Calculate the change in the entropies of the system and the surroundings, and the total change in entropy, when a sample of nitrogen gas of mass 14 g at 298 k and 1.00 bar doubles its volume in (a) an isothermal reversible expansion, (b) an isothermal irreversible expansion against pex = 0, and (c) an adiabatic reversible expansion.

Our values are:

a) For isothermal reversible expansion, We have that the change in the Internal Energy is 0, that is,

We can solve for the Work made in the system.

With work made it, this same quantity is necessary to add to the system through Heat. Then,

For Surrounding we apply the same relation,

Therefore,

b) For an isothermal irreversible expansion

We consider the external presion as 0, by this way, the work done is also 0.

Since isothermal irreversible expansion change in Internal Energy is 0, so

, since isothermal

Therefore

How the condition are the same, for the System the entropy is the same

But

c) And an adiabatic reversible expansion

Since the process is Adiabatic,

Therefore,

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explanation: