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+//(11.10)  A mixture consisting of 0.18 kmol of methane (CH4) and 0.274 kmol of butane (C4H10) occupies a volume of 0.241 m3 at a temperature of 238C. The experimental value for the pressure is 68.9 bar. Calculate the pressure, in bar, exerted by the mixture by using (a) the ideal gas equation of state, (b) Kay’s rule together with the generalized compressibility chart, (c) the van der Waals equation, and (d) the rule of additive pressures employing the generalized compressibility chart. Compare the calculated values with the known experimental value.
+
+//solution
+
+//analysis
+V = .241                                                                        //volume of the mixture in m^3
+T = 511                                                                         //temperature of the mixture in kelvin
+n1 = .18                                                                        //number of moles of methane in kmol
+n2 = .274                                                                       //number of moles of butane in kmol
+n = n1 + n2                                                                     //The total number of moles of mixture
+y1 = n1/n                                                                       //mole fraction of methane
+y2 = n2/n                                                                       //mole fraction of butane
+Rbar = 8314                                                                     //universal gas constant in (N.m)/(kmol.K)
+vbar = V/(n)                                                                    //The specific volume of the mixture on a molar basis in m^3/kmol
+
+//part(a)
+p = (Rbar*T/vbar)*10^-5                                                         //in bar
+printf('the pressure in bar obtained using ideal gas equation is:  %f',p)
+
+//part(b)
+//from table A-1
+Tc1 = 191                                                                        //critical temperature for methane in kelvin 
+Pc1 = 46.4                                                                      //critical pressure for methane in bar
+Tc2 = 425                                                                       //critical temperature for butane in kelvin
+Pc2 = 38                                                                        //critical pressure for butane in bar
+
+Tc = y1*Tc1 + y2*Tc2                                                            //critical temperature in kelvin
+Pc = y1*Pc1 + y2*Pc2                                                            //critical pressure in bar
+
+TR = T/Tc                                                                       //reduced temperature of the mixture
+vRdash= vbar*Pc/(Rbar*Tc)
+
+Z = .88
+p = ((Z*Rbar*T)/vbar)*10^-5                                                     //mixture pressure in bar
+printf('\npressure obtained using Kay’s rule together with the generalized compressibility chart, is:  %f',p)
+
+//part(c)
+//Table A-24 gives the following van der Waals constants values for methane
+a1 = 2.293                                                                      //in (m^3/kmol)^2
+b1 = .0428                                                                      //in m^3/kmol
+//Table A-24 gives the following van der Waals constants values for butane
+a2 = 13.86                                                                      //in (m^3/kmol)^2
+b2 = .1162                                                                      //in m^3/kmol
+
+a = (y1*a1^.5 + y2*a2^.5)^2                                                     //in bar*(m^3/kmol)^2
+b = y1*b1+y2*b2                                                                 //in m^3/kmol
+//from van der Waals equation
+p = ((Rbar*T)/(vbar-b))*10^-5 - a/(vbar^2)
+printf('\nthe pressure in bar from van der Waals equation is:  %f ',p)
+
+//part(d)
+//for methane
+TR1 = T/Tc1
+vR1dash = (.241/.18)*10^5*Pc1/(Rbar*Tc1)
+Z1 = 1
+//for butane
+TR2 = T/Tc2
+vR2dash = (.88*10^5*Pc2)/(Rbar*Tc2)
+Z2 = .8
+Z = y1*Z1 + y2*Z2
+//Accordingly, the same value for pressure as determined in part (b) using Kay’s rule results:
+p = 70.4
+printf('\nthe pressure in bar obtained using the rule of additive pressures employing the generalized compressibility chart is:  %f',p)
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