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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:

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$\frac{S_{1}}{S_{2}}$

$S_{1} + S_{2}$

$S_{1} \times S_{2}$

$S_{1} - S_{2}$

answer is B.

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Detailed Solution

Before,

$S_{1} = n_{1} (\frac{f R}{2}) and S_{2} = n_{2} (\frac{f R}{2})$

Gas in both parts is same. So, f is also same.

After,

$\begin{array}{l} S_{sys} = (n_{1} + n_{2}) (\frac{f R}{2}) \\ \Rightarrow S_{sys} = n_{1} (\frac{f R}{2}) + n_{2} (\frac{f R}{2}) \\ \Rightarrow S_{sys} = S_{1} + S_{2} \end{array}$

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