110 lb_m of liquefied natural gas (LNG) is stored in a rigid, sealed 5 ft³ vessel. Due to a failure in the cooling/insulation system, the temperature increases to –100°F, which is above the critical temperature; thus the natural gas will no longer be in the liquid phase. What is the resulting pressure of the supercritical methane? If the vessel is rated as safe for pressures of up to 500 atmospheres, will the vessel rupture? In this problem, again model LNG as 100% methane.

Determine the answer using

A. The ideal gas law.

B. The van der Waals EOS.

The van der Waals parameters for methane are a = 8496 ft⁶ psia/lb-mol² and b = 0.685 ft³/lb-mol.