The Joule and Joule–Thomson Experiments

In the Joule-Thomson experiment, gas expands through a porous plug in an adiabatic system with no heat transfer. The left piston performs work p₁V₁ on the gas while the gas does work p₂V₂ on the right piston. Since q = 0, the change in internal energy equals net work: ΔU = p₁V₁ - p₂V₂. Rearranging gives U₁ + p₁V₁ = U₂ + p₂V₂, which means H₁ = H₂, making the process isenthalpic.

The Joule-Thomson coefficient (μ) is an intensive property that measures the rate at which temperature changes with pressure at constant enthalpy. It can be expressed as the negative of the change in enthalpy with pressure at constant temperature, divided by heat capacity at constant pressure. The coefficient depends on temperature, pressure, and gas type, determining whether a gas cools or warms during isenthalpic expansion.

For ideal gases, the Joule-Thomson coefficient equals zero, so temperature remains unchanged during expansion. Real gases have non-zero coefficients that can be positive or negative. A negative coefficient means temperature rises as pressure decreases (heating upon expansion), while a positive coefficient means temperature falls as pressure decreases (cooling upon expansion).

Inversion temperature is the specific temperature at which the Joule-Thomson coefficient changes sign from negative to positive. Below this temperature, a gas cools during isenthalpic expansion. Above it, the gas warms. To liquefy gases using the Joule-Thomson method, the gas must be cooled below its inversion temperature first.

The porous plug is a rigid barrier that forces gas to flow from the high-pressure region (chamber A at p₁) to the low-pressure region (chamber B at p₂). The significant pressure drop occurs across the plug itself as gas molecules navigate through its narrow passages. A piston on the right maintains the constant lower pressure p₂, while the left piston applies pressure p₁.

Although enthalpy remains constant (ΔH = 0) during the isenthalpic process, internal energy changes. The change in internal energy equals the net work done: ΔU = p₁V₁ - p₂V₂. Since enthalpy is defined as H = U + pV, the constant enthalpy condition ensures that any increase in volume work is offset by changes in internal energy and pressure-volume product.

In Joule-Thomson liquefaction, the porous plug is replaced with a narrow opening or needle valve to produce the required pressure drop. The gas must first be cooled below its inversion temperature. An alternative method uses nearly reversible adiabatic expansion against a piston, which achieves cooling through work done by the gas rather than through a pressure drop alone.