JEE Main · 2015 · 04 Apr 2015 · Offline · Heat & Thermodynamics

A solid body of constant heat capacity

1 J /^{\circ} C

is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature

10 0^{\circ} C

to final temperature

20 0^{\circ} C

. Entropy change of the body in the two cases respectively is:

(A) $ln 2, ln 2$ ✓ Correct
(B) $ln 2, 2 ln 2$
(C) $2 ln 2, 8 ln 2$
(D) $ln 2, 4 ln 2$

Answer: (A)

Solution

Entropy is a state function, so its change depends only on the initial and final states, not on how many reservoirs are used along the way. With heat capacity

C = 1 J /^{\circ} C

and the temperatures converted to kelvin,

10 0^{\circ} C \to 373 K

and

20 0^{\circ} C \to 473 K

, both heating schemes give the same

Δ S = C ln \frac{T _{f}}{T _{i}} = ln \frac{473}{373} \approx 0.24 J/K

. None of the printed choices, which are all multiples of

ln 2

, equals this value; the

ln 2

figures arise only if the temperatures are mistakenly read as

100 K \to 200 K

. The authoritative solution records that a correct option is not available, so this item is defective.

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option

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JEE Main · 2015 · 04 Apr 2015 · Offline · Heat & Thermodynamics

Solution

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