Joule inversion temperature

Expansion from high to low pressures at room temperature cools most gases. Hydrogen is an exception in that it heats upon expansion at room temperature. Only below the inversion temperature, which is a function of pressure, does hydrogen cool upon expansion. Values of the Joule-Thorns on expansion coefficients for hydrogen have been tabulated up to 253 MPa (36,700 psi) (48), and the Joule-Thorns on inversion curve for i7n -hydrogen has been determined (49,50). 

Figure 3.6 shows that pj.r. is negative at high temperatures and pressures. Therefore, a gas heats up as it expands under these conditions. At lower temperatures, the gas continues to increase in temperature if the expansion occurs at high pressures. However, at lower pressures, the slope, and hence, Hj.t., becomes positive, and the gas cools upon expansion. Intermediate between these two effects is a pressure and temperature condition where //j.t. = 0. This temperature is known as the Joule-Thomson inversion temperature Tt. Its value depends upon the starting pressure and temperature (and the nature of the gas). The dashed line in Figure 3.6 gives this inversion temperature as a function of the initial pressure. Note that when Joule-Thomson inversion temperatures occur, they occur in pairs at each pressured... 

The reader interested in the liquefaction technologies can see, for example, ref. [14,15], We will only remind that in most cases, the gas cooling is obtained by the Joule-Thomson process an isothermal compression of the gas is followed by an expansion. This procedure leads to a cooling only if the starting temperatures are lower than the inversion temperature 7] = 6.75 TCI (for a Van der Waals gas), where TCI is the critical temperature. 

Joule-Thomson Inversion Temperature. The Joule-Thomson coefficient is a function of temperature and pressure. Figure 5.8 shows the locus of points on a temperature-pressure diagram for which p,jx. is zero. Those points are at the Joule-Thomson inversion temperature 7). It is only inside the envelope of this... 

Figure 5.8. Locus of Joule Thomson inversion temperatures for nitrogen. Data from J. R. Roebuck and H. Osterberg, Phys. Rev. 48, 450 (1935).

As Cpm is positive, the sign of the Joule-Thomson coefficient depends on the sign of the expression in parentheses in Equations (10.79) and (10.80). The expression in Equation (10.79) is a quadratic in T, and are two values of T exist at any value of P for which p.j x, = 0. Thus, Equation (10.79) predicts two values of the Joule-Thomson inversion temperature T,- for any pressure low enough for Equation (10.75) to be a good approximation for a. As we saw in Section (5.2) and Figure 5.8, this prediction fits, at least qualitatively, the experimental data for the Joule-Thomson experiment for N2 at low pressure. 

Positive values JT > 0 are the usual low-7 case for most common gases (i.e., all except He and H2 at room temperature). In this case, the gas cools on expansion under adiabatic conditions, indicative of the dominance of attractions between molecules. The contrary high-7 case of /xJT < 0 (e.g., for H2 above 193K) leads to the gas warming on adiabatic expansion, indicative of the dominance of intermolecular repulsions. The crossover from positive to negative values of occurs at the Joule-Thomson inversion temperature Tj, where... 

We conclude that the Joule-Thomson coefficient is a function of both the temperature and the pressure, but, unlike the Joule coefficient, it does not go to zero as the pressure goes to zero. The inversion temperature, the temperature at which fi,T = 0, is also a function of the pressure. The value usually reported in the literature is the limiting value as the pressure goes to zero. 

The temperatures on the envelope where pn = 0 are called inversion temperatures, Tt. At any given pressure, up to a maximum pressure, a given gas exhibits two inversion temperatures. The Joule-Thomson effect is important in refrigeration and in the liquefaction of gases. Modern refrigeration uses the larger effect of the evaporation of working fluids such as the chlorofluorocarbons. 

We have already seen how gases below their Joule-Thomson inversion temperature (7)) cool upon rapid expansion. By Joule-Thomson expansion, N2 can be liquefied (77 K). Liquid N2 can be used to cool H2 below its Tt (195 K), and then further Joule-Thomson expansion can produce liquid H2 (20.4 K), which can be used to cool He below its Tt (44.8 K). Joule-Thomson expansion of this cooled He can produce liquid He (4.2 K), and reducing the pressure above the liquid can conveniently produce temperatures as low as about 1 K. 

Experiments have shown that gases become cooler during Joule-Thomson s expansion only if they are below a certain temperature known as inversion temperature (Tt). The inversion temperature is characteristic of each gas and is given by,... 

Hydrogen and helium have very low inversion temperatures, i.e., -80°C, and -240°C, respectively. Thus, at ordinary temperatures, these gases get heated up instead of being cooled in Joule-Thomson s expansion. But, if hydrogen is first cooled below -80°C and helium below -240°C, then these gases also get cooled down on Joule-Thomson expansion. Joule-Thomson effect was used by Linde in the liquefaction of the gases. The Linde s process is described below ... 

In the process of liquefaction, one must also consider the inversion temperature (-361°F or -183°C or 90°K) of H2, because the behavior of this gas changes (inverses) at that temperature. Below the inversion temperature, when the pressure is reduced, the H2 temperature will drop. Above that temperature the opposite occurs a drop in pressure causes a rise in temperature. Therefore, in the process of liquefaction, H2 first has to be cooled below its inversion temperature—by such means as cooling with LN2—before the Joule-Thomson effect can be utilized. 

Pressure (Pt), Van Der Waals Coefficients a and b, Second Virial Coefficients B(T) at 273 K, and Joule-Thomson Inversion Temperature 7 (at 1 atm) for Several Elements and Compounds [1-3] ... 

At the inversion temperature there is no Joule-Thomson effect. Thus, if a gas under pressure passes through a porous plug and expands adiabatically into a region of very low pressure at the inversion temperature, there is neither fall nor rise in temperature. If, however, the expansion takes place above the inversion temperature, there is a small rise of temperature and if it takes... 

In most gases, this temperature lies within the range of ordinary temperature. Hence, they get cooled in the Joule-Thomson expansion. Hydrogen and helium, however, have very low inversion temperatures. Thus, at ordinary temperatures, these gases get warmed up instead of getting cooled in the Joule-Thomson expansion. But if hydrogen is first cooled to -80 C which is its inversion temperature and helium is first cooled to -240 C which is its inversion temperature, then these gases also get cooled on expansion in accordance with the Joule-Thomson effect. 

For a van der Waals gas determine the Joule Thomson coefficient and inversion temperature Ti in terms of a, b, P, T, and Cp. Make a sketch of versus T note and comment on the double-valued nature of the function. 

For most gases under ordinary conditions, 2a RT > b (the attractive forces predominate over the repulsive forces in determining the nonideal behavior) and the Joule-Thomson coefficient is therefore positive (gas cools on expansion). At a sufficiently high temperature, the inequality is reversed, and the gas warms on expansion. The temperature at which the Joule-Thomson coefficient changes sign is called the inversion temperature Tj. For a van der Waals gas,... 

It is necessary to define the conception of the inversion temperature a little more closely. In the literature of the subject we find this term used with two distinct meanings first, as the temperature at which the Joule-Thomson effect vanishes when the gas is allowed to expand from a high pressure p to the pressure of the atmosphere, and, secondly, as the tempera-... 

The liquefaction of helium by a controlled expansion process necessitates preliminary cooling because its Joule-Thomson coefficient is negative (spontaneous expansion heats the gas) down to an inversion temperature of 40 All the gases have C /C ratios very close to 5/3, the theoretical value for an ideal monatomic gas. The elements are liquid over very small temperature ranges. Plelium can be solidified only under pressure under 26 atmospheres it solidifies at 0.9 °K. 

TABLE XIV. JOULE-THOMSON INVERSION TEMPERATURES FOR NITBOQEN... 

A generalized expression for the Joule-Thomson inversion temperature may be obtained by the use of a reduced equation of state. By setting equation (22.2) equal to zero, the condition for the inversion temperature Ti is then seen to be... 

By using equation (22.2) in conjunction with the compressibility factor (x), derive a simple condition for the Joule-Thomson inversion temperature of a gas at any (reduced) pressure in terms of the variation of k with the (reduced) temperature. 

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