Joule Thomson process

For this reason, also pV = nRT is constant. When we plot TS viz. pV, then we arrive at a vertical straight line. When the entropy increases, the chemical potential must continuously decrease. A plot in the remaining third dimension, pm viz. TS thus will give a straight line. Note that TS, —pV, and fin, all have the dimension of an energy. 

Since both the energy U and the term pV are constant, we have U + pV = H and thus the enthalpy in the Gay - Lussac process is constant. Conversely, we can state that for an ideal gas, when we set pF = C as a constant, then the energy remains constant. 

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. 

Using the method of undetermined multipliers, from Eqs. (5.26) and (5.27) the condition for stationary energy turns out as 

We emphasize that Eq. (5.28) refers to stationary energy and not to thermodynamic equilibrium. Therefore in general, T T and p p . At this stage, we recall that the molar energy tj is 

---

Since the Joule-Thomson process is isenthalpic, the slope of each line can be represented as (dT/dp)lf. This quantity is referred to as the Joule Thomson coefficient, pj j.. Thus1... 

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. 

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... 

Thus, the initial and final states of a Joule-Thomson expansion he on a curve of constant enthalpy (isoenthalp) and the Joule-Thomson process occurs at constant enthalpy. The Joule-Thomson coefficient, pJT, is defined as... 

During the expansion the gas does not exchange heat with its environment. However, it exchanges work because of the expansion against the nonzero pressure P2. It is then a simple matter to demoiLstrate that the gas expands isenthalpically [26, 199-203]. This makes it convenient to discuss the Joule-Thomson process quantitatively in terms of a Joule-Thomson coefficient... 

The Joule-Thomson process therefore occurs at constant enthalpy, and the Joule-Thomson coefficient is equal to a partial derivative at constant H and n ... 

E. H. Brown and J. W. Dean, "Joule-Thomson process in the liquefaction of helium,"... 

Recently this gap in our information has been filled by a paper by Nesselmann [4]. In this paper Nesselmann discusses the refrigeration usefulness of three conventional cycles, i.e., the evaporation process, the Joule—Thomson process, and the adiabatic expansion (Claude process), and compares their theoretical efficiency with the experimentalefficiency of the small Stirling-type refrigerator. His summary of results is reproduced here as Fig. 1 and shows the efficiency... 

The Joule—Thomson process will also not be considered here, since this essentially is an irreversible process. It is no surprise that it shows a lower efficiency than processes that are at least in principle reversible. Its importance, however, lies in the fact that it can easily handle gas and liquid at the same time, the normal situation with gas liquefaction. 

---