First slide

Heat engine

Question

Engine A receives three times more input heat, produces five times more work, and rejects two times more heat than engine B. The efficiency of engine A is

Moderate

A

5/9
B

1/3
C

2/9
D

2/3

Solution

For A, 3Q, 5W and 3Q-5W are heat absorbed, work done and heat rejected respectively and for B. Q, W, Q–W are the corresponding values for A. Equate (3Q-5W) to 2×(Q $-$ W)
$\therefore \left( {3Q - 5W} \right) = 2\left( {Q - W} \right)$
⇒ Q = 3W
$\therefore {\eta _A} = \frac{{5W}}{{3Q}} = \frac{5}{3}.\frac{1}{3} = \frac{5}{9}$

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