# Efficiency of Heat Engine

The efficiency may be defined as “The fraction of heat absorbed by an engine which it can convert into work”.

Thus,

$\text{Effieiency} = \dfrac{\text{Work done by the engine}}{\text{Energy fed into the eigine}}$

$\dfrac{\text{Maximum work obtainable}}{\text{Heat absorbed}}$

$= \dfrac{\text{Temperature difference}}{\text{Temp. at which heat is absorbed}}$

$or \hspace{3mm} \text{Efficiency} = \dfrac{w}{q_2} = \dfrac{T_2- T_1}{T_2}$

Since $( T_2 - T_1) / T_2)$ is always less than 1, hence the efficiency of a heat engine is always less than one. In fact, No heat engine has yet been constructed which may have and efficiency equal to unity”.

Example :

Calculate the entropy change when 1 mole of an ideal gas expands reversibly from an initial volume of 2 litres to an final volume of 20 litres at $25^0C$.

Solution:

We know that,

$\Delta S = n R ln \dfrac{V_2}{V_1}$

$= 2.303 n R \log \dfrac{20}{2}$

$= 2.303 \times 1 \times 8.314 \times 1$

$= 19.15 J K^{-1}$

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