The Joule-Thomson effect

The Joule-Thomson Coefficient.—Although the subject matter of this section has no direct connection with entropy, it may be considered here because the results are based on one of the thermodynamic equations of state derived in 20d to this extent the material may be regarded as a consequence of the entropy concept. In equation (20.20), viz.. 

This expression is based upon thermodynamic considerations only, and hence is exact the Joule-Thomson coefficient, at any temperature, may thus 

Problem At 20 C, the value of the dimensionless quantity T/V)(dV/dT)p for nitrogen was found to be 1.199 at 100 atm. the specific volume was then 8. ml. g. and Cp was 8.21 cal. deg. mole. Calculate the Joule-Thomson coefficient of nitrogen under these conditions. 

For an ideal gas, satisfying the equation PV = RT under all conditions, dV/dT)p is equal to V/T it follows, therefore, from equation (22.2), that the Joule-Thomson coefficient is always zero. For a real gas, however, this coefficient is usually not zero even at very low pressures, when ideal behavior is approached in other respects. That this is the case may be seen by making use of an equation of state for a real gas. 

For a van der Waals gasj for example, it is seen from the results in 21a that 

In an idealized Joule-Thomson experiment (also called the Joule-Kelvin experiment) a gas is confined by pistons in a cylinder that is divided into two parts by, a rigid porous membrane (see Fig. 7.3). The gas, starting at pressure P, and temperature 7, is expanded adiabatically and quasi-statically through the membrane to pressure P2 and temperature T2. The two pressures are kept constant during the experiment. If V1 is the initial volume of the number of moles of gas that pass through the membrane and V2 is the final volume of this quantity of gas, then the work done by the gas 

For an ideal gas this quantity is zero. The Joule-Thomson process is isenthalpic. When Equation (7.13) is used for the equation of state, the numerator of the right-hand term becomes 

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. 

Some useful relationships may be derived involving the Joule-Thomson coefficient. Let us start with H = H(T, P), to get 

A well-known experiment, first carried out by Joule and Thomson in the period 1852-62, consists in passing a steady stream of gas through a thermally insulated tube in which there is a throttle valve or porous plug. When the conditions are steady, let pi and Ti be the pressure and temperature of the gas at one side of the plug andpa and T2 be the corresponding values at the other side. Let hi and be the enthalpies per mole of the gas under the two sets of Conditions. It follows from equation (2 8) that 

In general there is a change in temperature Ti T whenever the gas is imperfect. Since the expansion takes place at constant enthalpy, this temperature change is appropriately described by the Jovler-Thomaon coefficient defined as 

The magnitude of the Joule-Thomson effect is thus determined by (dhldp )j and not by duldv)j,.  

On account of the second law— the existence of entropy as a function of state—the Joule-Thomson coefficient can be related to other measurable properties of the gas. Thus from (2 95) 

The perfect gas, as defined by equation (3 2), is one whose chemical potential, at constant temperature, is a linear function of the logarithm of its pressure. In the case of gases which are not perfect it is convenient to define a kind of fictitious pressure, called the fugacity, to which the chemical potential of the gas bears the same linear relationship. 

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Many gases can be liquefied by making use of the Joule-Thomson effect, cooling... 

FIGURE 4.31 Cooling bv the Joule-Thomson effect can be visualized as a slowing of the molecules as they climb away from each other against the force of attraction between them. 

Joule-Thomson Coefficient. Knowing that a process is isenthalpic, we can formulate the Joule-Thomson effect quantitatively. 

In a relatively new process for production and fractionation of fine particles by the use of compressible media - the PGSS process (Particles from Gas-Saturated Solutions) - the compressible medium is solubilized in the substance which has to be micronized [58-61]. Then the gas-containing solution is rapidly expanded in an expansion unit (e.g., a nozzle) and the gas is evaporated. Owing to the Joule-Thomson effect and/or the evaporation and the volume-expansion of the gas, the solution cools down below the solidification temperature of the solute, and fine particles are formed. The solute is separated and fractionated from the gas stream by a cyclone and electro-filter. The PGSS process was tested in the pilot- and technical size on various classes of substances (polymers, resins, waxes, surface-active components, and pharmaceuticals). The powders produced show narrow particle-size distributions, and have improved properties compared to the conventional produced powders. 

Temperature changes as pressure is reduced when a flowing stream of gas passes through a throttle, i.e., a valve, choke, or perforations in casing. This is called the Joule-Thomson effect. The change in temperature is directly related to the attraction of die molecules for each other. 

Figure 7.4. Isenthalps for nitrogen and the Joule-Thomson effect.

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. 

Refrigerators and air conditi-ioners function because of the relationship between pressure and temperature. Research the Joule-Thomson Effect. Go to the web site above. Go to Science Resources, then to Chemistry 11 to find out where to go next. 

The Joule-Thomson Effect The English physicists, James Joule and William Thomson (later Lord Kelvin), observed that when a gas imder high pressure is permitted to expand into a region of low pressure it suffers a fall in temperature. This phenomenon is known as the Joule-Thomson effect. 

The Joule-Thomson effect offers further support to the view that attractive forces do exist between gas molecules. As the gas expands, the molecules fall apart from one another. Therefore, work has to be done in order to overcome the cohesive or attractive forces which tend to hold the molecules together. Thus work is done by the system at the expense of the kinetic energy of the gases molecules. Consequently, the kinetic energy decreases and since this is proportional to temperature, cooling results. It may be noted that in this case no external work has been done by the gas in expansion. 

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. 

The Joule-Thomson effect is a measure of the deviation of the behavior of a real gas from what is defined to be ideal-gas behavior. In this experiment a simple technique for measuring this effect will be applied to a few common gases. 

The compression of the gas in the tank to be filled also causes its temperature to rise. This effect even outweighs the Joule-Thomson effect. A simulation can be done based on the first law of thermodynamics. Regarding the reservoir and the tank as a closed adiabatic system, the internal energies of the two containers before and after... 

According to Kosinska,i the viscosity of a fluid streaming under pressure is increased by a factor (2—T)3), where j8=(dp/d7)z /p, owing to the Joule-Thomson effect ( 24.VII A). 

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