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JEE Main 2015 · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from JEE Main 2015

Q71JEE Main 2015Difficult

Heat Engines, Refrigerators & Second Law

A solid body of constant heat capacity 1 J/∘C1\ J/{}^\circ C is being heated by keeping it in contact with reservoirs in two ways:

(i)(i) Sequentially keeping in contact with 22 reservoirs such that each reservoir

supplies same amount of heat.

(ii)(ii) Sequentially keeping in contact with 88 reservoirs such that each reservoir

supplies same amount of heat.

In both the cases body is brought from initial temperature 100∘C100^\circ C to final temperature 200∘C200^\circ C. Entropy change of the body in the two cases respectively is:

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Answer: (d)

  1. Entropy is a state function: ΔS\Delta S depends only on the initial and final states of the body.
  2. ΔS=∫C dTT=Cln⁡TfTi=ln⁡473373\Delta S = \int \frac{C\,dT}{T} = C\ln\frac{T_f}{T_i} = \ln\frac{473}{373} in both cases.
  3. The number of reservoirs used does not matter, so both changes are equal.
  4. So the answer is (d): the same value in both cases.
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