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Thermodynamics Part 1

Section: Physics

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Question : 45 of 100

Marks: +1, -0

A solid body of constant heat capacity 1 J/°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 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is:

ln2,ln2
None
2ln2,8ln2
ln2,4ln2

Solution:

Case (i):

\int dS = C\left[ \int\limits_{373}^{423} \frac{dT}{T} + \int\limits_{423}^{473} \frac{dT}{T} \right] = \ln\left(\frac{473}{373}\right)

Case (ii):

\int dS = C\left[ \int\limits_{373}^{385.5} \frac{dT}{T} + \int\limits_{385.5}^{398} \frac{dT}{T} + \int\limits_{398}^{410.5} \frac{dT}{T} + \int\limits_{410.5}^{423} \frac{dT}{T} + \int\limits_{423}^{435.5} \frac{dT}{T} + \int\limits_{435.5}^{448} \frac{dT}{T} + \int\limits_{448}^{460.5} \frac{dT}{T} + \int\limits_{460.5}^{473} \frac{dT}{T} \right] = \ln\left(\frac{473}{373}\right)

Note: If given temperatures are in Kelvin then answer will be option (1).

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