Question

A Carnot engine whose low temperature reservoir is at $7{}^{\circ }C$ has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees should the temperature of the high temperature reservoir be increased?

• A. 840 K
• B. 280 K
• C. 560 K
• D. 373 K

Answer 1

Answer: (D)

Initially ${\eta }_1=\frac{T_1-T_2}{T_1}$ $\Rightarrow$ $0.5=\frac{T_1-(273+7)}{T_1}$ $\Rightarrow$ $\frac{1}{2}=\frac{T_1-280}{T_1}$ $\Rightarrow$ $T_1=560K$ Finally ${\eta }_1=\frac{T_1-T_2}{T_1}$ $\Rightarrow$ $0.7=\frac{T_1-(273+7)}{T_1}$ $\Rightarrow$ $T_1=933K$ $\therefore$ Increase in temperature $=933-560$ $=373K$