# Irreversible work

I'm having some trouble trying to find the irreversible work done by a perfect gas when expanding. I know that the reversible work is greater than the irreversible one, but how can I find the irreversible work for an isothermal process?

The exercise asks me to find the irreversible work for the expansion of a perfect gas from 10000 to 2000 bar at 315 K with $T_{cte}$. I also found that the irreversible work is simply $P\Delta V$, and even though the volume does vary, the exercise also tells me the pressure does too. I found the volumes for each state and got $V_1=2.619*10^{-3}L$ and $V_2=0.013095 L$. But now I'm not sure what pressure I should use? Or why should I just use one pressure. Thanks in advance.

Also, is the irreversible work for a gas the same independently of the process? Is it the same for an isothermal, an adiabatic and isobaric process? Or just like the reversible work, does it change?

The expansion takes place when the pressure is changed suddenly and drastically modifying the initial equilibrium state, remember that at difference of the reversible case the pressure is not changed infinitesimally. So in the formula $P \Delta V$ use the final pressure.