Enthalpy Joule-Thomson experiment

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,... 

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

The temperatures T and T can be measured directly. When values of T" versus p" are plotted for a series of Joule-Thomson experiments having the same values of T and p and different values of p", the curve drawn through the points is a curve of constant enthalpy. The slope at any point on this curve is equal to the Joule-Thomson coefficient (or Joule-Kelvin coefficient) defined by... 

The combination U + pV is the original definition of H, the enthalpy, so for the gas in this Joule-Thomson experiment,... 

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. 

The experiment conceived by Joule and Thomson (Kelvin) demonstrated that on adiabatic expansion, without performing additional work, the enthalpy of a gas (ideal or real) remains constant. From this it follows that the internal energy U of an ideal gas is independent of the volume and is, thus, determined by the temperature alone. 

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... 

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