A carnot engine, whose efficiency is $40 \%$ takes heat from a source maintained at temperature 600 K . It…

A carnot engine, whose efficiency is $40 \%$ takes heat from a source maintained at temperature 600 K . It is desired to have an efficiency $60 \%$, then the intake temperature for the same exhaust (sink) temperature should be
  1. 1800 K
  2. 1200 K
  3. 900 K
  4. 600 K

Solution

For Carnot's engine, $\begin{aligned} & \eta=1-\frac{T_L}{T_H} \\ \therefore \quad & \frac{40}{100}=1-\frac{T_L}{600} \\ & \frac{T_L}{600}=\frac{60}{100} \\ \therefore \quad & T_L=360 \mathrm{~K} \\ \quad & \text { Now, } \frac{60}{100}=1-\frac{360}{T_H} \\ \therefore \quad & \frac{360}{T_H}=\frac{40}{100} \quad \Rightarrow T_H=900 \mathrm{~K} \end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 1)

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