Two carnot engines A and B are operated in series. The first one A receives heat at 900 K and reject to a reservoir at temperature T K. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 400 K calculate the temperature T when (i) The efficiencies of the two engines are equal (ii) The work output of the two engines are equal

Two carnot engines A and B are operated in series. The first one A rec

1.	Two carnot engines A and B are operated in series. The first one A receives heat at 900 K and reject to a reservoir at temperature T K. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 400 K calculate the temperature T when (i) The efficiencies of the two engines are equal (ii) The work output of the two engines are equal
Answer» Solution :`W_A=W_B` `W/Q_1=(1-(T_2)/(T_1))` `W=Q_1(1-T_2//T_1)` `Q_2(1-(T_3)/T_2)=Q_1(1-T_2/T_1)` `(1-T/(900))Q_1 = (1-(400)/T)Q_2` `(1-T/900)Q_1=(1-(4000)/T)T/900` `1-T/900=T/900-400/900` `(2T)/900=13/9` `T = 650 K` `eta_A=eta_B` `1-T/900=(1-400)/T` `T^2=900xx400` `=600k` `T_1=273k, T_2=673k` MASS of gas = 10 MOLE `W_(adia)=(10R)/((gamma-1))(T_1-T_2)` `=(10xx8.4)/((1.4-1))(273-673)` `=-8.4 xx10^(4)J` work being done on the gas `DU = -DW = 8.4 xx10^(4)J`