Consider a carnot's cycle operating between $T_1 = 500\,K$ and $T_2 = 300\,K$ producing $1\,kJ$ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs  .... $J$
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$\eta=1-\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=1-\frac{300}{500}=\frac{2}{5}$

$\eta=\frac{W}{Q} \quad Q=\frac{W}{\eta}=\frac{1000 J}{2 / 5}$

$\mathrm{Q}=2500 \mathrm{J}$

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