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. $\frac{S_1}{S_2}$

Answer 1

The correct option is A $S_1+S_2$

Before removal of piston:

For part $1$, $S_1=\frac{n_{1}fR}{2}$

For part $2$, $S_2=\frac{n_{2}fR}{2}$

After removal of piston:

Gas is identical, so $f$ will be the same.

$S=\frac{(n_1+n_2)fR}{2}$

$\Rightarrow S=S_1+S_2$

Hence, option $\left(A\right)$ is the correct answer.