High pressure gas cylinders containing flammable gases can cause enormous damage and potential loss of life if they fail. One such a failure mode is exposure to excessive temperatures during transport. Due to the dramatic decrease in the ultimate strength of the steel used in gas cylinders with increasing temperature, a critical design point is at 80C where the cylinder will fail if the internal pressure is above 25 MPa. When a 47 L cylinder is filled with pure methane gas at -10C, what is the maximum pressure the cylinder can be filled to so as to not cause the cylinder to fail if the cylinder temperature is raised to 80C in transport? Assume the pressure measurement after bottle filling is undertaken when the gas in equilibrium in the cylinder with a temperature of -10C. Solve this problem considering the flowing three approaches: i)The ideal gas equation ii) The compressibility factor corrected ideal gas equation iii) Van der Waals equation