We can usually expand and cool a gas stream by using either a Joule-Thompson throttling valve or a turbine. To measure the relative efficiency of these two options, the expansion ratio: H/S is often used. Here H is the Joule Thompson coefficient (T/P)H; and S is the isentropic coefficient (T/P)S. Please find a way to express the expansion ratio in terms of variables that we can measure, and then use your result with an appropriate equation of state to find the expansion ratio expression