b. Using equation (Q3.2) and equation (Q3.4), derive an analytical expression to solve for the maximum inversion pressure, \( P_{i, \max } \). Using the equation derived, first calculate the \( P_{i, \max } \) values and then plot the Joule-Thomson inversion curves for methane \( \left(\mathrm{CH}_{4}\right) \), carbon monoxide \( (\mathrm{CO}) \) and nitrogen \( \left(\mathrm{N}_{2}\right) \) gases. Use at least 10 pressure points when plotting the curves; i.e. between 0 and \( P_{i, \max } \), for each gas. You may use the data given in Table Q3.1.
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