Enthalpy (H) – William Thomson and others
Internal energy U is the natural property for analyzing closed, non-flowing systems — a gas inside a piston-in-cylinder assembly, a bomb calorimeter, a sealed batch reactor. In each case the system boundary is fixed or moves only mechanically, and U captures everything we need.
But U alone is insufficient for flowing systems, where material crosses boundaries under pressure and carries energy with it. When a fluid flows from one region to another, pressure forces do work on it — pushing it in from upstream and being pushed back by it downstream. This flow work, equal to PV at each boundary, must be accounted for alongside U. In a non-flowing system this bookkeeping isn’t needed. In a flowing system it is essential.
The need for a new property became clear when James Joule and William Thomson performed one of the more fascinating experiments in the history of thermodynamics. They forced a gas through a porous plug — a flow resistance — under adiabatic conditions and measured a temperature change on the downstream side. The result surprised many. To understand it, Thomson and others applied the First Law.
For an adiabatic process (Q = 0) with no shaft work, meaning no work done by mechanically rotating a shaft inside a pump, turbine, or compressor, for example, the only work terms are the flow work done on the system upstream (P₁V₁) and the flow work done by the system downstream (P₂V₂):
ΔU = U₂ − U₁ = P₁V₁ − P₂V₂
Rearranging:
U₁ + P₁V₁ = U₂ + P₂V₂
The quantity U + PV is conserved across the plug. This combination was given the name enthalpy:
H = U + PV
H₁ = H₂
ΔH = 0 for adiabatic, isenthalpic fluid flow — meaning no heat transfer and no shaft work beyond the flow work itself.
Just as U is the conserved property of choice for non-flowing systems, H becomes the conserved property of choice for flowing systems. Enthalpy wasn’t invented arbitrarily. It was constructed to solve a specific physical problem: how to account for both the internal energy of a flowing fluid and the work required to push it downstream. H = U + PV does exactly that — and nothing more.
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