Recall that the van der Waals equation of state—an extension of the ideal gas equation—attempts to better capture the behavior of real gases. It can be written to parallel the PV = nRT form of the ideal gas equation: (P + an2/V2) (V − nb) = nRT a) For one mole of a van der Waals gas, derive an expression for the work done by a reversible and isothermal change in volume. In other words, evaluate the following integral for the van der Waals gas w = − {integral with limits from v1 to v2} PdV. b) What are physical interpretations of the van der Waals constants a and b? c) If for helium, the van der Waals constant b is equal to 2.43 × 10–5m3 mol-1, using this value for b, calculate the diameter of the helium atom.
Recall that the van der Waals equation of state—an extension of the ideal gas equation—attempts to better capture the behavior of real gases. It can be written to parallel the PV = nRT form of the ideal gas equation:
(P + an2/V2) (V − nb) = nRT
a) For one mole of a van der Waals gas, derive an expression for the work done by a reversible and isothermal change in volume. In other words, evaluate the following integral for the van der Waals gas
w = − {integral with limits from v1 to v2} PdV.
b) What are physical interpretations of the van der Waals constants a and b?
c) If for helium, the van der Waals constant b is equal to 2.43 × 10–5m3 mol-1, using this value for b, calculate the diameter of the helium atom.
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