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An engine performs $2000 \mathrm{~J}$ of mechanical work and discards $4000 \mathrm{~J}$ of heat each cycle. What is the thermal efficiency of the engine?
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The correct answer is:
$33.3 \%$
Work done, $W=2000 \mathrm{~J}$
Heat transferred to surrounding, $Q_2=4000 \mathrm{~J}$
Let heat supplied to the engine $=Q_1$
Since, $Q_1=Q_2+W=2000+4000=6000 \mathrm{~J}$
Thermal efficiency, $\begin{aligned} \eta & =\frac{W}{Q_1} \times 100 \% \\ & =\frac{2000}{6000} \times 100 \%=33.3 \%\end{aligned}$
Heat transferred to surrounding, $Q_2=4000 \mathrm{~J}$
Let heat supplied to the engine $=Q_1$
Since, $Q_1=Q_2+W=2000+4000=6000 \mathrm{~J}$
Thermal efficiency, $\begin{aligned} \eta & =\frac{W}{Q_1} \times 100 \% \\ & =\frac{2000}{6000} \times 100 \%=33.3 \%\end{aligned}$
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