Answer
a) $T=434.98R$
b) $T=637.46R$
c) $T=659.67R$
Work Step by Step
a) Based on the ideal gas equation:
$T=\frac{P\upsilon}{R}=\frac{400psia*0.1144\frac{ft^3}{lbm}}{0.1052\frac{psiaft^3}{lbmR}}=434.98R$
b) Using the Van Der Waals equation:
$a=\frac{27R^2T_{cr}^2}{64P_{cr}}=\frac{27*(0.1052\frac{psiaft^3}{lbmR})^2*(673.6R)^2}{64*588.7psia}=3.599\frac{ft^6kPa}{lbm^2}$
$b=\frac{RT_{cr}}{8P_{cr}}=\frac{0.1052\frac{psiaft^3}{lbmR}*673.6R}{8*588.7psia}=0.01505\frac{ft^3}{lbm}$
$T=\frac{1}{R}(P+\frac{a}{\upsilon^2})(\upsilon-b)=\frac{1}{0.1052}(400+\frac{3.599}{0.1144^2})(0.1144-0.01505)=637.46R$
c) From table A-13E
$T=200^{\circ}F=659.67R$
