Two heat engines are operated in series. The first one receives heat at 800 K and rejects to a reservoir at temperature TK. The second one receives heat rejected by first one and rejects heat to a sink at -730C. The temperature T, if the two outputs of two engines are equal

For first engine, efficiency of heat engine =η=1−T2T1 =1-Q2Q1⇒Q2Q1=T2T1  ;givenT1=800K=temperature of source; T2=T=temperature of sink, substitute⇒Q2Q1=T800---(1)Q1=heat absorbed;Q2=heat rejectedη1=W1Q1 for first engine⇒W1=Q1.η1⇒W1=Q11−T2T1 ⇒W1=Q11−T800---(2)       for second engineη2=W2heat absorbed by second engine Q2 =1−T21T11 Heat absorbed by II engine= Heat rejected by I engine =Q2 temperature of sink for II engine=-73+273=200K=T21⇒W2=Q2 1−T21T11W2=Q2 1−200T---(3) given W2=W1    ∵outputs are same ; substitute equations (2) and (3)Q2 1−200T=Q11−T800Q2Q11−200T=1−T800    ;substitute equation (1)T8001−200T=1−T800T800−14=1−T800⇒2T800=54⇒T=500K