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

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 &#62; T 2 &#62; T 3 &#62; T 4 . The three engines are equally efficient if:

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Correct answer: C. T 2 = T 1 2 T 4 1 3 ; T 3 = T 1 T 4 2 1 3

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 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:

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Correct answer

Step-by-step solution

More from Thermodynamics

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 &#62; T 2 &#62; T 3 &#62; T 4 . The three engines are equally efficient if:

Options

Correct answer

Step-by-step solution

More from Thermodynamics

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: