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}}=560\,\,K $ Finally $ {{\eta }_{1}}=\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}} $ $ \Rightarrow $ $ 0.7=\frac{{{T}_{1}}-(273+7)}{{{T}_{1}}} $ $ \Rightarrow $ $ {{T}_{1}}=933\,\,K $ $ \therefore $ Increase in temperature $ =933-560 $ $ =373\,\,K $