Perhaps the most significant thing here is that ∫ PdV is the specific work for a closed system, as in a piston and cylinder, while ∫ VdP is the specific work for an open system, as in a steam or gas turbine. There is also the relationship between these two and PV, which arises from integration by parts. An interesting fact that many engineers don't know... In a typical steam power plant with three separate machines (high pressure, intermediate pressure, and low pressure turbines), the LPT produces about 45% of the total shaft power. It's also by far the largest in size. People think that because the pressure is much higher (say 200 atm) entering the HPT and much lower (say 3 atm) entering the LPT that the HPT should put out much more power, but it doesn't. This is because steam (and gas) turbines are volumetric flow devices, described by ∫ VdP, not pistons described by ∫ PdV.

This term defines enthalpy H(s,P) and Gibbs free energy G(T,p). This second term, PdV, is defining how much, for example, free energy G will change under constant temperature T. Same for enthalpy: (dH/dp)_T = T(dS/dp)_T + V. It can be transformed into the equation for Joule-Thomson expansion for an ideal gas.

So why Gibbs free energy G(T,p) is important? From G you can get all the other potentials (S,H,U) or, for example, volume V from its p and T: V = (dG/dp)_T. The PdV part is, of course, not very important for solids and liquids.

Dear Amit Katyal :

Let me say something more mathematical about this, which is related to Maxwell's Relations in Thermodynamics

https://en.wikipedia.org/wiki/Maxwell_relations

The term PdV comes from a Thermodynamic relation where the V of the system is changed with respect to Temperature(Entropy), leaving the Entropy(Temperature) of the system fixed.

And the term VdP is the other way around. It comes from changing the Pressure of the system maintaining the Temperature (or Entropy) of the system fixed.

See Maxwell's Relations of Thermodynamics.

Regards ! :)

Perhaps the most significant thing here is that ∫ PdV is the specific work for a closed system, as in a piston and cylinder, while ∫ VdP is the specific work for an open system, as in a steam or gas turbine. There is also the relationship between these two and PV, which arises from integration by parts. An interesting fact that many engineers don't know... In a typical steam power plant with three separate machines (high pressure, intermediate pressure, and low pressure turbines), the LPT produces about 45% of the total shaft power. It's also by far the largest in size. People think that because the pressure is much higher (say 200 atm) entering the HPT and much lower (say 3 atm) entering the LPT that the HPT should put out much more power, but it doesn't. This is because steam (and gas) turbines are volumetric flow devices, described by ∫ VdP, not pistons described by ∫ PdV.

Dudley J Benton , sir, your answer is direct to the point, and answer the question completely, I liked.

Regards to all !