Fill Vacuum
The above left is a thermal insulating box separated by a divider, with one part filled with ideal gas and the other vacuum. Now, as in the above right, we remove the divider so that the ideal gas fills the whole box uniformly. Which of the following is NOT correct?
a) The temperatures of [A] and [B] are the same.
b) The internal energies of [A] and [B] are the same.
c) The entropy of the gas of [A] is larger than that of [B].
d) The change from [A] to [B] is an irreversible process.
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Since the whole system is an isolated system covered by a thermal insulator, so the temp. T and internal energy U remain the same in both A and B . Also, the change from A to B is an irreversible process as once the gas is uniformly filled in the box on removing the panel in A , it is impossible to shift all the gas molecules to one side and make the other part vacuum like before without disturbing the system but this would cause the system to become non-isolated.
However, the entropy in B is greater than that in A . We can define entropy as the degree of randomness of a system, or in other words, the volume available for the isolated system where the system shows randomness in movement of particles in the system. In case B , we can see that gas gets more volume to expand but the mass of the gas remains same and so the gas molecules are now more loosely packed and the degree of randomness in the system is now more in B than in A .
So, the incorrect statement is -- (c) The entropy of the gas of [A] is larger than that of [B].