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The van der Waals equation of state is (P + a(n/V )^2)(V/n − b) = RT,...

The van der Waals equation of state is (P + a(n/V )^2)(V/n − b) = RT, where a and b are gas-specific constants. For Hydrogen gas, a = 2.45 × 10^-2P a · m^6 and b = 26.61 × 10^-6m^3/mol, while for an ideal gas a = b = 0. (a) Consider trying to measure the ideal gas constant in a lab from the relation R = P V/(nT), where P, V, n, and T are all measured parameters. However, your working gas is hydrogen rather than a true ideal gas. Would your measurement of R be more accurate at low density or high density? (b) You try to measure R by measuring the pressure using 2000 moles of Hydrogen in a 1 m^3 volume at room temperature. How far off will your measurement be from the true ideal gas constant, in percentage terms? (c) Calculate the work done on a van der Waals gas to contract it from volume Vi = 2m^3 to Vf = 1m^3.

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