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Q.

A heat engine operates between a cold reservoir at temperature $T_{2} = 400 K$ and a hot reservoir at temperature $T_{1}$ . It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be _____K.

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answer is 500.

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Detailed Solution

$Q_{i n} = 300 J; Q_{o u t} = 240 J$
Work done $Q_{i n}$ - $Q_{o u t}$ =300-240 =60 J
Efficiency= $\frac{W}{Q_{i n}} = \frac{60}{300} = \frac{1}{5}$
Efficiency = $1 - \frac{T_{2}}{T_{1}}$
$\frac{1}{5} = 1 - \frac{400}{T_{1}} \Rightarrow \frac{400}{T_{1}} = \frac{4}{5}$
$T_{1}$ =500 K

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