 # Entropy Physics 202 Professor Lee Carkner Ed by CJV Lecture -last.

## Presentation on theme: "Entropy Physics 202 Professor Lee Carkner Ed by CJV Lecture -last."— Presentation transcript:

Entropy Physics 202 Professor Lee Carkner Ed by CJV Lecture -last

Entropy  What do irreversible processes have in common?  They all progress towards more randomness  The degree of randomness of system is called entropy  For an irreversible process, entropy always increases  In any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically:  S = S f –S i = ∫ (dQ/T)

Isothermal Entropy  In practice, the integral may be hard to compute  Need to know Q as a function of T  Let us consider the simplest case where the process is isothermal (T is constant):  S = (1/T) ∫ dQ  S = Q/T  This is also approximately true for situations where temperature changes are very small  Like heating something up by 1 degree

State Function  Entropy is a property of system  Like pressure, temperature and volume  Can relate S to Q and thus to  E int & W and thus to P, T and V  S = nRln(V f /V i ) + nC V ln(T f /T i )  Change in entropy depends only on the net system change  Not how the system changes  ln 1 = 0, so if V or T do not change, its term drops out

Entropy Change  Imagine now a simple idealized system consisting of a box of gas in contact with a heat reservoir  Something that does not change temperature (like a lake)  If the system loses heat –Q to the reservoir and the reservoir gains heat +Q from the system isothermally:  S box = (-Q/T box )  S res = (+Q/T res )

Second Law of Thermodynamics (Entropy)  If we try to do this for real we find that the positive term is always a little larger than the negative term, so:  S>0  This is also the second law of thermodynamics  Entropy always increases  Why?  Because the more random states are more probable  The 2nd law is based on statistics

Reversible  If you see a film of shards of ceramic forming themselves into a plate you know that the film is running backwards  Why?  The smashing plate is an example of an irreversible process, one that only happens in one direction  Examples:  A drop of ink tints water  Perfume diffuses throughout a room  Heat transfer

Randomness  Classical thermodynamics is deterministic  Adding x joules of heat will produce a temperature increase of y degrees  Every time!  But the real world is probabilistic  Adding x joules of heat will make some molecules move faster but many will still be slow  It is possible that you could add heat to a system and the temperature could go down  If all the molecules collided in just the right way  The universe only seems deterministic because the number of molecules is so large that the chance of an improbable event happening is absurdly low

Statistical Mechanics  Statistical mechanics uses microscopic properties to explain macroscopic properties  We will use statistical mechanics to explore the reason why gas diffuses throughout a container  Consider a box with a right and left half of equal area  The box contains 4 indistinguishable molecules

Molecules in a Box  There are 16 ways that the molecules can be distributed in the box  Each way is a microstate  Since the molecules are indistinguishable there are only 5 configurations  Example: all the microstates with 3 in one side and 1 in the other are one configuration  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  The equal distribution configurations are thus more probable  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:  = N! /(n L ! n R !)  Where N is the total number of molecules and n L and n R are the number in the right or left half n! = n(n-1)(n-2)(n-3) … (1)  Configurations with large W are more probable  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  They also have the highest entropy  We can express the entropy with Boltzmann’s entropy equation as: S = k ln W  Where k is the Boltzmann constant (1.38 X 10-23 J/K)  Sometimes it helps to use the Stirling approximation: ln N! = N (ln N) - N

Irreversibility  Irreversible processes move from a low probability state to a high probability one  Because of probability, they will not move back on their own  All real processes are irreversible, so entropy will always increases  Entropy (and much of modern physics) is based on statistics  The universe is stochastic

Engines and Refrigerators  An engine consists of a hot reservoir, a cold reservoir, and a device to do work  Heat from the hot reservoir is transformed into work (+ heat to cold reservoir)  A refrigerator also consists of a hot reservoir, a cold reservoir, and a device to do work  By an application of work, heat is moved from the cold to the hot reservoir

Refrigerator as a Thermodynamic System  We provide the work (by plugging the compressor in) and we want heat removed from the cold area, so the coefficient of performance is: K = Q L /W  Energy is conserved (first law of thermodynamics), so the heat in (Q L ) plus the work in (W) must equal the heat out (|Q H |): |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: K = Q L /(Q H -Q L )  From the 2nd law (for a reversible, isothermal process): Q H /T H = Q L /T L  So K becomes: K C = T L /(T H -T L )  This the the coefficient for an ideal or Carnot refrigerator  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

Download ppt "Entropy Physics 202 Professor Lee Carkner Ed by CJV Lecture -last."

Similar presentations