Question 3 Peng-Robinson equation given in equation (3) is one of the Equations of States (EOS) that relates specific volume 1 (V) of gases to temperature (T) and pressure (P) P=VbRTV(V+b)+b(Vb)a The constants a, b are determined as follows: abmTr=0.45724(pcR2Tc2)[1+m(1Tr21)]=0.07780(pcR2Tc)=0.37464+1.54220.269922=TcT where T is the temperature in K,p is the pressure in atm, V is the specific molar volume in L/kgmol, R is the molar gas constant in kgmol.Katm.L, is the acentric factor, Tc and pc are critical temperature and critical pressure, in K, and atm, respectively, and Tr is reduced temperature. (a) For n-hexane at 1atm and 25C, perform the first three iterations to estimate the specific molar volume using bisection method, taking the boundary of the solution to be in the range 50 to 200 . Take pc=29.92 atm, Tc=507.85K,=0.3007, and R=83.14kgmol.Katm,L (b) Perform the first three iterations to estimate the specific volume for the same case in (a) using regula-falsi method, taking the boundary of the solution to be in the range 50 to 200 . (c) Perform the first three iterations to estimate the specific volume for the same case in (a) using Newton method, taking the guess for the solution to be 200