A rigid container is divided into two compartments of equal volume by a partition. one compartment contains 1 mole of ideal gas a at 1 atm, and the other contains 1 mole of ideal gas b at 1 atm. calculate the increase in entropy which occurs when the partition between

The volume of compartment is equal. One compartment has 1 mole of ideal gas a at pressure 1 atm and other compartment have 1 mole of ideal gas b at pressure 1 atm.

If the partition between the compartment is removed, the volume of gas a with 1 mole become twice of its initial value. Similarly, volume of gas b with 1 mole doubles.

Change in entropy is calculated as follows:

For gas a, / Delta S_{a}=Rln/frac{V_{2}}{V_{1}}

Since, V_{2}=2V_{1}

Thus,

/Delta S_{a}=Rln/frac{2V_{1}}{V_{1}}=Rln2

Similarly, change in entropy for gas b will be / Delta S_{b}=Rln2

Total entropy will be:

/Delta S_{a}+/Delta S_{b}=Rln2+Rln2=Rln4