Question

An ideal heat engine exhausting heat at $27^{\circ }C$ is to have $25\%$ efficiency. It must take heat at

• A. $127^{\circ }C$
• B. $227^{\circ }C$
• C. $327^{\circ }C$
• D. None of these

Answer 1

Answer: (A)

$T_2=27^{\circ }C=\left(27+273\right)$
$K=300K$,
$\eta =25\%=\frac{1}{4}$
We know that,
$\eta =1-\frac{T_2}{T_1}$
$\Rightarrow \frac{1}{4}=1-\frac{300}{T_1}$
or $\frac{300}{T_1}=1-\frac{1}{4}$
$\Rightarrow \frac{300}{T_1}=\frac{3}{4}$
or $T_1=\frac{300\times 4}{3}$
$\Rightarrow T_1=400K$
or $T_1={\left(400-273\right)}^{\circ }C$
$=127^{\circ }C$