1. Entropy Physics 202 Professor Lee Carkner Lecture 17 “Entropy isn’t what it used to be.” --Anonymous

2. PAL #16 Internal Energy  3 moles of gas, temperature raised from 300 to 400 K  He gas, isochorically  Q = nC V  T, C V = (f/2)R = (3/2) R  Q = (3)(3/2)R(100) = 3740 J   He gas, isobarically  Q = nC P  T, CP = C V + R = (5/2) R  Q = (3)(5/2)R(100) = 6333 J   H2 gas, isochorically  Q = nC V  T, CV = (5/2) R, f = 5 for diatomic  Q = (3)(5/2)R(100) = 6333 J   H2 gas, isobarically  Q = nC P  T, CP = C V + R = (7/2) R  Q = (3)(7/2)R(100) = 8725 J 

3. Randomness  Classical thermodynamics is deterministic   Every time!  But the real world is probabilistic   It is possible that you could add heat to a system and the temperature could go down   The universe only seems deterministic because the number of molecules is so large that the chance of an improbable event happening is absurdly low

4. Random Gas Motions

5. Gas Motions   Why don’t gasses diffuse more rapidly?   They do not travel in a straight line   Energy and information is quickly transmitted through the gas

6. Mean Free Path  The average distance between collisions: = 1 /[√2  d 2 (N/V)]  Where:    V is the volume    Millions of collisions per second!

7. Maxwell’s Distribution

8. Speed Distribution  Maxwell’s distribution is not symmetrical   This means there are several ways to characterize a “average” speed  Most probable speed, v p   v p = (2RT/M) ½  Average speed, v avg   v avg = (8RT/  M) ½  root-mean-squared speed, v rms   v rms = (3RT/M) ½  rms speed reflects the way the molecules produce pressure and carry energy

9. Titan   Why does it have an atmosphere?  What type of gas might the atmosphere be made of?

10. Planetary Atmospheres  Why do some planets have atmospheres and others do not?    So equating escape velocity to thermal velocity should define conditions for atmosphere retention   Escape velocity needs to be about 10 times large than rms velocity in order to keep an atmosphere for a long time: (2GM planet /R planet ) > (300kT/m molecule )

13. The Arrow of Time   Why?  The smashing plate is an example of an irreversible process, one that only happens in one direction  Examples:  

15. Entropy   They all progress towards more randomness   For an irreversible process, entropy always increases

16. Determining Entropy  In any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically:

17. Isothermal Expansion   A cylinder of gas rests on a thermal reservoir with a piston on top   Heat also flows into the system from the reservoir  The temperature is constant so  S=Q/T

18. Closed Systems  Consider a closed system   The heat lost by the reservoir was gained by the gas so there is no net heat loss or gain   For a reversible process in a closed system the entropy is constant

19. Second Law of Thermodynamics   No real process is truly reversible (due to friction, turbulence etc.), so we can say:  S>0   Entropy always increases 