The Carnot Cycle Physics 313 Professor Lee Carkner Lecture 14

Exercise #13 Air Conditioner  Heat removed from room (and added to AC system)  Q L = cm  T = (0.72)(800)(32-20) =  What is work?   W = Q L /K = 6912/2.5 = 2764 kJ  P = W/t = 2764 kJ/15 min = J/ 900 s 

Reversibility   e.g. a piston is heated and raises a weight   A reversible process must not change any other system anywhere 

Mechanical Reversibility   In order to reverse them you would have to completely convert heat into work   Virtually every process converts some work into heat, so mechanical irreversibility cannot be avoided

Isothermal Work   e.g. rub two blocks together under water in a lake  Heat is produced but no temperature change   e.g. get it to run a perfect engine  common examples:  Friction, stirring, or compression of systems in contact with air or water

Adiabatic Work  Work done on insulated systems that changes the internal energy   Work is converted completely into internal energy and raises the temperature of the system   To reverse, must restore temperature by removing heat and converting completely to work  Examples:  Friction, stirring or compression of insulated systems

Dissipation   Dissipative effects produce external mechanical irreversibility   Any real machine involves dissipation and is thus irreversible   i.e. frictionless

Thermal Irreversibility  Heat flowing from hotter to cooler systems   To reverse need to have heat flow from cool to hot   Example:   can re-freeze, but that requires work

17 th Century Perpetual Water Wheel

Charles Redheffer’s Machine (Philadelphia 1812)

Perpetual Motion  Three kinds of perpetual motion  1st kind:   violates 1st law  2nd kind:   violates 2nd law  3rd kind:   violates 2nd law

Ideal and Real Systems  Real systems are not reversible    We can approximate reversibility is several ways:   Use a heat reservoir 

Carnot Cycle  A Carnot engine is a device that operates between two reservoirs (at high and low T) with adiabatic and isothermal processes   An isothermal addition of heat Q H at T H   An isothermal subtraction of heat Q L at T L  Engine Applet  notC.html

Carnot Info  Carnot cycles can operate with many different systems:   Carnot cycle defined by:   only two heat reservoirs and thus only two temperatures   All other cycles involve heat transfers across temperature changes and thus are irreversible

Carnot Refrigerator  If you reverse a Carnot engine, you get a Carnot refrigerator   Adiabatic rise from T L to T H   Adiabatic fall from T H to T L  If the two reservoirs are the same, the heats and work are the same for a Carnot refrigerator and engine

Carnot’s Theorem   Reversible processes are the most efficient   Carnot efficiency is an upper limit for any engine

Corollary   Efficiency only depends on the temperatures of the reservoirs  Thus:  Maximum efficiency of any engine depends only on the temperatures of the reservoirs

Comparison with Other Engines   For Carnot heat exchange occurs at max and min temperatures of system   Can never achieve true reversibility due to dissipation 