Joule–Thomson effect

In thermodynamics, the Joule–Thomson effect describes the temperature change of a real gas or liquid when it is expanding, typically caused by the pressure loss from flow through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. This procedure is called a throttling process or Joule–Thomson process. The effect is purely due to deviation from ideality, as any ideal gas has no JT effect.
At room temperature, all gases except hydrogen, helium, and neon cool upon expansion by the Joule–Thomson process when being throttled through an orifice; the temperature of hydrogen, helium and neon rises when they are forced through a porous plug at room temperature, but lowers when they are already at lower temperatures. The temperature at which the JT effect switches sign is the inversion temperature.
The gas-cooling throttling process is commonly exploited in refrigeration processes such as liquefiers in air separation industrial process. Most liquids such as hydraulic oils will be warmed by the Joule–Thomson throttling process. In hydraulics, the warming effect from Joule–Thomson throttling can be used to find internally leaking valves as these will produce heat which can be detected by thermocouple or thermal-imaging camera. Throttling is a fundamentally irreversible process. The throttling due to the flow resistance in supply lines, heat exchangers, regenerators, and other components of machines is a source of losses that limits their performance.
Since it is a constant-enthalpy process, it can be used to experimentally measure the lines of constant enthalpy on the diagram of a gas. Combined with the specific heat capacity at constant pressure it allows the complete measurement of the thermodynamic potential for the gas.

History

The effect is named after James Prescott Joule and William Thomson, 1st Baron Kelvin, who discovered it in 1852. It followed upon earlier work by Joule on Joule expansion, in which a gas undergoes free expansion in a vacuum and the temperature is unchanged, if the gas is ideal.

Description

The adiabatic expansion of a gas may be carried out in a number of ways. The change in temperature experienced by the gas during expansion depends not only on the initial and final pressure, but also on the manner in which the expansion is carried out.

If the expansion process is reversible, meaning that the gas is in thermodynamic equilibrium at all times, it is called an isentropic expansion. In this scenario, the gas does positive work during the expansion, and its temperature decreases.
In a free expansion, on the other hand, the gas does no work and absorbs no heat, so the internal energy is conserved. Expanded in this manner, the temperature of an ideal gas would remain constant, but the temperature of a real gas decreases, except at very high temperature.
The method of expansion discussed in this article, in which a gas or liquid at pressure P₁ flows into a region of lower pressure P₂ without significant change in kinetic energy, is called the Joule–Thomson expansion. The expansion is inherently irreversible. During this expansion, enthalpy remains unchanged. Unlike a free expansion, work is done, causing a change in internal energy. Whether the internal energy increases or decreases is determined by whether work is done on or by the fluid; that is determined by the initial and final states of the expansion and the properties of the fluid.

The temperature change produced during a Joule–Thomson expansion is quantified by the Joule–Thomson coefficient,. This coefficient may be either positive or negative ; the regions where each occurs for molecular nitrogen, N₂, are shown in the figure. Note that most conditions in the figure correspond to N₂ being a supercritical fluid, where it has some properties of a gas and some of a liquid, but can not be really described as being either. The coefficient is negative at both very high and very low temperatures; at very high pressure it is negative at all temperatures. The maximum inversion temperature occurs as zero pressure is approached. For N₂ gas at low pressures, is negative at high temperatures and positive at low temperatures. At temperatures below the gas-liquid coexistence curve, N₂ condenses to form a liquid and the coefficient again becomes negative. Thus, for N₂ gas below 621 K, a Joule–Thomson expansion can be used to cool the gas until liquid N₂ forms.

Physical mechanism

There are two factors that can change the temperature of a fluid during an adiabatic expansion: a change in internal energy or the conversion between potential and kinetic internal energy. Temperature is the measure of thermal kinetic energy, so a change in temperature indicates a change in thermal kinetic energy. The internal energy is the sum of thermal kinetic energy and thermal potential energy. Thus, even if the internal energy does not change, the temperature can change due to conversion between kinetic and potential energy; this is what happens in a free expansion and typically produces a decrease in temperature as the fluid expands. If work is done on or by the fluid as it expands, then the total internal energy changes. This is what happens in a Joule–Thomson expansion and can produce larger heating or cooling than observed in a free expansion.
In a Joule–Thomson expansion the enthalpy remains constant. The enthalpy,, is defined as
where is internal energy, is pressure, and is volume. Under the conditions of a Joule–Thomson expansion, the change in represents the work done by the fluid. If increases, with constant, then must decrease as a result of the fluid doing work on its surroundings. This produces a decrease in temperature and results in a positive Joule–Thomson coefficient. Conversely, a decrease in means that work is done on the fluid and the internal energy increases. If the increase in kinetic energy exceeds the increase in potential energy, there will be an increase in the temperature of the fluid and the Joule–Thomson coefficient will be negative.
For an ideal gas, does not change during a Joule–Thomson expansion. As a result, there is no change in internal energy; since there is also no change in thermal potential energy, there can be no change in thermal kinetic energy and, therefore, no change in temperature. In real gases, does change.
The ratio of the value of to that expected for an ideal gas at the same temperature is called the compressibility factor,. For a gas, this is typically less than unity at low temperature and greater than unity at high temperature. At low pressure, the value of always moves towards unity as a gas expands. Thus at low temperature, and will increase as the gas expands, resulting in a positive Joule–Thomson coefficient. At high temperature, and decrease as the gas expands; if the decrease is large enough, the Joule–Thomson coefficient will be negative.
For liquids, and for supercritical fluids under high pressure, increases as pressure increases. This is due to molecules being forced together, so that the volume can barely decrease due to higher pressure. Under such conditions, the Joule–Thomson coefficient is negative, as seen in the figure [|above].
The physical mechanism associated with the Joule–Thomson effect is closely related to that of a shock wave, although a shock wave differs in that the change in bulk kinetic energy of the gas flow is not negligible.

The Joule–Thomson (Kelvin) coefficient

The rate of change of temperature with respect to pressure in a Joule–Thomson process is the Joule–Thomson coefficient. This coefficient can be expressed in terms of the gas's specific volume, its heat capacity at constant pressure, and its coefficient of thermal expansion as:
See the below for the [|proof] of this relation. The value of is typically expressed in °C/bar and depends on the type of gas and on the temperature and pressure of the gas before expansion. Its pressure dependence is usually only a few percent for pressures up to 100 bar.
All real gases have an inversion point at which the value of changes sign. The temperature of this point, the Joule–Thomson inversion temperature, depends on the pressure of the gas before expansion.
In a gas expansion the pressure decreases, so the sign of is negative by definition. With that in mind, the following table explains when the Joule–Thomson effect cools or warms a real gas:

If the gas temperature is	then is	since is	thus must be	so the gas
below the inversion temperature	positive	always negative	negative	cools
above the inversion temperature	negative	always negative	positive	warms

Helium and hydrogen are two gases whose Joule–Thomson inversion temperatures at a pressure of one atmosphere are very low. Thus, helium and hydrogen warm when expanded at constant enthalpy at typical room temperatures. On the other hand, nitrogen and oxygen, the two most abundant gases in air, have inversion temperatures of 621 K and 764 K respectively: these gases can be cooled from room temperature by the Joule–Thomson effect.
For an ideal gas, is always equal to zero: ideal gases neither warm nor cool upon being expanded at constant enthalpy.

Theoretical models

For a Van der Waals gas, the coefficient iswith inversion temperature.
For the Dieterici gas, the reduced inversion temperature is, and the relation between reduced pressure and reduced inversion temperature is. This is plotted on the right. The critical point falls inside the region where the gas cools on expansion. The outside region is where the gas warms on expansion.