At a Friday team meeting for your division at Massillon Chemical and Energy Company, you hear your supervisor comment that your company has just licensed the use of a heat transfer fluid from a local vendor. You look at the Gantt chart that has been presented on the TV monitor and see your initials associated with the "Process Evaluation" heading. Later that afternoon, a colleague stops by your office to drop off some information about the process evaluation step and this new heat transfer fluid. After reading the limited details provided, the process information basically says you are swapping out your current heat transfer fluid with this new fluid. Since the previous process required evaporation of some of the heat transfer fluid, you surmise that you will need to know the heat of vaporization of this new heat transfer fluid. The old process operated at $15C,$ so you want to find information at that temperature.

You email your supervisor to ask about the substance $($i$.$e$.$ its name, etc.$),$ but your supervisor responds that the licensing agreement comes with a non$-$disclosure agreement $($NDA$)...$and you are not at the level to be covered by the NDA.

After the phone call, your supervisor emails you Antoine coefficients for this substance.

$A=7\mathrm{.}47680$

$B=1362\mathrm{.}39$

$C=178\mathrm{.}77$

$P$ is in $mmHg$ and $T$ is in $C.$

$lo{g}_{10}(P^{\text{s}\text{t}\text{a}\text{t}})=A-\frac{B}{T+C}$

$($a$)$ Based on the above information, estimate the heat of vaporization at $15C.($Hint: Clausius$-$Clapeyron$).$

$($b$)$ Later that day, your supervisor sends you additional information about the substance.

$TC=563\mathrm{.}05K$

$PC=44\mathrm{.}23$ bar

$w=0\mathrm{.}590$

Based on this information, estimate the heat of vaporization at $15C$ using the Peng$-$Robinson equation of state.