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Prove that the pressure and the volume o...

Prove that the pressure and the volume of a degenerate electron gas are related by an equation similar to the Poisson equation, and find the adiabatic index `gamma=C_(p)//C_(v)`.

Text Solution

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The correct Answer is:
`PV^(5//3)="const";gamma=5//3`
Making use of the result of the previous problem, we obtain
`P=(2h^(2))/(5m)(3/(8pi))^(2//3)N^(5//3)V^(-5//3)`
which yields
`PV^(5//3)` = const
The ..adiabatic index.. is `gamma=5//3`.
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