Question

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

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

Answer 1

The correct option is B ${227}^{\circ }C$

Given,

$\eta =30$%

$T_2={77}^{0}C=77+273=350K$

The efficiency of heat engine,

$\eta =1-\frac{T_2}{T_1}$

$\frac{30}{100}=1-\frac{350}{T_1}$

$T_1=500K$

$T_1=500-273={227}^{0}C$

The correct option is B.