A reversible heat engine runs between 500ºC and 200ºC temperature reservoirs. This heat engine is used to drive an auxiliary and a reversible heat pump which runs between reservoir at 200ºC and the body at 450ºC. The auxiliary consumes one third of the engine output and remaining is consumed for dr

Question

A reversible heat engine runs between 500ºC and 200ºC temperature reservoirs. This heat engine is used to drive an auxiliary and a reversible heat pump which runs between reservoir at 200ºC and the body at 450ºC. The auxiliary consumes one third of the engine output and remaining is consumed for driving heat pump. Determine the heat rejected to the body at 450ºC as fraction of heat supplied by reservoir at 500ºC.

Accepted Answer

Let the output of heat engine be W. So

[latex]\frac{W}{3}[/latex] is consumed for driving auxiliary and remaining [latex]\frac{2W}{3}[/latex] is consumed for driving heat

pump for heat engine

[latex]\begin{aligned}η&= \frac{W}{Q_{1}} = 1 - \frac{473}{773}\\frac{W}{Q_{1}} &= 0.3881\end{aligned}[/latex]

COP of heat pump}

[latex]\begin{aligned}&= \frac{723}{723 − 473} = \frac{Q_{3}}{2W/3}\⇒ \qquad\qquad \qquad \qquad 2.892&= \frac{3Q_{3}}{2W}\end{aligned}[/latex]

Substituting W,

[latex]\begin{aligned}\frac{Q_{3}}{Q_{1}}&= 0.7482\end{aligned}[/latex]

Ratio of heat rejected to body at 450ºC to the heat supplied by the reservoir =

0.7482

Question 4.15: A reversible heat engine runs between 500ºC and 200ºC temper...

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