This question stems from the online thermodynamics notes provided by web.mit.edu. I'm having some trouble understanding the example given of air expanding into a vacuum.
Consider the transient, unsteady process of filling a tank, initially evacuated, from a surrounding atmosphere, which is at pressure $P_0$ and temperature $T_0$. The tank is insulated, so the process is adiabatic.
The author of the notes states that work of magnitude $P_0V_0$ is done on the system. However, I thought that because the pressure in the tank is zero, the work done ($PdV$) would be zero.
Why is it the case that the work done on the system is $P_0V_0$ and not zero?