The ideal gas equation of state is very simple, but its range of applicability is limited. A more accurate but complicated equation is the Van der Waals equation of state given by

where a and b are constants depending on critical pressure and temperatures of the gas. Predict the coefficient of compressibility of nitrogen gas at T = 175 K and ν = 0.00375 m³/kg, assuming the nitrogen to obey the Van der Waals equation of state. Compare your result with the ideal gas value. Take a = 0.175 m⁶·kPa/kg² and b = 0.00138 m³/kg for the given conditions. The experimentally measured pressure of nitrogen is 10,000 kPa.

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P = RT v- b a