First slide

Heat engine

Question

A heat engine has an efficiency . Temperatures of source and sink are each decreased by 100K. Then, the efficiency of the engine

Easy

A

Increases
B

Decreases
C

Remains constant
D

Becomes 1

Solution

Assuming source and sink temperature to be T₁ and T₂
$\large \eta \, = \,\frac{{1 - {T_2}}}{{{T_1}}}\, = \,\frac{{{T_1} - {T_2}}}{{{T_1}}}$
Once the temperatures have been decreased by 100k
$\large \eta \, = \,\frac{{1 - {T_2} - 100}}{{({T_1} - 100)}}\, = \,\frac{{({T_1} - 100) - ({T_2} - 100)}}{{({T_1} - 100)}}$
$\large \eta \, = \,\frac{{{T_1} - {T_2}}}{{{T_1} - 100}}$

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