Consider a gas contained in volume V at temperature T. The gas is composed of N distinguishable particles at zero rest mass, so that the energy E and momentum p are related by E = pc. The number of single-particle energy states in the range p to p + dp is [tex] 4\pi Vp^2 dp [/tex]. Find the equation of state and the internal energy of the gas and compare with an ordinary (ideal?) gas.(adsbygoogle = window.adsbygoogle || []).push({});

In how I understand the problem, you must integrate [tex] 4\pi Vp^2 dp [/tex] and [tex] E = pc [/tex] to get the partition function [tex] Z(E) [/tex] then use the entropy [tex] S = k_b ln Z [/tex] to get the equation of state given by

[tex] \left(\frac{\partial S}{\partial V}\right)_{N, E} = \frac{P}{T} [/tex]

and the internal energy by,

[tex] \left(\frac{\partial}{\partial E}\right)_{N, V} = \frac{1}{T}. [/tex]

Did I understand the problem correctly?

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# Homework Help: Finding the equation of state and internal energy of a given gas.

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