Refrigerators Physics 202 Professor Lee Carkner Lecture 17

PAL # 16 Engines  Carnot engine  At point a, v = 0.3, P =  At point c, v = 0.5, P =11000  Find max and min T  T = PV/nR  T max = (30500)(0.3)/(2)(8.31) = 551 K  T min = (11000)(0.5)/(2)(8.31) = 331 K  Carnot effciency   C = 1 – (T C /T H ) = 1 – (331/551) = 0.4  Input heat is 2634 J per cycle   = 1 – (Q L /Q H )  Q L = (1-  )Q H = (1-0. 4)2634 = 1580 J  W = Q H -Q L = = 1054 J

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

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

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

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

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

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

Gas Motions   Why don’t gasses diffuse more rapidly?  The molecules collide with each other constantly and are scattered  They do not travel in a straight line   Energy and information is quickly transmitted through the gas

Mean Free Path  = 1 /[√2  d 2 (N/V)]  Where:   N is the number of molecules   N/V is the number density  For typical gases ~ 0.1  m 

Next Time  Test #3  Same format as tests 1 and 2  Sample equation sheet and practice problems posted  For Monday  Read:

Rank the following engines from most to least work per cycle: I: inputs 100 J of heat, outputs 80 J of heat II: inputs 100 J of heat, outputs 90 J of heat III: inputs 100 J of heat, has an efficiency of 0.25 A)I, II, III B)II, I, III C)III, I, II D)I, III, II E)III, II, I

Rank the following engines from best to worst: I: inputs 100 J of heat, outputs 80 J of heat II: operates between 300 K and 350 K III: inputs 100 J of heat, outputs 60 J of heat, operates between 300 K and 400 K A)I, II, III B)II, I, III C)III, I, II D)I, III, II E)III, II, I