The p-V diagram of a Carnot's engine is shown | vedclass

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(C) The efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$.From the $p-V$ diagram,the process $AB$ is isoth

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$3000$

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(C) The efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$.From the $p-V$ diagram,the process $AB$ is isothermal expansion at $T_1$ and $CD$ is isothermal compression at $T_2$.For an isothermal process,$pV = 	ext{constant}$.At point $A$: $p_A = 1600 \ kPa$,$V_A = 2.5 \ cm^3$. So,$p_A V_A = 1600 	imes 2.5 = 4000$.At point $C$: $p_C = 400 \ kPa$,$V_C = 6.25 \ cm^3$. So,$p_C V_C = 400 	imes 6.25 = 2500$.Since $pV = \mu RT$,we have $\frac{T_2}{T_1} = \frac{p_C V_C}{p_A V_A} = \frac{2500}{4000} = \frac{5}{8} = 0.625$.The efficiency is $\eta = 1 - 0.625 = 0.375$.Given heat supplied $Q_1 = 8000 \ J$.Work done $W = \eta 	imes Q_1 = 0.375 	imes 8000 = 3000 \ J$.

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