Carnot Engine

Carnot Engine Heat engine is a device which converts heat to mechanical energy. A reversible heat engine operating between two temperatures is called Carnot Engine.

Parts of heat engine: Reservoir Heat engine operates between two temperatures heat is absorbed from the hot reservoir isothermally and released to the cold reservoir isothermally Hot Reservoir

Source of heat, any amount of heat can be extracted from it

Cold Reservoir Or Sink

Any amount of heat can be given to it

Working Substance Certain quantity of matter in a heat engine undergoes addition and subtraction of heat, expansion, compression and change of phase. In ideal case we consider that working substance carried through a cyclic process in which it eventually returns to its original state.

Work Function of Heat Engine In every heat engine the working substance absorbs heat QH from a reservoir at high temperature and converts some of this heat energy into mechanical work W , discards the remaining energy QL to sink and returns back to its original state and there no change occurs in its internal energy.

According to the 1st Law of Thermodynamics Net work done by the gas = Heat gained by the gas

W = QH − QL Efficiency of heat engine n =

n=

W QH

n=

QH − QL QH

n = 1−

QL QH

or

Workdone Engery Supplied

n = 1−

TL TH

Thus the efficiency of Carnot’s engine depends only on the temperature of the source and sink and not on the nature of the substance. By making

TL less TH

efficiency (η) can be increased. Two engines working between the same two temperatures TL and TH have equal efficiency.

The Refrigerator A Refrigerator may be considered to be a heat engine operated in reverse. A refrigerator takes heat from a cold reservoir. The compressor supplies mechanical work input and heat is rejected into a hot reservoir, for example: in home refrigerator. -

QC =

Food, Ice cubes – Cold reservoir Air in the room – Hot reservoir Work is done by the electric motor Heat enters the refrigerator at temperature TC

W = Work done on the refrigerator QH = Heat leaves at high temperature TH Thus QH = QCTW

Coefficient of performance of refrigerator K =

QC W

K=

In terms of temperature

K=

QC QH − QC

TC TH − TC

K=

we know

1− n n

n = 1−

TC TH