(Solved): The Joule-Thomson 5 process is a technique used to cool a gas in a refrigerat ...

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The Joule-Thomson 5 process is a technique used to cool a gas in a refrigerator and also for the liquefaction of gases. A gas is passed through a porous plug (see drawing), thus reducing the pressure of the gas, and - we hope-its temperature; the process can be considered adiabatic. The flow of gas is continuous, but to analyze the process one can imagine another process where a quantity of gas is forced to pass through the plug by a piston on the left (which exerts a constant pressure \( P_{i} \) that of the gas before the cap) and which is pulled by a piston on the right (which exerts a constant pressure \( P_{f} \) - that of the gas after the stopper). The volumes of this quantity of gas are \( V_{i} \) before passing through the plug and \( V_{f}>V_{i} \) afterwards. (a) What is the work done on the gas by (i) the left piston; (ii) the right piston during the process? Show that the enthalpy of the gas is conserved in this process. b) Show that \( \mu=-\frac{1}{C_{p}}\left(\frac{\partial H}{\partial P}\right)_{T} \) where \( \mu \) is the Joule-Thomson coefficien c) Derive an equation for \( \left(\frac{\partial H}{\partial P}\right)_{T} \) in terms of \( \mathrm{P}, \mathrm{V}, \mathrm{T}, \beta, \kappa \) et \( C_{p} \).