Joule-Thomson expansion inversion temperature

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. 

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 ... 

Experiment has shown that gases become cooler during the Joule-Thomson expansion only if they are below a certain temperature known as the inversion temperature, TrThe inversion temperature is characteristic of each gas. It is related to the van der Waals constants a and b of the gas concerned by the following expression ... 

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. 

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. 

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... 

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... 

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,... 

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. 

This observation is important because it also permits us to conclude that it will not be possible to construct a tangent through the origin at any point of the curve B2 T) no matter whether we consider a bulk or confined ideal quantum gas and irrespective of whether the quantum particles are Fermions or Bosons. In other words, for the ideal (bulk and confined) quantum gases, an inversion temperature Tj v does not exist because Eq. (5.155) does not have a solution. However, the reader should note that a Joule-Thomson effect does exist as pointed otit in Section 5.7.1, namely a dilute gas of Bosons is always cooled upon an iscnthalpie expansion B2 T) < 0), whereas a gas of Fermions is always heated during this process B2 (T) > 0). Tire extent to which this happens is modified in a nontrivial way by confinement according to the above discussion. 

The inversion temperature of Nj is 850 K. Inversion temperature is the temperature below which a gas cools down by adiabatic expansion (Joule-Thomson-Effect). Therefore, Nj can be liquefied from room temperature by means ofcounter[Pg.10]

This rapid adiabatic expansion is sufficient to cool the nitrogen to below its boiling point of 77°K, so this is a way to make liquid nitrogen. There is a temperature for each gas called the Joule-Thomson inversion temperature and cooling occurs if the initial temperature is below that temperature but the gas heats upon expansion if the initial temperature is above the inversion temperature. At room temperature He is above its inversion temperature and will actually heat up upon expansion. Although there is also a pressure effect, there are absolute temperatures for this effect. For He the temperature is 51°K, for H2 202°K, for N2 621°K, and for O2 it is 764°K (see discussion at http //en.citizendium.org/wiki/Joule-Thomson effect). Thus, air (N2 + O2) can be liquefied by adiabatic expansion starting from room temperature and 1 atm, but He and H2 must be precooled to below their Joule-Thomson inversion temperatures. 

Joule-Thomson effect Most gases cool down while expanding (process of decompression). However, hydrogen stored at a temperature exceeding the inverse temperature (r > Tin = 193 K) is heated upon expansion. For example, at hydrogen expansion from 20 to 0.1 MPa the temperature rise is 6-8 K. 

For any gas, the sign of the Joule-Thomson effect depends on tanperature and pressure. The positive effect for each gas is observed only in the limited interval of temperatures and pressures. For each gas there are values of temperature and pressure at which the Joule-Thomson effect is equal to zero (no temperature changes occur at gas expansion in vacuum). These points (T, p,) are called points of inversion. At these points, the influence of forces of attraction is completely compensated for by the influence of repulsion forces consequently the gas temperature does not change. The set of inversion points forms an inversion curve in a p-T diagram. 

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