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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3td052

A reversible Carnot engine absorbs $1000 J$ from a reservoir at $500 K$ and rejects heat to a reservoir at $300 K$ . Which statements are correct?

AIts efficiency is 40 percent.
BThe heat rejected to the cold reservoir is 600 J.
CThe total entropy change of the two reservoirs is positive.
DIf the cold reservoir were at $200 K$ , the heat rejected would be 400 J.

Answer: A, B, D

Reversible cycle:

q_{h} / T_{h} + q_{c} / T_{c} = 0

in sign convention, so

∣ q_{c} ∣ = q_{h} T_{c} / T_{h} = 600 J

and

w = 400 J

, efficiency

1 - 300/500 = 40

percent (A, B true). Entropy changes of reservoirs are

- 1000/500 = - 2.0

and

+ 600/300 = + 2.0 J K^{- 1}

, total zero (C false). With

T_{c} = 200 K

:

∣ q_{c} ∣ = 1000 (200) /500 = 400 J

(D true).

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