If the temperature of the source is 227° C and the efficiency of the Carnot engine is 40 % then find the temperature of the sink.

CONCEPT:

Carnot engine:

• The theoretical engine which works on Carnot cycle is called as a Carnot engine.
• It gives the maximum possible efficiency among all types of heat engine.

There are mainly three parts of the engine

Heat source:

• The part of the Carnot engine which provides heat to the engine is called as heat source.
• The temperature of the source is maximum among all the parts.

Heat sink:

• The part of the Carnot engine in which extra amount of heat is rejected by the engine is called as heat sink.
• The temperature of this part is lowest.

Work done:

• The amount of work which is done by the engine is called as work done.

The efficiency (η) of a Carnot engine is given by:

\(\eta = 1 - \frac{{{T_C}}}{{{T_H}}} = \;\frac{{Work\;done\left( W \right)}}{{{Q_{in}}}}\)

Where T_C is the temperature of the sink, T_H is the temperature of the source, W is work done by the engine and Q_in is the heat given to the engine/heat input.

EXPLANATION:

Given that,

T_H  = Temperature of heat source = 227 °C = 273 +227 = 500 K

Efficiency of engine = η = 40% = 0.4

\(\eta = 1 - \frac{{{T_C}}}{{{T_H}}}\)

\(0.4 = 1 - \frac{{{T_C}}}{{500}}\)

T_C = 0.6 × 500 = 300 K.