Question

The efficiency of a Carnot engine world between two temperatures is 0.2, when th temperature of the source is increased by ${25}^{o}C$, the efficiency increases to 0.25. Th temperatures of the source and the sink will be

• A. 375 K, 300 K
• B. 475 K, 400 K
• C. 400 K, 800 K
• D. 375 K, 400 K

Answer 1

Answer: (A)

375 K, 300 K

We have $\eta =1-\frac{T_2}{T_1}$
$0.2=1-\frac{T_2}{T_1}$
$\frac{T_2}{T_1}=1-0.2=0.8$
$0.25=1-\frac{T_2}{T_1+25}$
$\frac{T_2}{T_1+25}=1-0.25=0.75$
$\frac{0.8T_1}{T_1+25}=0.75$
$0.8T_1=0.75T_1+0.75\times 25$
$0.05T_1=0.75\times 25$
$T_1=\frac{0.75\times 25}{0.05}=15\times 25=375K$
$T_2=0.8T_1=0.8\times 375=300K$