An ideal gas, consisting of n moles, undergoes an irreversible process in which the temperature has the same value at the beginning and end. If the volume changes from Vi to Vf, the change in entropy is given by:

ΔS = nR(In (Vf/Vi))

Explanation:

We are told the temperature has the same value and therefore it's constant.

Formula for change in entropy isothermally is;

ΔS = nR(In (V2/V1))

V2 is final volume and V1 is initial volume.

We are told that the volume changes from Vi to Vf.

Thus, V2 = Vf and V1 = Vi

Hence;

ΔS = nR(In (Vf/Vi))

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