Chapter 8, Problem 7P

The Redlich-Kwong equation of state is given by

$p=\frac{RT}{v-b}-\frac{a}{v\left(v+b\right)\sqrt{T}}$

where $R=$ the universal gas constant $\left[=0.518\text{kJ/}\left(\text{kg}\text{K}\right)\right]$, $T=$ absolute temperature $\left(\text{K}\right),p=$ absolute pressure $\left(\text{kPa}\right),\text{ and }v=$ the volume of a kg of gas $\left({\text{m}}^3/\text{kg}\right)$. The parameters a and b are calculated by

$a=0.427\frac{R^2{T}_c^{2.5}}{p_c}b=0.0866R\frac{T_c}{p_c}$

where $p_c=$ critical pressure $\left(\text{kPa}\right)\text{ and }{T}_c=$ critical temperature $\left(\text{K}\right)$. As a chemical engineer, you are asked to determine the amount of methane fuel $\left(p_c=4600\text{ kPa and }{T}_c=191\text{ K}\right)$ that can be held in a ${\text{3-m}}^3$ tank at a temperature of $-40°\text{C}$ with a pressure of $65,000\text{ kPa}$. Use a root-locating method of your choice to calculate v and then determine the mass of methane contained in the tank.