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thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
, the Joule–Thomson effect (also known as the Joule–Kelvin effect or Kelvin–Joule effect) describes the temperature change of a ''real'' gas or
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...
(as differentiated from an ideal gas) when it is forced through a
valve A valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fitting ...
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''. At room temperature, all gases except
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
,
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
, and
neon Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypt ...
cool upon expansion by the Joule–Thomson process when being
throttle A throttle is the mechanism by which fluid flow is managed by constriction or obstruction. An engine's power can be increased or decreased by the restriction of inlet gases (by the use of a throttle), but usually decreased. The term ''throttle' ...
d through an orifice; these three gases experience the same effect but only at lower temperatures. Most liquids such as hydraulic oils will be warmed by the Joule–Thomson throttling process. The gas-cooling throttling process is commonly exploited in refrigeration processes such as liquefiers in
air separation An air separation plant separates atmospheric air into its primary components, typically nitrogen and oxygen, and sometimes also argon and other rare inert gases. The most common method for air separation is fractional distillation. Cryogenic a ...
industrial 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 A thermocouple, also known as a "thermoelectrical thermometer", is an electrical device consisting of two dissimilar electrical conductors forming an electrical junction. A thermocouple produces a temperature-dependent voltage as a result of th ...
or thermal-imaging camera. Throttling is a fundamentally
irreversible process In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ...
. The throttling due to the flow resistance in supply lines, heat exchangers, regenerators, and other components of (thermal) machines is a source of losses that limits their performance.


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 A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often ...
and the temperature is unchanged, if the gas is
ideal Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered ...
.


Description

The '' adiabatic'' (no heat exchanged) 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 Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
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 ''P''1 flows into a region of lower pressure ''P''2 without significant change in kinetic energy, is called the Joule–Thomson expansion. The expansion is inherently irreversible. During this expansion,
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
remains unchanged (see proof below). 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, \mu_. This coefficient may be either positive (corresponding to cooling) or negative (heating); 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 A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point (chemistry), critical point, where distinct liquid and gas phases do not exist, but below the pressure required to compress it into a solid. It ca ...
, 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 (621 K for N2) occurs as zero pressure is approached. For N2 gas at low pressures, \mu_ 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 Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
is the measure of thermal kinetic energy (energy associated with molecular motion); 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.Pippard, A. B. (1957). "Elements of Classical Thermodynamics", p. 73. Cambridge University Press, Cambridge, U.K. 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, H, is defined as :H = U + PV where U is internal energy, P is pressure, and V is volume. Under the conditions of a Joule–Thomson expansion, the change in PV represents the work done by the fluid (see the proof below). If PV increases, with H constant, then U 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 PV 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, PV 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, PV does change. The ratio of the value of PV to that expected for an ideal gas at the same temperature is called the
compressibility factor In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas ...
, Z. For a gas, this is typically less than unity at low temperature and greater than unity at high temperature (see the discussion in
compressibility factor In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas ...
). At low pressure, the value of Z always moves towards unity as a gas expands.Atkins, Peter (1997). ''Physical Chemistry'' (6th ed.). New York: W.H. Freeman and Co. pp. 31–32. . Thus at low temperature, Z and PV will increase as the gas expands, resulting in a positive Joule–Thomson coefficient. At high temperature, Z and PV 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, PV 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 In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
, 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 T with respect to pressure P in a Joule–Thomson process (that is, at constant enthalpy H) is the ''Joule–Thomson (Kelvin) coefficient'' \mu_. This coefficient can be expressed in terms of the gas's volume V, its heat capacity at constant pressure C_, and its coefficient of thermal expansion \alpha as: :\mu_ = \left( \right)_H = \frac V (\alpha T - 1)\, See the below for the proof of this relation. The value of \mu_ is typically expressed in °C/
bar Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar * Chocolate bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a layer of cloud * Bar ( ...
(SI units: K/ Pa) 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 \mu_ 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 \partial P is negative by definition. With that in mind, the following table explains when the Joule–Thomson effect cools or warms a real gas:
Helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
and
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
are two gases whose Joule–Thomson inversion temperatures at a pressure of one
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...
are very low (e.g., about 45 K, −228 °C for helium). Thus, helium and hydrogen warm when expanded at constant enthalpy at typical room temperatures. On the other hand,
nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
and
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
, the two most abundant gases in air, have inversion temperatures of 621 K (348 °C) and 764 K (491 °C) respectively: these gases can be cooled from room temperature by the Joule–Thomson effect. For an ideal gas, \mu_\text is always equal to zero: ideal gases neither warm nor cool upon being expanded at constant enthalpy.


Applications

In practice, the Joule–Thomson effect is achieved by allowing the gas to expand through a throttling device (usually a
valve A valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fitting ...
) which must be very well insulated to prevent any heat transfer to or from the gas. No external work is extracted from the gas during the expansion (the gas must not be expanded through a
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating ...
, for example). The cooling produced in the Joule–Thomson expansion makes it a valuable tool in refrigeration. The effect is applied in the Linde technique as a standard process in the
petrochemical industry The petrochemical industry is concerned with the production and trade of petrochemicals. A major part is constituted by the plastics (polymer) industry. It directly interfaces with the petroleum industry, especially the downstream sector. Comp ...
, where the cooling effect is used to liquefy gases, and also in many
cryogenic In physics, cryogenics is the production and behaviour of materials at very low temperatures. The 13th IIR International Congress of Refrigeration (held in Washington DC in 1971) endorsed a universal definition of “cryogenics” and “cr ...
applications (e.g. for the production of liquid oxygen, nitrogen, and
argon Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice a ...
). A gas must be below its inversion temperature to be liquefied by the Linde cycle. For this reason, simple Linde cycle liquefiers, starting from ambient temperature, cannot be used to liquefy helium, hydrogen, or
neon Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypt ...
. However, the Joule–Thomson effect can be used to liquefy even helium, provided that the helium gas is first cooled below its inversion temperature of 40 K.


Proof that the specific enthalpy remains constant

In thermodynamics so-called "specific" quantities are quantities per unit mass (kg) and are denoted by lower-case characters. So ''h'', ''u'', and ''v'' are the specific enthalpy, specific internal energy, and specific volume (volume per unit mass, or reciprocal density), respectively. In a Joule–Thomson process the specific
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
''h'' remains constant. To prove this, the first step is to compute the net work done when a mass ''m'' of the gas moves through the plug. This amount of gas has a volume of ''V''1 = ''m'' ''v''1 in the region at pressure ''P''1 (region 1) and a volume ''V''2 = ''m'' ''v''2 when in the region at pressure ''P''2 (region 2). Then in region 1, the "flow work" done ''on'' the amount of gas by the rest of the gas is: W1 = ''m'' ''P''1''v''1. In region 2, the work done ''by'' the amount of gas on the rest of the gas is: W2 = ''m'' ''P''2''v''2. So, the total work done ''on'' the mass ''m'' of gas is :W = mP_1 v_1 - mP_2 v_2. The change in internal energy minus the total work done ''on'' the amount of gas is, by the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant am ...
, the total heat supplied to the amount of gas. : U - W = Q In the Joule–Thomson process, the gas is insulated, so no heat is absorbed. This means that :\begin (mu_2 - mu_1) &- (mP_1 v_1 - mP_2 v_2) = 0 \\ mu_1 + mP_1 v_1 &= mu_2 + mP_2 v_2 \\ u_1 + P_1 v_1 &= u_2 + P_2 v_2 \end where ''u''1 and ''u''2 denote the specific internal energies of the gas in regions 1 and 2, respectively. Using the definition of the specific enthalpy ''h = u + Pv'', the above equation implies that :h_1 = h_2 where h1 and ''h''2 denote the specific enthalpies of the amount of gas in regions 1 and 2, respectively.


Throttling in the ''T''-''s'' diagram

A very convenient way to get a quantitative understanding of the throttling process is by using diagrams such as ''h''-''T'' diagrams, ''h''-''P'' diagrams, and others. Commonly used are the so-called ''T''-''s'' diagrams. Figure 2 shows the ''T''-''s'' diagram of nitrogen as an example. Various points are indicated as follows: As shown before, throttling keeps ''h'' constant. E.g. throttling from 200 bar and 300K (point a in fig. 2) follows the isenthalpic (line of constant specific enthalpy) of 430kJ/kg. At 1 bar it results in point b which has a temperature of 270K. So throttling from 200 bar to 1 bar gives a cooling from room temperature to below the freezing point of water. Throttling from 200 bar and an initial temperature of 133K (point c in fig. 2) to 1 bar results in point d, which is in the two-phase region of nitrogen at a temperature of 77.2K. Since the enthalpy is an extensive parameter the enthalpy in d (''h''d) is equal to the enthalpy in e (''h''e) multiplied with the mass fraction of the liquid in d (''x''d) plus the enthalpy in f (''h''f) multiplied with the mass fraction of the gas in d (1 − ''x''d). So :h_d = x_d h_e + (1 - x_d) h_f. With numbers: 150 = ''x''d 28 + (1 − ''x''d) 230 so ''x''d is about 0.40. This means that the mass fraction of the liquid in the liquid–gas mixture leaving the throttling valve is 40%.


Derivation of the Joule–Thomson coefficient

It is difficult to think physically about what the Joule–Thomson coefficient, \mu_, represents. Also, modern determinations of \mu_ do not use the original method used by Joule and Thomson, but instead measure a different, closely related quantity. Thus, it is useful to derive relationships between \mu_ and other, more conveniently measured quantities, as described below. The first step in obtaining these results is to note that the Joule–Thomson coefficient involves the three variables ''T'', ''P'', and ''H''. A useful result is immediately obtained by applying the cyclic rule; in terms of these three variables that rule may be written :\left(\frac\right)_H\left(\frac\right)_P \left(\frac\right)_T = -1. Each of the three partial derivatives in this expression has a specific meaning. The first is \mu_, the second is the constant pressure
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat cap ...
, C_, defined by :C_ = \left(\frac\right)_P and the third is the inverse of the ''isothermal Joule–Thomson coefficient'', \mu_, defined by :\mu_ = \left(\frac\right)_T . This last quantity is more easily measured than \mu_ . Thus, the expression from the cyclic rule becomes :\mu_ = - \frac . This equation can be used to obtain Joule–Thomson coefficients from the more easily measured isothermal Joule–Thomson coefficient. It is used in the following to obtain a mathematical expression for the Joule–Thomson coefficient in terms of the volumetric properties of a fluid. To proceed further, the starting point is the fundamental equation of thermodynamics in terms of enthalpy; this is :\mathrmH = T \mathrmS + V \mathrmP. Now "dividing through" by d''P'', while holding temperature constant, yields :\left(\frac\right)_T = T\left(\frac\right)_T + V The partial derivative on the left is the isothermal Joule–Thomson coefficient, \mu_, and the one on the right can be expressed in terms of the coefficient of thermal expansion via a
Maxwell relation file:Thermodynamic map.svg, 400px, Flow chart showing the paths between the Maxwell relations. P is pressure, T temperature, V volume, S entropy, \alpha coefficient of thermal expansion, \kappa compressibility, C_V heat capacity at constant volu ...
. The appropriate relation is :\left(\frac\right)_T= -\left(\frac\right)_P= -V\alpha\, where ''α'' is the cubic coefficient of thermal expansion. Replacing these two partial derivatives yields :\mu_ = - T V\alpha\ + V. This expression can now replace \mu_ in the earlier equation for \mu_ to obtain: :\mu_ \equiv \left( \frac \right)_H = \frac V (\alpha T - 1).\, This provides an expression for the Joule–Thomson coefficient in terms of the commonly available properties heat capacity, molar volume, and thermal expansion coefficient. It shows that the Joule–Thomson inversion temperature, at which \mu_ is zero, occurs when the coefficient of thermal expansion is equal to the inverse of the temperature. Since this is true at all temperatures for ideal gases (see expansion in gases), the Joule–Thomson coefficient of an ideal gas is zero at all temperatures.


Joule's second law

It is easy to verify that for an ideal gas defined by suitable microscopic postulates that ''αT'' = 1, so the temperature change of such an ideal gas at a Joule–Thomson expansion is zero. For such an ideal gas, this theoretical result implies that: :''The internal energy of a fixed mass of an ideal gas depends only on its temperature (not pressure or volume).'' This rule was originally found by Joule experimentally for real gases and is known as Joule's second law. More refined experiments found important deviations from it.Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, , p. 81.


See also

*
Critical point (thermodynamics) In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions ...
*
Enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
and Isenthalpic process * Ideal gas *
Liquefaction of gases Liquefaction of gases is physical conversion of a gas into a liquid state (condensation). The liquefaction of gases is a complicated process that uses various compressions and expansions to achieve high pressures and very low temperatures, using ...
* MIRI (Mid-Infrared Instrument), a J–T loop is used on one of the instruments of the James Webb Space Telescope * Refrigeration *
Reversible process (thermodynamics) In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature. Throughout an ...


References


Bibliography

* * *


External links

* * *
Joule–Thomson effect module
University of Notre Dame {{DEFAULTSORT:Joule-Thomson effect Thermodynamics Cryogenics Engineering thermodynamics Gases Heating, ventilation, and air conditioning James Prescott Joule William Thomson, 1st Baron Kelvin