A Carnot engine absorbs an amount $Q$ of heat from a reservoir at an abosolute temperature $T$ and rejects heat to a sink at a temperature of $T/3.$ The amount of heat rejected is
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(b) $\because \;\eta = 1 - \frac{{{T_2}}}{{{T_1}}} = \frac{W}{{{Q_1}}}$ ${T_2} = 300\,K$
where ${Q_1} = $ heat absorbed, ${Q_2} = $ heat rejected
==> $1 - \frac{{T/3}}{T} = \frac{W}{{{Q_1}}}$ ==> $\frac{2}{3} = \frac{W}{{{Q_1}}} = \frac{{{Q_1} - {Q_2}}}{{{Q_1}}}$
==> $\frac{2}{3} = 1 - \frac{{{Q_2}}}{{{Q_1}}}$ ==> $\frac{{{Q_2}}}{{{Q_1}}} = \frac{1}{3}$ ==> ${Q_2} = \frac{{{Q_1}}}{3} = \frac{Q}{3}$
where ${Q_1} = $ heat absorbed, ${Q_2} = $ heat rejected
==> $1 - \frac{{T/3}}{T} = \frac{W}{{{Q_1}}}$ ==> $\frac{2}{3} = \frac{W}{{{Q_1}}} = \frac{{{Q_1} - {Q_2}}}{{{Q_1}}}$
==> $\frac{2}{3} = 1 - \frac{{{Q_2}}}{{{Q_1}}}$ ==> $\frac{{{Q_2}}}{{{Q_1}}} = \frac{1}{3}$ ==> ${Q_2} = \frac{{{Q_1}}}{3} = \frac{Q}{3}$
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