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Dazed&Confused
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Homework Statement
Consider ##n## moles of gas, initially confined within a volume ##V## and held at temperature ##T##. The gas is expanded to a total volume ##\alpha V##, where ##\alpha## is a constant, by a reversible isothermal expansion. Assume that the gas obeys the van der Waals equation of state $$\left ( p + \frac{n^2a}{V^2} \right )(V - nb) = nRT$$. Derive an expression for the change of entropy of the gas.
Show further that removing a partition and allowing a free expansion into the vacuum results in the temperature of the van der Waals gas falling by an amount proportional to
##( \alpha-1)/ \alpha ##.
Homework Equations
##dU = TdS - pdV ##
##dU = dQ + dW##
The Attempt at a Solution
Since the total energy for a van der Waals gas is a function of ##T## as well as ##V##, ##dU## is not 0 in the first process.
I need an extra piece of information but I'm not sure where to look.