A Carnot engine whose heat sink is at 27 ° C has an efficieny of 40 % . By how much should its source…

Efficiency of the engine, $\eta =1-\frac{T_{\mathrm{sink}}}{T_{\mathrm{source}}}$

Given, Sink temperature, $T_{\mathrm{sink}}=27° \mathrm{C}=300 \mathrm{K}$

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

$\Rightarrow \frac{300}{T_{\mathrm{source}}}=0.6$

$\Rightarrow T_{\mathrm{source}}=500 \mathrm{K}$

For $\eta =60\%$,

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

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

$\Rightarrow T_{\mathrm{source}}=750 \mathrm{K}$

Change in source temperature, $750-500=250 \mathrm{K}$