Question

A Carnot engine 'X' operates between temperature T(1) and T(2) And (T(1)>T(2)). A second Carnot engine 'Y' uses all the heat rejected by the engine 'X' and operates between temperature T(2) and T(3)
( where T(2)>T(3)). The efficiency of this combined X and Y together engine is?
ANS:1- {[T(2)+T(3)]/T(1)}

Answer 1

$\eta_x=\frac{T_1-T_2}{T_1}=1-\frac{T_2}{T_1},$

$\eta_y=\frac{(T_1-T_2)-T_3}{T_1-T_2}=1-\frac{T_3}{T_1-T_2},$

$\eta=\eta_x\eta_y=(1-\frac{T_2}{T_1})\cdot(1-\frac{T_3}{T_1-T_2})=\frac{T_1-T_2}{T_1}\cdot\frac{T_1-T_2-T_3}{T_1-T_2}=\frac{T_1-T_2-T_3}{T_1}=1-\frac{T_2+T_3}{T_1}.$