(Solved): (a) Show that the Joule-Thomson coefficient, j, given by the equation cp=j1[T(T ...

(a) Show that the Joule-Thomson coefficient, ${?}_j$, given by the equation $c_p=\frac{1}{{?}_j}\left[T{\left(\frac{?v}{?T}\right)}_p?v\right]$ Can be written as ${?}_j=\frac{T^2}{c_p}{\left(\frac{?(v/T)}{?T}\right)}_p$ (b) Using this result, obtain an expression for the Joule-Thomson coefficient for a gas obeying the equation of state $v=\frac{RT}{p}?\frac{Ap}{T^2}$ Where $\mathrm{A}$ is a constant. (c) Using the result of part (a), determine $c_p$, in $\mathrm{kJ}/\mathrm{kg}?\mathrm{K}$ for ${\mathrm{CO}}_2$ at $400\mathrm{K}$, 1 atm, where ${?}_{\mathrm{j}}=0.57\mathrm{K}/\mathrm{atm}$. For ${\mathrm{CO}}_2,A$ $=2.78\times 10^{?3}{\mathrm{m}}^5?{\mathrm{K}}^2/\mathrm{kg}?\mathrm{N}$.