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An ideal Carnot's engine with an efficiency of \(30 \%\) operates between a source and a sink. If the temperature of the source is \(500 \mathrm{~K}\), that of the sink is
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\(77^{\circ} \mathrm{C}\)
Efficiency of Carnot's engine, \(\eta=30 \%=0.3\)
Temperature of source, \(T_1=500 \mathrm{~K}\)
Temperature of sink, \(T_2=\) ?
We know that, efficiency of Carnot engine,
\(\begin{array}{rlrl}
\eta & =1-\frac{T_2}{T_1} \Rightarrow 0.3=1-\frac{T_2}{500} \\
\Rightarrow \quad & \frac{T_2}{500} & =1-0.3 \\
\Rightarrow \quad & T_2 & =0.7 \times 500 \\
& = & 350 \mathrm{~K}=(350-273)^{\circ} \mathrm{C}=77^{\circ} \mathrm{C}
\end{array}\)
Temperature of source, \(T_1=500 \mathrm{~K}\)
Temperature of sink, \(T_2=\) ?
We know that, efficiency of Carnot engine,
\(\begin{array}{rlrl}
\eta & =1-\frac{T_2}{T_1} \Rightarrow 0.3=1-\frac{T_2}{500} \\
\Rightarrow \quad & \frac{T_2}{500} & =1-0.3 \\
\Rightarrow \quad & T_2 & =0.7 \times 500 \\
& = & 350 \mathrm{~K}=(350-273)^{\circ} \mathrm{C}=77^{\circ} \mathrm{C}
\end{array}\)
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