Joule-Thomson Porous Plug Experiment

In the period 1852-62, J. P. Joule and W. Thomson (later Lord Kelvin) perfected a clever method for measuring the isenthalpic property (dT/dP)Ih which has come to be called the Joule-Thomson coefficient, symbolized /xJT  

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

Let us now analyze the conditions of the Joule-Thomson expansion in more detail. From the adiabatic character ( q = 0) of the expansion, the first law tells us that 

Because the pressures Pi5 Pf are fixed constants, we can see that work wL = P (V — 0) was performed on the gas in the left chamber, while work wR = Pf (0 — Vf) was performed by the gas in the right chamber, leading to net work w given by 

From (3.63) and (3.64), we recognize that AU = — A(PV), i.e., that Joule-Thomson expansion occurs under conditions of constant enthalpy  

---

Figure 5.7. Schematic representation of a Joule-Thomson porous-plug experiment. The entire experimental apparatus is kept well insulated from the surroundings.

Figure 3.11 Joule-Thomson porous-plug experiment, showing the initial state P, L, Tx (left) and final state Pf, Vf, 7> (right) of the gas as it passes reversibly through the porous plug under fixed pressures PA, Pf and adiabatic conditions.

The Joule-Thomson porous plug experiment has received an important technical application in that it is the basis of one of the methods used m the liquefaction of gases Cf infra... 

Fig. 1.15.1. Porous plug experiment of Joule and Thomson, (a) Initial state the gas is on the left in volume Vi and at pressure A pressure P slightly greater than Pi is applied to the piston to drive the gas throng the porous plug, (h) Final state the gas has heen reversibly and under isenthalpic conditions forced through the plug and appears on the right-hand side in volume V2 and at pressure P2 < Pi.

It must be borne in mind, however, that the above definition of a perfect gas, though true as fai as it goes, is not a complete thermodynamical definition The complete definition will be given after we have considered the porous plug experiment of Joule and Thomson (afterwards Lord Kelvin)... 

The Porous Plug Experiment of Joule and Thomson and the Phenomena of Inversion Points... 

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

The denominator on the right side of Eq. (4) is the heat capacity at constant pressure Cp. The numerator is zero for an ideal gas [see Eq. (1)]. Accordingly, for an ideal gas the Joule-Thomson coefficient is zero, and there should be no temperature difference across the porous plug. Eor a real gas, the Joule-Thomson coefficient is a measure of the quantity [which can be related thermodynamically to the quantity involved in the Joule experiment, Using the general thermodynamic relation ... 

One of the classic experiments on gases was the measurement by Joule and Thomson (1853) of the change in temperature when a gas flows through a porous plug (throttling valve) from a pressure to a pressure / 2... 

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. 

Before starting, we explicitly state that the Joule Thomson process is not an equilibrium process, in contrast to most of the processes dealt with ordinary thermodynamics. The important issue in the Joule Thomson process is that the enthalpy is constant in the course of the process. However, the arguments to justify that the enthalpy is constant are usually somewhat dubious. The flow through the porous plug does not occur in the usual derivation, but rather the initial and the final states are considered. This means that only the states when the gas is entirely on the left side and on the right side are evaluated and we could not stop the experiment before at all. 

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... 

For further cooling of a fluid, a common procedure is to use a continuous throttling process in which the fluid is forced to flow through a porous plug, valve, or other constriction that causes an abrupt drop in pressure. A slow continuous adiabatic throttling of a gas is called the Joule-Thomson experiment, or Joule-Kelvin experiment, after the two scientists who collaborated between 1852 and 1862 to design and analyze this procedure. ... 

---