The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is

Concept:

Freezing point- The temperature at which liquid freezes i.e., it is converted into solid is called as freezing point. The temperature at which water freezes is 0 ⁰C or 273 K.

Boiling point- It is defined as the temperature at which liquid boils or get converted into vapors. Also at this temperature the vapor pressure of liquid is equal to the atmospheric pressure around it. Boiling point of a liquid depends upon the pressure of the surrounding.

Boiling point of water at 1 atm pressure is equal to 100 ⁰C or 373 K.

Ideal Heat Engine-

In 1824, Ideal heat engine was developed by Nicolas Leonard Sadi Carnot. It works on Carnot cycle. It is based on second law of thermodynamics. Heat engine converts heat energy into mechanical energy. Theoretically, there are no loss of energy due to friction. The working substance of the heat engine undergoes a reversible cycle which have two isothermal as well as two adiabatic changes.

Efficiency of ideal heat engine is defined as the fraction of the total heat given to the engine which is converted into work.

Let Q is the amount of heat given to ideal heat engine from the source, W is the work done by it, the heat left Q^' is rejected to the sink. Then

Q = W + Q^'

Work done by heat engine is W = Q - Q^'

Efficiency, \(η =\frac{W}{Q}\)

\(η = \left( {1 - \frac{{{Q'}}}{{{Q}}}} \right)\)

where \(η \) is the efficiency of the heat engine.

In terms of temperature 

Efficiency of ideal heat engine, \(η = \left( {1 - \frac{{{T_2}}}{{{T_1}}}} \right)\)

where T2 is Sink temperature 

T1 is Source temperature 

Calculation:

Freezing point of water = 273 K

Boiling point of water = 373 K

Efficiency of ideal heat engine, \(η = \left( {1 - \frac{{{T_2}}}{{{T_1}}}} \right)\)

T₂ : Sink temperature 

T₁ : Source temperature 

\(\% \eta = \left( {1 - \frac{{{T_2}}}{{{T_1}}}} \right) \times 100\)

\(= \left( {1 - \frac{{273}}{{373}}} \right) \times 100\)

\(= \left( {\frac{{100}}{{373}}} \right) \times 100\)

= 26.8%