Two heat engines $X$ and $Y$ of same efficiency are connected in series in such a way that the sink of $X$ works as source of $Y . X$ receives heat at $900 \mathrm{~K}$ and rejects some heat to its sink at $T \mathrm{~K}$ and in turn $Y$ rejects heat to its sink at \(400…

Question

Two heat engines $X$ and $Y$ of same efficiency are connected in series in such a way that the sink of $X$ works as source of $Y . X$ receives heat at $900 \mathrm{~K}$ and rejects some heat to its sink at $T \mathrm{~K}$ and in turn $Y$ rejects heat to its sink at $400 \mathrm{~K}$, then the temperature $T$ is

Aicharya · Accepted Answer

According to the question, a series combination of two heat engines are shown in the figure below,

Given, temperature of $X$ heat engine, $T_1=900 \mathrm{~K}$ and temperature of $Y$ heat engine, $T_2=400 \mathrm{~K}$ So, efficiency of $x$ heat engine, $\eta_x=1-\frac{T}{T_1}=1-\frac{T}{900}$ Similarly, $\eta_y=1-\frac{T_2}{T}=1-\frac{400}{T}$ $\because$ Given, $\eta_x=\eta_y$ $\begin{aligned} 1-\frac{T}{900} & =1-\frac{400}{T} \\ T^2 & =900 \times 400 \\ T & =600 \mathrm{~K} \end{aligned}$ Hence, the correct option is (b).

Two heat engines \(X\) and \(Y\) of same efficiency are connected in series in such a way that the sink of…

Solution