Question Involving Ideal Gas!
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Need help with Fermi Dirac Statistics/Bose Einstien Statistics Question Involving Ideal Gas!
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Need help with Fermi Dirac Statistics/Bose Einstien Statistics Question Involving Ideal Gas!
Need help with Fermi Dirac Statistics/Bose Einstien Statistics
Question Involving Ideal Gas!
Recall that one can show that for an ideal monatomic (and nonrelativistic) gas, p = 35. However, often one has to assume that, in equilibrium, the mean pressure on every wall of the rectangular container was the same. Now, you can prove that fact under rather general conditions. Proceed as follows: (a) Show that the mean pressure on the wall perpendicular to the direction is given by 2 2 P= = Σ Tr (er, 0, 3) 1²² (1²) ²₁ α,β) mV where the orbital r has energy and is specified by the quantum numbers na, ny, and n. (,,a, B) is the mean occupation number (in either FD, BE, or "fudged classical" statistics) of orbital r. Corresponding expresions hold for py and p.. (b) Assume that the temperature is high enough that a large number of orbitals are occupied. In that case, n, ny, and n, may be treated as continuous variables. Use this fact to rewrite p above as an integral over n, ny, and n. (This is the same manipulation we've done plenty of times here.)
Question Involving Ideal Gas!
Recall that one can show that for an ideal monatomic (and nonrelativistic) gas, p = 35. However, often one has to assume that, in equilibrium, the mean pressure on every wall of the rectangular container was the same. Now, you can prove that fact under rather general conditions. Proceed as follows: (a) Show that the mean pressure on the wall perpendicular to the direction is given by 2 2 P= = Σ Tr (er, 0, 3) 1²² (1²) ²₁ α,β) mV where the orbital r has energy and is specified by the quantum numbers na, ny, and n. (,,a, B) is the mean occupation number (in either FD, BE, or "fudged classical" statistics) of orbital r. Corresponding expresions hold for py and p.. (b) Assume that the temperature is high enough that a large number of orbitals are occupied. In that case, n, ny, and n, may be treated as continuous variables. Use this fact to rewrite p above as an integral over n, ny, and n. (This is the same manipulation we've done plenty of times here.)
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