Problem 6. A vessel has two identical compartments (e.g. left and right), but ga

Question

Problem 6. A vessel has two identical compartments (e.g. left and right), but gas molecules can go from each compartment into the other.

(a) Initially there are 12 molecules in the left compartment and 0 molecules in the right compartment. Finally there are 6 molecules in the left compartment and 6 molecules in the right compartment. What happens with the total entropy of the gas in such a process?

(b) Is it possible that the gas can go spontaneously from 6 molecules in the left compartment, 6 molecules in the right compartment to 12 molecules in the left compartment, 0 molecules in the right compartment?

Explanation / Answer

(A) As the molecules move from one compartment to other compartment the total disorder has increased. So the entropy increases.

(B) Gas molecules can not move spontaneously 6 molecules in left compartment, 6 molecules in right compartment to 12 molecules in left compartment. The entropy change for such a process will be negative i.e. entropy decreases. So to make this process happen we must supply energy.

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