In a classic experiment designed by Joule and Thomson to measure the dependence of enthalpy on pressure a gas was forced through a porous plug of cotton wool [84, 85]. The core of the experimental apparatus of Joule and Thomson is shown in Fig. 2.8. The pipe was made of beechwood and insulated. Thermometers were located on both sides of the cotton wool. Pressure on each side of the wool plug were maintained by cylindrical reservoirs with weighted covers [, p. 138]. The gas flowed very slowly through the cotton wool plug under pressure. The gas velocities on either side of the plug could then be neglected. The dashed line is a system boundary enclosing a constant amount of air. Using the first law for open systems, show that in this experiment the thermal enthalpy is a constant. In the experiment pressures and temperatures were measured on both sides of the wool plug. So the experiment measured (∂T/∂P)H, which has become known as the Joule-Thomson, or simply Joule coefficient μJ = (∂T/∂P)H. How to extract (∂H/∂P)T from μJ is a mathematical question that will be investigated in Chap. 3.
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