[Elianna]

Are the Gibbs and Helmholtz free energy both equal to 0 when the process is irreversible? such as a sudden expansion or compression?

[mjc123]

No. Why should they be? and why should they be equal?
G and A are state functions; ΔG and ΔA depend only on the initial and final states, not on the route between them, whether reversible or irreversible.

[Elianna]

Thank you.
I asked because I cannot figure out a homework problem that i have already tried a bunch of times and I cannot figure out the direction.
this is it:

6 mol of an ideal gas is confined in a closed system and is in thermal contact with the environment (isothermal) and in a mechanical equilibrium with external pressure. The gas is suddenly compressed to a final volume. The final external pressure is 2 times greater than the initial pressure (and is equal to the final pressure prevailing in the system). calculate the change in the Helmholtz free energy as a result of the this process. Given that the environment is at 10 degrees Celsius.

can I say the dA=-Pdv? which in this case would be A=p2v2=nRT?

[mjc123]

No.
The change is isothermal (that is, initial and final T are the same, so the change in state functions is equal to that of an equilibrium isothermal process).
T does not change. So what is ΔU?
In an isothermal process, what is Δ(PV)? so what is ΔH?
What is ΔS for an isothermal volume change?
So what are ΔA and ΔG?