A Carnot engine takes 5000 k cal of heat from a source at $727^0C$ and rejects heat to a sink at $12

Question

A Carnot engine takes 5000 k cal of heat from a source at $727^0C$ and rejects heat to a sink at $127^{\circ} \mathrm{C}$. The work done is

Professor PC Thomas Classes · Answer

(c) : Given : $Q_{1}=5000 \mathrm{~K} \mathrm{cal}$,\ $T_{1}=727^{\circ} \mathrm{C}=1000 \mathrm{~K}$\ $T_{2}=127^{\circ} \mathrm{C}=400 \mathrm{~K}, W=$ ?\ $\frac{Q_{2}}{Q_{1}}=\frac{T_{2}}{T_{1}} \Rightarrow Q_{2}=5000 	imes \frac{400}{1000}$\ $Q_{2}=2000 \mathrm{~K} \mathrm{cal} ; W=Q_{1}-Q_{2}=5000-2000 =3000 \mathrm{KJ}$\ $W=3000 	imes 10^{3} 	imes 4.2=12.6 	imes 10^{6} \mathrm{~J}$