Question

Efficiency of a heat engine whose sink is at a temperature of $300K$ is $40$%. To increase the efficiency to $60$%, keeping the sink temperature constant, the source temperature must be increased by :

• A. $750K$
• B. $500K$
• C. $250K$
• D. $1000K$

Answer 1

The correct option is C $250K$

We know that in heat engine, sink is at lower temperature than source, hence,

$\eta =1-\frac{T_{sink}}{T_{source}}$

$0.4=1-\frac{300}{T_{source}}$

$T_{source}=500K$

In the second case,

$0.6=1-\frac{300}{T_{source}}$

$T_{source}=\frac{300}{0.4}$

$T_{source}=750K$

Hence, an increment of $250K$ in source temperature is required.