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A reversible cyclic process involves 6 steps. In step -1 and 3 system absorbs 500 J, 800 J of heat from a heat reservoir at temperature 250 K and 200 K respectively. Step 2, 4, 6 are adiabatic such that the temperature of one reservoir changes to that of next. Total work done by the system in whole cycle is 700 J. Find the temperature during step 5 if it exchanges heat from a reservoir at temperature $T_{5}$ .

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Detailed Solution

Let heat involved in step 5 is $Q_{5}$

$\begin{array}{l} q_{total} = - W_{total} \\ 500 + 800 + Q_{5} = 700 \\ Q_{5} = - 600 J \\ Since Δ S total = 0 \\ \frac{500}{250} + \frac{800}{200} - \frac{600}{T_{5}} = 0 \\ \Rightarrow T_{5} = 100 K \end{array}$

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