Question

Two engines are working in such a way that sink of one is source of the other. Their efficiencies are equal. Find the temperature of the sink of first if its source temperature is ${927}^{\circ }\text{C}$ and temperature of sink of the second is ${27}^{\circ }\text{C}$

• A. $327\text{K}$
• B. ${327}^{\circ }\text{C}$
• C. ${600}^{\circ }\text{C}$
• D. none of these

Answer 1

The correct option is B ${327}^{\circ }\text{C}$

Efficiency $\left(\eta \right)=1-\frac{T_2}{T_1}=1-\frac{T_3}{T_2}$
Where, $T_1=$ temperature of first source
$T_2=$ temperature of first sink$=$ temperature of second source
$T_3=$ temperature of second sink
$\therefore T_2^2=T_1{T}_3$

$T_2=\sqrt{1200\times 300}=600\text{K}={327}^{\circ }\text{C}$