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Since conduction across a finite temperature difference will produce entropy, will work done due to pressure difference generates entropy because system tends towards mechanical equilibrium which indicates a spontaneous process.

Unlike VdP work, PdV work does not generate entropy (reversible) since it is in mechanical equilibrium as there is no pressure difference. For instance a system with oscillating boundary.

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  • $\begingroup$ Pressure work by a piston against a constant external pressure is not reversible. $\endgroup$
    – Buck Thorn
    Oct 26, 2022 at 12:15
  • $\begingroup$ VdP work doesn't need to generate entropy. It can happen reversibly. $\endgroup$
    – Curt F.
    Oct 31, 2022 at 3:17

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Yes, you describe one of many sources of "friction"

Friction is any irreversible process.

Friction generally takes on three forms: "Dry" friction applies an (approximately) constant force regardless of velocity. Mechanical parts directly rubbing against each-other.

"Resistor" friction acts in proportional to velocity (or electric current). Such as sliding machinery lubricated by an oil film, a mammoth getting stuck in a tar pit, or electrical resistance in a wire. Heat transfer over a finite temperature is another example, but instead of energy lost to heat free energy is lost.

"Snow plough" friction is proportional to velocity squared. Energy is lost in pushing the mass of fluid out of your way high speed. The swirling masses left in your wake later dissipate energy as heat.

How your vdP example dissipates energy.

Mechanical friction in a piston means that we have to apply an extra dP to get/keep it moving, overcoming "dry" and/or "resistor" friction depending on oil levels. VdP is lost to heat at the seal. If the piston is expanding, the heat from the seal can recover some of this energy as work in expansion, but there is still a net loss.

Gas speed of sound if the piston expands very fast (such as half the speed of sound), the gas pressure will be lower at the piston head and less work is done. Conversely, more work would be needed for compression. In this case dP is the pressure difference between the head pressure and the ideal head pressure. VdP is lost to heat in the gas, cooling it off less upon expansion and heating it up more upon compression. This is a form of "snow-plough" friction, although it is complicated by transonic effects.

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VdP describes the shaft work done in a continuous flow process for an open system if the process is occurring isentropically (i.e. reversibly). PdV describes the P-V work occurring in a closed system process, and, if this process is reversible, P can be determined from the equation of state of the fluid; otherwise, P must be specified by way of external constraints.

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