Question

The operating temperatures for a Carnot engine are TcT_{\mathrm{c}} and Th=Tc+55 KT_{\mathrm{h}}=T_{\mathrm{c}}+55 \mathrm{~K}. The efficiency of the engine is 11%11 \%. Find TcT_{\mathrm{c}} and ThT_{\mathrm{h}}.

Solution

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The operating temperatures for a carnot engine are given as: TcT_{c} : temperature of the cold reservoir

ThT_{h} : temperature of the hot reservoir = TcT_{c} + 55

η\eta = 1 - TcoldThot\dfrac{T_{cold}}{T_{hot}}

0.11 = 1 - TcTc+55\dfrac{T_{c}}{T_{c} + 55}

TcTc+55\dfrac{T_{c}}{T_{c} + 55} = 0.89

0.89 TcT_{c} + 48.95 = TcT_{c}

48.95 = 0.11 TcT_{c}

TcT_{c} = 445 K

ThT_{h} = 500 K

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