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Suppose that a gas expands adiabatically into a vacuum.

(a) What is the work done by the gas?

(b) Suppose that the total energy of the gas is given by the van der Waals energy equation of state:

where a is a positive constant. Initially the gas occupies a volume V1 at a temperature T1. The gas then expands adiabatically into a vacuum so that it occupies a total volumeV2. What is the final temperature of the gas?

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