Problem $1.(2$ points$)$ Recall the Peng$-$Robinson equation of state

$(P+\frac{a(T)}{v(v+b)+b(v-b)})(v-b)=RT.$

Given parameters a and b$,$ derive critical pressure, critical molar volume, critical

temperature and critical compressibility factor for the Peng$-$Robinson fluid. Does

the critical compressibility factor depend on parameter a or b$?$ Derive the Peng$-$

Robinson equation in terms of reduced pressure, reduced molar volume, and reduced

temperature.