A carnot engine having efficiency 1/6, operates between the source temperature TH and the sink temperature TC. Its efficiency increases to 1/3, when TC is decreased by 64 K. The temperatures TH and TC are repectively (a) 374 K, 310 K (b) 384 K, 320 K (c) 384 K, 340 K (d) 320 K, 256 K

Answer: (b). 1/6 = 1 - (TC)/(TH) ⇒ TC = 5/6TH 1/3 = 1 - (TC - 64)/(TH) ⇒ TC - 64 = 2/3TH Subtract: 5/6TH - 2/3TH = 64 ⇒ TH = 384 K, TC = 320 K So the answer is (b).

A carnot engine having efficiency 1/6, operates between the source… | MHT CET 2026 (17 Apr, Shift 2)

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Heat Engines, Refrigerators & Second Law

A carnot engine having efficiency $\frac{1}{6}$ , operates between the source temperature $T_H$ and the sink temperature $T_C$ . Its efficiency increases to $\frac{1}{3}$ , when $T_C$ is decreased by 64 K. The temperatures $T_H$ and $T_C$ are repectively

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Answer: (b)

$\frac{1}{6} = 1 - \frac{T_C}{T_H} \Rightarrow T_C = \frac{5}{6}T_H$
$\frac{1}{3} = 1 - \frac{T_C - 64}{T_H} \Rightarrow T_C - 64 = \frac{2}{3}T_H$
Subtract: $\frac{5}{6}T_H - \frac{2}{3}T_H = 64 \Rightarrow T_H = 384$ K, $T_C = 320$ K
So the answer is (b).

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