Question 184 of 190
A Carnot engine is working between two temperatures 473 K and 273 K . In a new system two engines - engine works between 473 K to 373 K and engine works between 373 K to 273 K .
If and are the efficiencies of the engines and , respectively, then
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Answer: (D)
Efficiencies of a carnot engine
$\begin{aligned}
\Rightarrow & \eta_1=1-\frac{373 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\
& \eta_2=1-\frac{273 \mathrm{~K}}{373 \mathrm{~K}}=\frac{100}{373} \\
& \eta_{12}=1-\frac{273 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\
& \eta_{12}-\eta_1=\frac{200}{473}-\frac{100}{473}=\frac{100}{473} \lt \frac{100}{373} \\
\Rightarrow & \eta_{12}-\eta_1 \lt \eta_2 \\
\text { or } & \eta_{12} \lt \eta_1+\eta_2
\end{aligned}$
$\begin{aligned}
\Rightarrow & \eta_1=1-\frac{373 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\
& \eta_2=1-\frac{273 \mathrm{~K}}{373 \mathrm{~K}}=\frac{100}{373} \\
& \eta_{12}=1-\frac{273 \mathrm{~K}}{473 \mathrm{~K}}=\frac{100}{473} \\
& \eta_{12}-\eta_1=\frac{200}{473}-\frac{100}{473}=\frac{100}{473} \lt \frac{100}{373} \\
\Rightarrow & \eta_{12}-\eta_1 \lt \eta_2 \\
\text { or } & \eta_{12} \lt \eta_1+\eta_2
\end{aligned}$