A Carnot's engine works between $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$. Another engine

Question

A Carnot's engine works between $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$. Another engine works between $0^{\circ} \mathrm{C}$ and $-200^{\circ} \mathrm{C}$. The ratio of the efficiencies of two engines is\

Professor PC Thomas Classes · Answer

$\eta_{1}=\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{~T}_{1}} \quad \mathrm{~T}_{1}=473 \mathrm{~K}$ $$ \begin{aligned} = & T_{2}=273 \mathrm{~K} \ \eta_{2}= & \frac{T_{1}^{1}-T_{2}^{1}}{T_{1}^{1}} \quad T_{1}^{1}=273 \mathrm{~K} \ & =T_{2}^{1}=-200+273 \end{aligned} $$ Find $\frac{\eta_{1}}{\eta_{2}}=\quad=73 \mathrm{~K}$\