Carnot engine

Objective is toexplain what a heat engine is, and

compute its thermal efficiency

Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat into work.

The different parts of heat engine are

HOT RESERVOIR or Source is a material kept at high temperature and having infinite thermal capacity. Any amount of heat can be taken from it without changing its temperature.

COLD RESERVOIR or Sink is a material kept at low temperature and having infinite thermal capacity. Any amount of heat can be given to it without changing its temperature.

Working substance is a material which converts heat energy in to work. It is taken in a cylinder fitted with tight movable frictionless piston. The lower side of the cylinder will be thermally conducting.

It insulates the working substance from thermal contact with the surroundings. That is used for performing the adiabatic process.

Insulating Stand

Source at Temp T1

Sink at Temp T2

Ideal Gas(working

Substance)

Cylinder

Piston

Carnot engine is an ideal heat engine whose efficiency is maximum. In carnot engine, carnot cycle is used.

In carnot engine, ideal gas is the working substance and all the dissipative forces are absent.

Carnot devised an ideal cycle of operation for a heat engine and is know as carnot cycle.

In one complete cycle of operation, there are four different thermodynamic processes.

At first, the working substance is kept in contact with the source. The piston of the cylinder is moved outwards. The gas expands at constant temperature. The amount of heat(Q1) is absorbed from the source to make the temperature constant. The volume increases and pressure decreases.

This is called isothermal expansion. It is represented by the curve AB in the indicator diagram.

V

P

(P1V1T1)

(P2V2T1)

A

B

V1 V2

Isothermal Expansion

The lower conducting side of the cylinder is kept in contact with the insulating stand. The piston of the cylinder is moved outwards. The gas expands such that no heat enters the system or leaves from it. The volume increases and pressure decreases. The temperature is decreased from T1 to T2.

This is called adiabatic expansion. It is represented by the curve BC in the indicator diagram.

V

P

(P1V1T1)

(P2V2T1)

(P3V3T2)

A

B

C

V1 V2 V3

AdiabaticExpansion

The cylinder is kept in contact with the sink. The piston of the cylinder is moved inwards. The gas is compressed at constant temperature. The excess heat produced(Q2) will flow to the sink to make the temperature constant. The volume decreases and pressure increases.

This is called isothermal compression. It is represented by the curve CD in the indicator diagram.

V

P

(P1V1T1)

(P2V2T1)

(P4V4T2)

A

B

C

D

V1 V2 V3V4

Isothermal Compression (P3V3T2)

The cylinder is kept in contact with the insulating stand. The piston of the cylinder is moved inwards. The gas is compressed such that no heat enters the system or leaves from it. The volume decreases and pressure increases. The temperature increases from T2 to T1.

This is called adiabatic expansion. It is represented by the curve DA in the indicator diagram.

V

P

(P1V1T1)

(P2V2T1)

(P4V4T2)

A

B

C

D

V1 V2 V3V4

AdiabaticCompression

(P3V3T2)

V

P

(P1V1T1)

(P2V2T1)

(P3V3T2)

(P4V4T2)

A

B

C

D

V1 V2 V3V4

Isothermal Expansion

AdiabaticExpansionIsothermal

Compression

AdiabaticCompression

We have the efficiency of heat engine,

= W/Q1 where ‘W’ is the work done and Q1 is the amount of heat absorbed from the source.

Also W = Q1 – Q2 where Q2 is the amount of energy

rejected to sink.

There fore, = ( Q1 – Q2)/Q1 = 1 – (Q2/Q1)

For a carnot engine, it can be shown that = 1 – (T2/T1) where T1 is the temperature

of source and T2 that of sink.

Carnot engine is purely an imaginary engine. But all real engines are constructed based on carnot cycle.

No other engine can have same efficiency as that of a carnot engine working between the same temperature range.