is the entropy (S) of a given state and it is a state variable Can’t integrate this Can integrate this

16. The 2nd Law of Thermodynamics • Another way of stating the 2nd Law • Entropy: It is impossible to reduce the entropy of an isolated system The entropy of the universe always increases

17. Allowed Processes Q  Tc Tc Th Th • Only processes allowed by the 2nd Law are observed to happen • Example: Heat Flow • Allowed (Heat Transfer, Hot to Cold) • Disallowed (Perfect Refrigerator) Q 

18. Allowed Processes • Example: Free Expansion/Contraction • Allowed • Disallowed  

19. The 2nd Law as a Statistical Law • Unlike other laws of physics, the 2nd law of Thermodynamics is only true in a statistical sense • What’s the probability all the molecules are on the left? • For 1 molecule: 1/2 • For 2: 1/4 • For 3: 1/8 • For NA:

20. The 2nd Law as a Statistical Law • Unlike other laws of physics, the 2nd law of Thermodynamics is only true in a statistical sense • But the probabilities are truly astronomical • The 2nd Law is also asymmetric with respect to time • Make a movie of an elastic collision; can run movie backward, it looks realistic • Newton’s Laws has “Time Reversal Symmetry” • Make a movie of dye dispersing in a liquid (which is governed by the 2nd Law); can’t run it backward • 2nd Law gives “arrow of time”