Question

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $S_1$ and that of the other part is $S_2$. Given that $S_1>S_2$. If the piston is removed then the total entropy of the system will be:

• A. $S_1+S_2$
• B. $S_1-S_2$
• C. $S_1\times S_2$
• D. $\raisebox{1ex}{$S_1$}\!\left/ \!\raisebox{-1ex}{$S_2$}\right.$

Answer 1

The correct option is A

$S_1+S_2$

Step1: Given data.

Entropy of one part$=S_1$

Entropy of the other part$=S_2$

And $S_1>S_2$

Step2: Finding the total entropy of the system.

• We know that, entropy is an extensive property.
• After removing the partition of the system, the gas will be mixed and the total entropy is simply additive.
• Therefore, total entropy of the system: $S_{total}=S_1+S_2$

Hence, option A is correct.