1. Refrigerators Physics 202 Professor Lee Carkner Lecture 19

2. PAL # 18 Engines  Engine #1 W = 10, Q H = 45   =W/Q H = 0.22   Engine #2 Q C = 25, Q H = 30   = 1 – Q C /Q H = 0.17   Engine #3 T H = 450 K, T C = 350 K   C = 1 – T C /T H = 0.22   Engine #4 W = 20, Q H = 30, T H = 500, T C = 400   = 0.66 >  C = 0.2   Engine #5 W = 20, Q H = 15   = 1.33 > 1 

3. Engines and Refrigerators   Heat from the hot reservoir is transformed into work (+ heat to cold reservoir)   By an application of work, heat is moved from the cold to the hot reservoir

4. A Refrigerator   The boiling point of a liquid depends on its pressure   Heat can be moved from a cold region to a hot region by adjusting the pressure so that the circulating fluid boils in the cold region and condenses in the hot  We can make heat flow “uphill” from cold to hot, but we must add work

5. Refrigerator Cycle Liquid Gas Compressor (work =W) Expansion Valve Heat removed from inside fridge by evaporation Heat added to room by condensation High Pressure Low Pressure QLQL QHQH

6. Refrigerator as a Thermodynamic System  K = Q L /W  K is called the coefficient of performance  Q H = Q L + W W = Q H - Q L  This is the work needed to move Q L out of the cold area

7. Refrigerators and Entropy  We can rewrite K as:  From the 2nd law (for a reversible, isothermal process):  So K becomes: K C = T L /(T H -T L )   Refrigerators are most efficient if they are not kept very cold and if the difference in temperature between the room and the refrigerator is small

8. Perfect Systems   A perfect refrigerator converts Q L directly into Q H with no work   But each violates the second law: Q L /T L = Q H /T H   Perfect systems are impossible

9. Gas Motions   Why don’t gasses diffuse more rapidly?  The molecules collide with each other constantly and are scattered   The constant collisions means the gas becomes thermalized  Energy and information is quickly transmitted through the gas

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

11. 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

12. Planetary Atmospheres  Why do some planets have atmospheres and others do not?   Gas molecules are moving and may escape  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: v escape > 10v rms

13. Next Time  Test #2  Same format as test #1  Sample equation sheet and practice problems posted  For Monday  Read: 33.1-33.7  Homework: Ch 33, P: 2, 10, 20, 21