Question

Two Carnot engines function in tandem, such that one rejects heat at a certain temperature, which the other absorbs at the same temperature. Let the first engine be A, and the second B. A intakes 13.4 kW of heat at 530K, and B rejects heat at 270K while doing 2.4kW of work. Determine the power output (work) of engine A.

Answer 1

Call T1 the temperature in at A

T2 = temperature out of A and temperature in B

T3 = temperature out of B

eA is efficiency of A, eB is efficiency of B, and eT is the efficiency of the combined engines A and B

eA = 1 - T2/T1

eB = 1 - T3/T2

eT = 1 - T3/T1

T2/T1 = 1 - eA so T1 = T2/(1 - eA)

T3/T2 = 1 - eB so T3 = T2(1 - eB)

eT = 1 - (1 - eA)(1 - eB) = 1 - (1 - eA - eB + eAeB) = eA + eB - eAeB

eT = (Power out of A + Power out of B)/Heat in A

eT = (1 - T2/530) + (1 - 270/T2) - (1 - T2/530)(1 - 270/T2) = 0.49 (if you do the algebra T2 cancels out)

0.49(13.4) = Power out of A + 2.4

Power out of A = 4.166 kW