By Edward B. Stuart, Alan J. Brainard, Benjamin Gal-Or

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2. 4 (Joule-Thomson Process) This process consists in the following idealized set-up: The two chambers in Fig. 3 are separated by a throttle. Each one of them is equipped with a movable piston. A gas or a liquid which fills the left chamber with volume V1 and pressure p1 , is forced through the throttle into the chamber on the right of the figure. The pressure in this part of the system is p2 . The two pistons are shifted in such a way that the pressures p1 and p2 stay constant. Furthermore, the whole system is assumed to be thermally isolated.

Furthermore, the Eq. 19) shows that has dimension energy, Œ D ŒE. Hence, also kT is an energy. 23) of Boltzmann’s constant one can convert energies kT to units eV etc. 25b) For example, the cosmic background radiation of 2:725 K corresponds to an energy 0:2348 meV. Another example is boiling water whose temperature, T ' 373 K, corresponds to about 32 meV. 25a), 4 Aloys Valerian Rudolf Plank, 1886–1973. 26) the thermodynamic entropy S and the energy E. This relation holds with particle number N and volume V fixed.

Via S 7! T (in the free energy) and N 7! C (see above). 8c) Thus, one is dealing here with a system for which temperature, chemical potential and volume are kept fixed while the system may exchange energy and/or particles with its environment. 3 (Grand Canonical Ensemble) A grand canonical ensemble is the set of all microstates in phase space which belong to the same macrostate with given temperature T, chemical potential C and volume V. Like in the case of the canonical ensemble, Sect. 7, we assume a thermodynamic system †1 which is immersed in a large heat bath †0 with energy E0 and number of particles N0 .