Joule Thomson Effect

The Joule-Thomson effect, also known as the Joule-Kelvin effect, refers to the change in temperature that occurs as a fluid flows from a region of higher pressure to a region of lower pressure. The Joule-Thomson effect can be described using the Joule-Thomson coefficient. In addition, at constant enthalpy, the Joule-Thomson coefficient is the partial pressure derivative with respect to temperature.

The Joule-Thomson coefficient would change with temperature and pressure. Furthermore, the Joule-Thomson coefficient varies from fluid to fluid. In addition, the inversion curve is the curve described by the Joule-Thomson coefficient equaling zero as a function of temperature and pressure.

Joule-Thomson Equation

The Joule Thomson effect formula can be found below:

μJT = (∂T/∂P)H

The μJT would be negative for a gas temperature above the inversion temperature. In this case, the ∂P must always be negative, implying ∂ that the must be positive. As a result, the gas will start to warm up.

Physical Mechanism

During an adiabatic expansion, two factors can cause a fluid’s temperature to change: a change in internal energy or a conversion between potential and kinetic internal energy. Because temperature is a measure of thermal kinetic energy (the energy associated with molecular motion), any change in temperature indicates a change in thermal kinetic energy. Internal energy is calculated as the sum of thermal kinetic energy and thermal potential energy. Even if the internal energy does not change, the temperature can change due to the conversion of kinetic and potential energy; this is what happens in a free expansion and usually results in a decrease in temperature as the fluid expands.

If the fluid does work on or by itself as it expands, the total internal energy changes. This is what happens in a Joule–Thomson expansion, and it can result in more heating or cooling than a free expansion.

The enthalpy remains constant in a Joule–Thomson expansion. The enthalpy, H, is defined as follows:

H=U+PV

where U denotes internal energy, P denotes pressure, and V denotes volume The change in PV represents the work done by the fluid under the conditions of a Joule–Thomson expansion . If PV rises while H remains constant, U must fall as a result of the fluid doing work on its surroundings. This results in a decrease in temperature and a positive Joule–Thomson coefficient.

Joule–Thomson coefficient

It is difficult to imagine what the physical representation of the Joule–Thomson coefficient, μJT, is. Furthermore, modern μJT determinations avoid the original method used by Joule and Thomson. Measuring is done with a different, closely related quantity.

The Joule–Thomson coefficient involves three variables: T, P, and H. Furthermore, by applying the cyclic rule, one can obtain a useful result immediately. Furthermore, the rule can be written in terms of these three variables as follows:

(∂T/∂P)H(∂H/∂T)P(∂P/∂H)T = −1

Each of the three partial derivatives in this expression has its own meaning. The first is μJT, and the second is Cp, or constant pressure heat capacity.

Cp = (∂H/∂T)P

third partial derivative being the inverse of  isothermal Joule–Thomson coefficient, μT:

μT = (∂H/∂P)T

Joule–Thomson Effect uses

Because of the cooling produced by the Joule–Thomson expansion, it is a useful tool in refrigeration. The effect is used in the Linde technique, which is a standard process in the petrochemical industry to liquefy gases, as well as in many cryogenic applications (e.g. for the production of liquid oxygen, nitrogen, and argon). To be liquefied by the Linde cycle, a gas must be below its inversion temperature. As a result, simple Linde cycle liquefiers that start at room temperature cannot liquefy helium, hydrogen, or neon. The Joule–Thomson effect, on the other hand, can be used to liquefy even helium if the helium gas is first cooled below its inversion temperature of 40 K.

Conclusion

The physical mechanism underlying the Joule–Thomson effect is similar to that of a shock wave, with the exception that the change in bulk kinetic energy of the gas flow is not negligible. In practice, the Joule–Thomson effect is achieved by allowing the gas to expand through a throttling device (typically a valve) that must be extremely well insulated to prevent any heat transfer to or from the gas. During the expansion, no external work is extracted from the gas.