Consider two vessels A and B which are connected to each other by a pipe and a valve.
Vessel A is initially filled with a fluid at a certain pressure and B is completely evacuated.
By opening the valve, the fluid in the vessel A will expand until it fills both vessels.
This process is known as free or unresisted expansion. It is an irreversible process
because it needs external work to be done to
restore the fluid to its initial condition. Consider a system, consisting of both vessels
which is perfectly thermally insulated. Apply the first law of thermodynamics to the
system, i.e.
Q + W = U2 - U1
where indices 1 and 2 represent initial and final states. Q = 0, because the thermal insulation will not allow any heat transfer between the system and the
surroundings. W=0 because the boundaries of the system are not moved. The result will then be:
