The Redlich-Kwong equation of state is given by p = RT v b a v(v + b) T where R = the

Chapter 6, Problem 6.15

(choose chapter or problem)

The Redlich-Kwong equation of state is given by

\(p=\frac{R T}{v-b}-\frac{a}{v(v+b) \sqrt{T}}\)

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

\(a=0.427 \frac{R^{2} T_{c}^{2.5}}{p_{c}} \quad b=0.0866 R \frac{T_{c}}{p_{c}}\)

where \(p_{c}=4600 \mathrm{kPa}\) and \(T_{c}=191 \mathrm{~K}\). As a chemical engineer, you are asked to determine the amount of methane fuel that can be held in a \(3-\mathrm{m}^{3}\) tank at a temperature of \(-40^{\circ} \mathrm{C}\) with a pressure of 65,000 kPa. Use a root-locating method of your choice to calculate v and then determine the mass of methane contained in the tank.