Show that for an ideal van der Waals fluid
h=−v2a+RT(c+v−bv)
where h is the molar enthalpy. Assuming such a fluid to be passed through a porous plug and thereby expanded from vi to vf (with vf>vi), find the final temperature Tf in terms of the initial temperature Ti and the given data.
Evaluate the temperature change if the gas is CO2, the mean temperature is 0∘C, the mean pressure is 107 Pa, and the change in pressure is 106 Pa. The molar heat capacity cP of CO2 at the relevant temperature and pressure is 29.5 J/mole-K. Carry calculation only to first order in b/v and a/RTv.