Question

An ideal heat engine exhausting heat at $77^{\circ }C$ is to have $30\%$ efficiency. It must take heat at

• A. $127^{\circ }C$
• B. $227^{\circ }C$
• C. $327^{\circ }C$
• D. $673^{\circ }C$

Answer 1

Answer: (B)

Given : $T_2=77+273=350K$
Efficiency $\eta =\left(1-\frac{T_2}{T_1}\right)\times 100$
$30=\left(1-\frac{350}{T_1}\right)100$
$1-\frac{350}{T_1}=\frac{3}{10}$
$\frac{350}{T_1}=\frac{7}{10}$
$T_1=\frac{350\times 10}{7}=500K$
$=500-273=227^{\circ }C$