[15] Thus at low temperature, [math]Z[/math] and [math]PV[/math] will increase as the gas expands, resulting in a positive Joule–Thomson coefficient.

{\displaystyle U} as:[1][3][17]. 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. The cooling produced in the Joule–Thomson expansion makes it a valuable tool in refrigeration. [7][8] 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. So h, u, and v are the specific enthalpy, specific internal energy, and specific volume (volume per unit mass, or reciprocal density), respectively. is always equal to zero: ideal gases neither warm nor cool upon being expanded at constant enthalpy.

Under the conditions of a Joule–Thomson expansion, the change in [math]PV[/math] represents the work done by the fluid (see the proof below).

B.

These physical effects are not the same, but all are frequently or occasionally referred to in literature as the "Joule effect" or "Joule law" These physical effects include: Between the years 1840 and 1843 Joule made a careful study of the heat produced by an electric current.

The effect is named after James Prescott Joule and William Thomson, 1st Baron Kelvin, who discovered it in 1852. 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. The ratio of the value of The physical mechanism associated with the Joule–Thomson effect is closely related to that of a shock wave,[16] although a shock wave differs in that the change in bulk kinetic energy of the gas flow is not negligible. Throttling is a fundamentally irreversible process.

T [18][19] The effect is applied in the Linde technique as a standard process in the petrochemical industry, where the cooling effect is used to liquefy gases, and also in many cryogenic applications (e.g.

In thermodynamics, 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 (as differentiated from an ideal gas) when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. H increases as pressure increases. Using the definition of the specific enthalpy h = u + Pv, the above equation implies that. increases, with

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, Each of the three partial derivatives in this expression has a specific meaning. This coefficient can be expressed in terms of the gas's volume [math]V[/math], its heat capacity at constant pressure [math]C_{\mathrm{p}}[/math], and its coefficient of thermal expansion [math]\alpha[/math] as:[1][3][17]. The first is [math]\mu_{\mathrm{JT}}[/math], the second is the constant pressure heat capacity, [math]C_{\mathrm{p}}[/math], defined by, and the third is the inverse of the isothermal Joule–Thomson coefficient, [math]\mu_{\mathrm{T}}[/math], defined by, This last quantity is more easily measured than [math]\mu_{\mathrm{JT}}[/math] . M.J. Moran and H.N. 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. ; Saville, G. (1995).

Throttling from 200 bar and an initial temperature of 133 K (point c in fig. De Waele, A. T. A. M. (2017). With that in mind, the following table explains when the Joule–Thomson effect cools or warms a real gas: Helium and hydrogen are two gases whose Joule–Thomson inversion temperatures at a pressure of one atmosphere are very low (e.g., about 45 K (−228 °C) for helium). V P This equation can be used to obtain Joule–Thomson coefficients from the more easily measured isothermal Joule–Thomson coefficient.

[/math], [math]C_{\mathrm{p}} = \left(\frac{\partial H}{\partial T}\right)_P [/math], [math]\mu_{\mathrm{T}} = \left(\frac{\partial H}{\partial P}\right)_T [/math], [math]\mu_{\mathrm{JT}} = - \frac{\mu_{\mathrm{T}}} {C_p}. μ "Elements of Classical Thermodynamics", p. 73. is volume. Thus, for N2 gas below 621 K, a Joule–Thomson expansion can be used to cool the gas until liquid N2 forms. constant, then where h1 and h2 denote the specific enthalpies of the amount of gas in regions 1 and 2, respectively. V 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). where [math]U[/math] is internal energy, [math]P[/math] is pressure, and [math]V[/math] is volume. [1][2][3] This procedure is called a throttling process or Joule–Thomson process.

T {\displaystyle \mu _{\mathrm {T} }}

and The temperature change produced during a Joule–Thomson expansion is quantified by the Joule–Thomson coefficient, [math]\mu_{\mathrm{JT}}[/math].

Z μ

On the other hand, nitrogen and oxygen, 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.[1].

Z {\displaystyle \mu _{\mathrm {JT} }} in the earlier equation for For such an ideal gas, this theoretical result implies that: This rule was originally found by Joule experimentally for real gases and is known as Joule's second law. [4] At room temperature, all gases except hydrogen, helium, and neon cool upon expansion by the Joule–Thomson process when being throttled through an orifice; these three gases experience the same effect but only at lower temperatures.

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