From class and the relevant videos, we derived an expression for how the enthalpy changed with pressure at constant temperature. We also showed how, if you utilize the ideal gas law, this derivative becomes zero $($as expected...we have been making this assumption since MEB$).$ We even spent some time in class on Wednesday discussing this point.

$($a$)$ In this problem, I would like you to derive an expression for that partial derivative using the van der Waals equation of state.

Note: You will need to use the "triple product" rule to allow you to write your required derivatives in terms of $P($in the numerator$)$ so you can easily take the derivative.

$($b$)$ If you are successful in part $($a$),$ you will have a nice function from your result to use $-$ let's use it$!$ R$-41($fluoromethane$)$; Tc $=317\mathrm{.}28K$;$Pc=5\mathrm{.}8970$MPa

You are interested in at $10$ bar and $250K.$

NOTE: To determine the values of $V_{?}$ that you need, please use the EOS spreadsheet for VDW$.$ I have given you the Tc and Pc to use above.

$($c$)$ Compare your work in part $($b$)$ with that from the NIST webbook. NOTE: You will have to approximate your derivative by using a finite difference approach...but by now you should be good at approximating derivatives from data $($we$\text{'}$ve done it a few times in class and you would have had to do this in problem $1,$ above$).$