Process function

Remarks

The work done on a gas is a process function. For a quasistatic process $\gamma$ in the $(p, V)$ plane, the work done on the gas is $W(\gamma) = -\int_\gamma p \, dV$. Take the states $A = (p_1, V_1)$ and $B = (p_2, V_2)$ with $p_1 < p_2$ and $V_1 < V_2$. The path that first expands at pressure $p_1$ and then raises the pressure gives $W = -p_1 (V_2 - V_1)$. The path that first raises the pressure and then expands gives $W = -p_2 (V_2 - V_1)$, which is different. Heat is also a process function. The change of internal energy is not a process function in this sense, because it equals $U(B) - U(A)$. Infinitesimal process functions are written $\delta W$ and $\delta Q$ to show that they are inexact differentials.