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Understanding how a real gas differs from an ideal gas

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In an industrial process, nitrogen has to be heated to 500K at constant volume. If it enters the system at 300 K and 100 atm, what pressure does it exert at its final working temperature? Treat it as a van der Waals gas. Assume the volume is 1 m^3 (where "^" means "to the exponent").

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The solution provides the required equations, as well as a description of how to use the equations to solve the problem. In addition, the complete solution (steps and final numerical answer) are shown.