Question

why is it that when you use an expression for work you don't use the -VdP but when you use an expression for dH you use PdV and VdP in it?

Answer 1

Work is given by -PdV.

It clearly means that when volume of the system changes, work is done either on the system or by the system depending upon volume change.

So, pressure change term -VdP is not included because it is indicating a constant volume.

But in case of enthalpy,

H = U + PV

So, for enthalpy change we can write

dH = dU + PdV + VdP

Because enthalpy change is the sum of all energy changes in the system that includes internal energy, P-V work and effect of pressure change.