The Carnot Cycle

Physics 313Professor Lee

CarknerLecture 14

Exercise #13 Air Conditioner

Heat removed from room (and added to AC system) QL = cmT = (0.72)(800)(32-20) =

What is work? W = QL/K = 6912/2.5 = 2764 kJ P = W/t = 2764 kJ/15 min = 2764000 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

17th 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 QH at TH

An isothermal subtraction of heat QL at TL

Engine Applet http://www.rawbw.com/~xmwang/javappl/

carnotC.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 TL to TH

Adiabatic fall from TH to TL

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