Joule—Thomson experiment

In 1843 Joule showed, within the limits of error of his apparatus, that the expansion of gas into a vacuum, as in Fig. 8.2, was accompanied by no temperature change. As in this experiment dw — 0, and since he observed that dq was also effectively zero, 

More careful measurements would have shown that for real gases f — ) was 

The net work is this work of compression less the work recovered when the gas expands on the far side of the plug. Thus 

If the gas on both sides of the plug followed the perfect-gas equation then w would be zero. As AU = q + w and q — 0 (Section 2.5), 

Thus the Joule-Thomson experiment occurs at constant enthalpy. The 

Equation (7-50) could have been derived directly from Eq. (7-38), making use of the relations 

In this section we discuss an experiment first performed by Joule and Thomson (1853) to measure the quantity 

V is the molal volume in the final state, and Vq is the molal volume in the initial state. Since the process is adiabatic, the heat absorbed by the system is zero, and Eq. (7-54) becomes 

Measurements of the temperature change in this process as a function of p, keeping Tq and po fixed, yield a curve whose slope is the Joule-Thomson coefficient 

In Fig. 7-4 we have drawn a number of typical experimental curves of T versus p in the throttling experiment. The enthalpy is constant along each of the curves each of the curves represents a different enthalpy value. The dashed line in Fig. 7-4 is a plot of the inversion temperature Tj the inversion temperature is the temperature at which 

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Isenthalpic Nature. As the Joule-Thomson experiment is carried out adiabati-cally, we can write... 

Thus, we have proved that the Joule-Thomson experiment is isenthalpic as well as adiabatic. 

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. 

Equations of state (EOS) offer many rich enhancements to the simple pV = nRT ideal gas law. Obviously, EOS were developed to better calculate p, V, and T, values for real gases. The point here is such equations are excellent vehicles with which to introduce the fact that gases cannot be really treated as point spheres without mutual interactions. Perhaps the best demonstration of the existence of intermolecular forces that can also be quantified is the Joule-Thomson experiment. Too often this experiment is not discussed in the physical chemistry course. It should be. The effect could not exist if intermolecular forces were not real. The practical realization of the effect is the liquefaction of gases, nitrogen and oxygen, especially. 

The Joule-Thomson experiment can be described as adiabatic expansion in a pipe through a porous plug, as pictured schematically in Fig. 3.11. 

Analysis of the Joule-Thomson experiment (Section 3.6.3) requires evaluation of the derivative (dT/dP)H at constant enthalpy (H = U + PV). The differential expression for dH,... 

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... 

There are two variations of the basic set-up of the Joule-Thomson experiment which both yield practical information. In the isothermal Joule-Thomson experiment the temperature is held constant with a downstream heater, and the resultant heat input for the pressure decrease permits an experimental evaluation of (8H/8P)T, the isothermal Joule-Thomson coefficient. In the other variation there is no throttling device used, and the pressure is held constant. For the steady-state flow of gas the temperature change is measured for measurable inputs of heat. This experiment, of course, yields (8H/8T)P, or CP. Thus, the variations of this constant-flow experiment can yield all three of the important terms in Equation (7.46). 

Schematic diagram of the Joule-Thomson experiment. The stippled area represents a porous plug.

The Joule-Thomson Experiment 1.15.1 Analysis of the Joule-Thomson Effect... 

If this coefficient is constant in an isothermal Joule-Thomson experiment, then the heat which must be supplied to maintain constant temperature is AH in the following relationship... 

Later experiments, notably the Joule-Thomson experiment, have shown that Joule s law is not precisely correct for real gases. In Joule s apparatus the large heat capacity of the vat of water and the small heat capacity of the gas reduced the magnitude of the effect below the limits of observation. For real gases, the derivative (dU/dV) is a very small quantity, usually positive. The ideal gas obeys Joule s law exactly. 

The derivative (dH/dp)j is very small for real gases, but can be measured. The Joule experiment, in which the gas expanded freely, failed to show a measurable difference in temperature between the initial and final states. Later, Joule and Thomson performed a different experiment, the Joule-Thomson experiment (Fig. 7.9). 

Also, the porous plug in the Joule - Thomson experiment is an idealized device. It has certain properties, such as lack of volume, common to the diathermic border, but it does not allow a flow of entropy without flow of matter. When matter flows though the porous plug, the pressure and the temperature are reduced. This is associated with an increase of entropy. 

There are three conditions for the ideality of a gas. The first two are issued from the Joule-Thomson experiments (Planck 1922) and the third one will be enunciated shortly after. The first one states that in an ideal gas the capacitive (internal) energy is invariant with the volume at constant temperature and substance amount. This is the first Joule s condition ... 

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