## Joule Thomson Effect Inversion Curve

The differential coefficient ^ was first investigated by James Joule and William Thomson in the 1850s , before Thomson was elevated to the peerage, to become the first Lord Kelvin. So it is also referred to as the Joule-Kelvin coefficient.

It is a measure of the effect of the throttling process on a gas, when it is forced through a porous plug, or a small aperture or nozzle. The drop in pressure, at constant enthalpy H, has an effect on temperature. The enthalpy of hydrogen as a Van der Waals gas is given by the specific values (per mole) of the extensive variables H and V, written h and v.

f a ( RT a\ if v \ 2a h = u + pv = RT - - + v -- - -r = RWi +----(4.24)

where u is the internal energy, f is the degree of freedom (5 for H2) and v is the molar volume of the gas. The change in enthalpy is given by the differential and is

Table 4.8 Coefficients C, as a function oftemperature

 60 -3.54561 io-4 1.66337 IO-7 -2.99498 io- l 77 -1.38130) 10-4 4.67096
2.42574 : -3.24527 : -2.63262 :

10-

-15

10-

-15

3.54211 )

< 10

10-

-15

2.40671 )

1-19

Table 4.9 The volume V, enthalpy H, Gibbs free energy G and entropy S of n-H2 at a temperature (T = 300 K) and pressures (p = 0.1 MPa-100GPa, i.e. 1 x 106 bar)a

 1 24943 8506 -30724 130.77 2 12485.9 8507 -28994 125 5 5003.08 8510 -26704 117.38 10 2508.87 8515 -24968 111.61 20 1261.83 8526 -23224 105.84 50 513.73 8560 -20895 98.18 100 264.51 8620 -19091 92.37 200 140.09 8747 -17210 86.52 500 65.78 9176 -14454 78.77 1000 40.98 9954 -11924 72.93 2000 27.96 11529 -8615 67.15 5000 18.75 15896 -1962 59.53 10000 14.58 22319 6189 53.77 20000 11.56 33414 19013 48 50000 8.64 60517 48402 40.39 100000 6.84 94585 86094 28.31 200000 5.52 154070 146981 23.63 500000 4.1 293183 287378 19.35 1000000 3.23 472676 467424 17.51

aThe values are taken from Hemme et al. . The complete set of data for temperatures (T = 100-2000 K) can be found in Fukai  and Sugimoto .

aThe values are taken from Hemme et al. . The complete set of data for temperatures (T = 100-2000 K) can be found in Fukai  and Sugimoto .

zero for an isoenthalpic expansion dK dh .

In a pressure-temperature plot, for any gas, the locus of points at which the drop in pressure, at constant enthalpy H, has no effect on the temperature is called the inversion curve for that gas. So the inversion curve has the simple form ^ = 0. These curves are plotted by first finding a family of isoenthalpies (H = const.) on the T-p plane, then connecting their stationary points. Except along the inversion curve, throttling either heats the gas (¡x< 0), or cools it 0). Cooling of gases, in order to subsequently liquefy them, is usually accomplished by throttling in a region where it causes cooling (Figure 4.6).

The specific values (per mole) of the extensive variables H, S and V, are written h, s and v. Then the specific enthalpy is Fig. 4.6 The Joule-Thomson coefficient for H2 in the Van der Waals approximation (Equation (4.26)) at a pressure of p = 0.1 MPa (solid line) and p = 10 MPa (dashed line).

Thus it follows that the Joule-Thomson coefficient is

dv ST

T2 d CP ST

The first thing to notice about the Joule-Thomson coefficient is that it vanishes for an ideal gas. The inversion "curve" is everywhere for an ideal gas! For real gases, the isoenthalpies have to be determined experimentally and the line connecting the stationary points is the inversion curve.

The simplest equation of state for a gas which predicts an inversion curve is the Van der Waals equation. It yields an inversion curve, that is fairly close, but not exactly correct. The Van der Waals equation in reduced variables (Equation (4.14)) used in the equation for the Joule-Thomson coefficient (Equation (4.29)) leads for H- = 0 and substituting index r by i to

Substituting Vi with pi one finds (Figure 4.7) Ti = —2 (45 - pi ± 12^9—^) Fig. 4.7 Inversion curve of n-hydrogen and calculated inversion curve (Equation (4.31)) using the critical pressure pk = 1.325 MPa and the critical temperature Tk = 33.19 K for hydrogen.

The two branches join at p = 9, where T = 3 and V = 1. They connect this point with the T axis, where p vanishes, at the two points T = | and T = 27/4. And of course, inside this curve is the region in which the Van der Waals equation predicts that throttling any gas will produce cooling.

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### Responses

• BELL
How to produce inversion curve from joule thomson?
1 year ago
• samwise
Why has hydrogen negative joule thompson effect?
4 days ago