Please solve all parts. Thank you

(a) The van der Waals equation of state can be used to estimate any one of the state variables, p, T, and , if the other two variable values are specified for a particular gas. Discuss. [20%] (b) Methane (CH4) is stored at 200 bar and 15C in a 12.4 m vessel. What is the state of the methane in the vessel under these conditions? (10%) (c) Using the ideal gas equation estimate the mass of methane contained in the vessel under the conditions specified in (b)? [20%) (d) Using the Van der Waals equation of state estimate the mass of methane contained in the vessel for those conditions specified in (b). [40%) (e) The storage vessel is fitted with a pressure relief valve which is set to vent the methane at a pressure of 300 bar. Using the van der Waals equation estimate the temperature to which the cylinder may be raised before the methane is released. (10%) The van der Waals equation of state is, RT a 27RT p= where and bu V-b 02 64p. 8p. For Methane Critical Temperature, T. = -82.45C Critical Pressure, P. = 46.4 bar Note: 1 bar = 1.0x105 N/m2 and R= 8.3145 J/mol K RT