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The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales…
The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincides and Kelvin-Fahrenheit scales coincides is (approximately)
$45 \%$ $35 \%$ $60 \%$ $50 \%$ Solution
When Celsius - Fahrenheit scale coincide,
$\begin{aligned}
& \frac{\mathrm{F}-32}{180}=\frac{\mathrm{C}-0}{100} \Rightarrow \frac{\mathrm{~T}_1-32}{9}=\frac{\mathrm{C}}{5} \\
& \therefore \quad \mathrm{~T}_1=-40^{\circ} \mathrm{C}
\end{aligned}$
When kelvin - Fahrenheit scale coincide,
$\begin{aligned}
& \frac{\mathrm{K}-273}{100}=\frac{\mathrm{F}-32}{180} \Rightarrow \frac{\mathrm{~T}_2-273}{5}=\frac{\mathrm{T}_2-32}{9} \\
& \therefore \quad \mathrm{~T}_2=574.25 \mathrm{~K} \\
& \therefore \quad \text { Efficiency, } \eta=1-\frac{\mathrm{T}_1}{\mathrm{~T}_2}=1-\frac{273-40}{574.25}=60 \%
\end{aligned}$
Asked in: AP EAMCET 2024 (22 May Shift 1)
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