The inversion temperature  ${\mathrm{T}}_{\mathrm{i}}( \mathrm{K})$of hydrogen is (given vander Waal’s constants a and b are 0.244 atm ${\mathrm{L}}^2{ \mathrm{mol}}^{-2}$ and $0.027\mathrm{L}{\mathrm{mol}}^{-1}\text{ respectively) }$

Gases become cooler during Joule Thomson’s expansion only  if they are below a certain temperature known as inversion temperature (T_i). The inversion temperature is characteristic of The inversion temperature is characteristic of each gas and is given by 
$$\begin{gathered} {\mathrm{T}}_{\mathrm{i}}=\frac{2\mathrm{a}}{\mathrm{bR}}\text{, where }\mathrm{R}\text{ is gas constant } \\ \text{ Given }\mathrm{a}=0.244{\mathrm{atmL}}^2{\mathrm{mol}}^{-2} \\ \mathrm{b}=0.027\mathrm{L}{\mathrm{mol}}^{-1} \\ \mathrm{R}=0.0821\mathrm{L}{\text{ atm deg }}^{-1}{\mathrm{mol}}^{-1} \\ \therefore {\mathrm{T}}_{\mathrm{i}}=\frac{2\times 0.244}{0.027\times 0.0821}=220\mathrm{K} \end{gathered}$$