Exact vs. Inexact Differentials

The power, or rate at which work is done, is the time derivative of work, dW / dt.


You should recall, from the previous chapter, that enthalpy is a property or state variable and its differential is therefore exact: dH. The process path that connects states 1 and 2 in no way affects the enthalpy change from state 1 to state 2.


In this lesson, we have learned that


is a

path variable

and its differential is


. We cannot evaluate


without knowing exactly how P and V changed during the process so that we can evaluate the area under the process path on the P-V Diagram.
The integral of dH is delta H.
The integral of dW from state 1 to state 2 is W12.
A PV diagram showing states 1 and 2 with no path shown because the change in enthalpy does NOT depend on the process path taken from the initial to the final state.
PV diagram that shows that the magnitude of work is the area under the process path between states 1 and 2.
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Ch 4, Lesson A, Page 12 - Exact vs. Inexact Differentials