Let $P_0$ be the ambient pressure, $V_1$ and $V_0$ be the initial and final volumes of the system respectively.

If in a process, the system comes into equilibrium with the surroundings, the work done in pushing back the ambient atmosphere is $P_0(V_0-V_1)$.

$Availability = W_{useful} = W_{max} - P_0(V_0-V_1)$

Consider a system which interacts with the ambient at $T_0$. Then,

$W_{max} = (U_1 - U_0) - T_0(S_1 - S_0)$

$Availability = W_{useful} = W_{max} - P_0(V_0-V_1)$

$= (U_1 - T_0S_1) - (U_0 - T_0S_0) - P_0(V_0 - V_1)$

$= (U_1 + P_0V_1 - T_0 S_1) - (U_0 + P_0V_0 - T_0S_0)$

$ = f_1 - f_0$

Where, $f = U + P_0V - T_0S$ is called the availability function for the non-flow process. Thus, the availability: $f_1 - f_0$

If a system undergoes a change of state from the initial state 1 (where the availability is $(f_1 - f_0)$) to the final state 2 (where the availability is $(f_2 - f_0)$), the change in the availability or the change in maximum useful work associated with the process, is $f_1 - f_2$.