2.6
The Joule and Joule–Thomson Experiments
Consider an adiabatic system composed of two chambers, A and B, designed such that no heat flows into or out of the system. Initially, chamber A is fi…
Consider an adiabatic system, where chamber A is filled with a gas at a fixed temperature, pressure, and volume, while chamber B is empty.
When the gas is forced through a rigid porous barrier from the high-pressure region in A to the low-pressure region in B, the gas expands, changing its volume and temperature, and, as a result, its internal energy.
Because no heat is transferred, the internal energy change equals the difference between work done on and by the gas.
Rearranging the terms and replacing the sum U + pV with enthalpy shows this process to be isenthalpic.
Whether the gas cools or warms during this expansion depends on the Joule–Thomson coefficient, 𝜇. It is defined as the rate at which temperature changes with pressure at constant enthalpy.
It can also be written as the negative of the change in enthalpy with pressure at constant temperature, divided by the heat capacity at constant pressure.
For ideal gases, μ equals zero, so expansion causes no temperature change. But for real gases, 𝜇 can be positive or negative, implying cooling or heating during expansion.
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Q1: Why does the Joule-Thomson experiment produce an isenthalpic process?
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.
Q2: What is the Joule-Thomson coefficient and how is it defined?
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.
Q3: How do ideal and real gases differ in their response to Joule-Thomson 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).
Q4: What is inversion temperature in the Joule-Thomson process?
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.
Q5: How does the porous plug create a pressure drop in the Joule-Thomson experiment?
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.
Q6: What happens to internal energy and enthalpy during gas expansion through the porous plug?
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.
Q7: How is the Joule-Thomson method used for gas liquefaction?
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.