 # Statistical Mechanics Physics 202 Professor Lee Carkner Lecture 19.

## Presentation on theme: "Statistical Mechanics Physics 202 Professor Lee Carkner Lecture 19."— Presentation transcript:

Statistical Mechanics Physics 202 Professor Lee Carkner Lecture 19

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

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  A refrigerator depends on 2 physical principles:   Boiling liquids absorb heat, condensing liquids give off heat (heat of vaporization)  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   n.b., the refrigerator is not the cold region (where we keep our groceries), it is the machine on the back that moves the heat

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

Refrigerator Diagram

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 Refrigerator

Perfect Systems  A perfect engine converts Q H directly into W with Q L = 0 (no waste heat)   Perfect refrigerators are impossible (heat won’t flow from cold to hot)  But why?   Violates the second law:  If T L does not equal T H then Q L cannot equal Q H  Perfect systems are impossible

Entropy   Entropy always increases for irreversible systems   Entropy always increases for any real, closed system (2nd law)  Why?   The 2nd law is based on statistics

Statistical Mechanics  Statistical mechanics uses microscopic properties to explain macroscopic properties   Consider a box with a right and left half of equal area 

Molecules in a Box  There are 16 ways that the molecules can be distributed in the box   Since the molecules are indistinguishable there are only 5 configurations  Example:  If all microstates are equally probable than the configuration with equal distribution is the most probable

Configurations and Microstates Configuration I 1 microstate Probability = (1/16) Configuration II 4 microstates Probability = (4/16)

Probability  There are more microstates for the configurations with roughly equal distributions   Gas diffuses throughout a room because the probability of a configuration where all of the molecules bunch up is low

Multiplicity  The multiplicity of a configuration is the number of microstates it has and is represented by: W = N! /(n L ! n R !)  n! = n(n-1)(n-2)(n-3) … (1)   For large N (N>100) the probability of the equal distribution configurations is enormous

Microstate Probabilities

Entropy and Multiplicity  The more random configurations are most probable   We can express the entropy with Boltzmann’s entropy equation as:  Where k is the Boltzmann constant (1.38 X 10 -23 J/K)  ln N! = N (ln N) - N

Irreversibility  Irreversible processes move from a low probability state to a high probability one   Increase of entropy based on statistics  Why doesn’t the universe seem random?  

Arrows of Time  Three arrows of time:  Thermodynamic   Psychological   Cosmological 

Entropy and Memory  When we remember things, order is increased   A brain or a computer cannot store information without the output of heat 

Fate of the Universe  The universe is expanding, and there does not seem to be enough mass in the universe to stop the expansion   Entropy keeps increasing   Stars burn out   Can live off of compact objects, but eventually will convert them all to heat  