Three Carnot engines operate in series between a heat source at a temperature $T_{1}$ and a heat sink at temperature $T_{4}$ (see figure). There are two other reservoirs at temperature $T_{2}$ and $T_{3},$ as shown, with $T_{1} > T_{2} > T_{3} > T_{4} .$ The three engines are equally efficient if:

Question

Three Carnot engines operate in series between a heat source at a temperature

T_{1}

and a heat sink at temperature

T_{4}

(see figure). There are two other reservoirs at temperature

T_{2}

and

T_{3},

as shown, with

T_{1} > T_{2} > T_{3} > T_{4} .

The three engines are equally efficient if:

Aicharya · Accepted Answer

η 1 = 1 - T 2 T 1 η 2 = 1 - T 3 T 2 η 3 = 1 - T 4 T 3 Given η 1 = η 2 = η 3 T 2 T 1 = T 3 T 2 = T 4 T 3 T 2 2 = T 1 T 3 ....(1) T 3 2 = T 2 . T 4 ....(2) From (1) and (2) T 3 = T 1 T 4 2 1 / 3 , T 2 = T 1 2 T 4 1 / 3

Three Carnot engines operate in series between a heat source at a temperature T 1 and a heat sink at…

Solution