Joule-Thomson effect

The Joule-Thomson effect or Joule-Kelvin effect describes the increase or decrease in the temperature of a real gas (as differentiated from an ideal gas) or a liquid when allowed to expand freely through a valve or other throttling device while kept insulated so that no heat is transferred to or from the fluid, and no external mechanical work is extracted from the fluid. The Joule-Thomson effect is an isenthalpic process, meaning that the enthalpy of the fluid is constant (i.e., does not change) during the process.

It is named for James Prescott Joule and William Thomson, 1st Baron Kelvin who established the effect in 1852, following earlier work by Joule on Joule expansion in which a gas expands at constant internal energy. The Joule-Thomson effect is sometimes referred to as the Joule-Kelvin effect. Engineers often refer to it as simply the J-T effect.

There is no temperature change when an ideal gas is allowed to expand through an insulated throttling device. In other words, the J-T effect does not apply for ideal gases.

Joule-Thomson inversion temperature

Isentropic expansion (meaning an expansion at constant entropy) — in which a gas does positive work in the process of expansion — always causes a decrease in the gas temperature. For example, when gas is expanded through an expansion turbine (also known as a turboexpander), the temperature of the gas always decreases.

However, when a real gas (as differentiated from an ideal gas) expands through a throttling device, the temperature may either decrease or increase, depending on the initial temperature and pressure. For any given pressure, real gases have a Joule-Thomson inversion temperature, above which the J-T expansion causes the temperature to rise, and below which the J-T expansion causes cooling. For most gases at atmospheric pressure, the inversion temperature is fairly high (above room temperature), and so most gases at those temperature and pressure conditions are cooled by the J-T expansion.

The Joule-Thomson coefficient

The change of temperature (T ) with a decrease of pressure (P ) at constant enthalpy (H ) in a Joule-Thomson process is the Joule-Thomson coefficient denoted as $\mu _{JT}$ and may be expressed as:

$\mu _{JT}=\left({\partial T \over \partial P}\right)_{H}$

The value of $\mu _{JT}$ is typically expressed in K/Pa or °C/bar and depends on the specific gas, as well as the temperature and pressure of the gas before expansion.

For all real gases, it will equal zero at some point called the inversion point and, as explained above, the Joule-Thomson inversion temperature is the temperature where the coefficient changes sign (i.e., where the coefficient equals zero). The Joule-Thomson inversion temperature depends on the pressure of the gas before expansion.

In any gas expansion, the gas pressure decreases and thus the sign of $\scriptstyle \partial P$ is always negative. With that in mind, the following table explains when the Joule-Thomson effect cools or heats a real gas:

If the gas temperature is	then $\mu _{JT}$ is	since $\scriptstyle \partial P$ is	thus $\scriptstyle \partial T$ must be	so the gas
below the inversion temperature	positive	always negative	negative	cools
above the inversion temperature	negative	always negative	positive	heats

For some gases, the Joule-Thomson inversion temperatures at 1 atm are very low: for helium, about 51 K (−222 °C), and for hydrogen, about 202 K (-71 °C). Thus, helium and hydrogen will warm during a J-T expansion at typical room temperatures. On the other hand, nitrogen has an inversion temperature of 621 K (348 °C) and oxygen has an inversion temperature of 764 K (491 °C). Hence, the two most abundant gases in air can be cooled by a J-T expansion at typical room temperatures.

It should be noted that $\mu _{JT}$ is always equal to zero for ideal gases. In other words, they will neither heat nor cool during an expansion through an insulated throttling device.

Applications

In practice, the Joule-Thomson effect is achieved by allowing the gas to expand through a throttling device (usually a valve) which must be very well insulated to prevent any heat transfer to or from the gas. External work must not be extracted from the gas during the expansion (meaning that the gas must not be expanded through a turboexpander).

The effect is applied in the Linde cycle, a process used in the petrochemical industry for example, where the cooling effect is used to liquefy gases, and also in many cryogenic applications (e.g., for the production of liquid oxygen, nitrogen and argon). Only when the Joule-Thomson coefficient for the given gas at the given temperature is greater than zero can the gas be liquefied at that temperature by the Linde cycle. In other words, a gas must be below its inversion temperature to be liquefied by the Linde cycle. For this reason, a simple Linde cycle cannot normally be used to liquefy helium, hydrogen and neon.