Determine the heat supplied by each thermal reservoir and thermal efficiency of the engine.

Given data$T_1$=750K,$T_2$=500K,$T_3$=250K,$W_engine$=100kw, $Q_1'$=3600KJ⁄min=60KW

$Q_1+Q_2$=$W+Q_r$ from the problem

$Q_1+Q_2=100+60$………(1)

$η_1$=$\frac{T_1-T_3}{T_1}$ =$\frac{750-250}{750}$=.66,

$η_2$=$\frac{T_2-T_3}{T_3}$ =$\frac{500-250}{500}$=0.5

$W_1=η_1 Q_1=0.66Q_1$

$W_1=η_1 Q_1=0.5Q_2$

total work(W)=$W_1+W_2=0.66Q_1+0.5Q_2$

100=0.66$Q_1+0.5Q_2$………(2)

Solving eq 1 and eq 2 we get values of Q1 and Q2

$Q_1=119.76KW$ , $Q_2=40.239KW$

Efficiency of the engine (η):

=$\frac{total work done}{(total heat absorbs}$=$\frac{100}{160}$=62.5%