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Grand Canonical Partition Function

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November 13th, 2022

For the grand canonical ensemble we’ve obtained two expressions for the pressure:

P = (k_B)(T)/Vln(x) or P = (k_B)(T)(dln(x))/dV_Bu,B

where is the grand canonical partition function. Check that the derivative does not give the first expression exactly. Nonetheless, the pressure calculated in the two ways agree – at least to any reasonable accuracy. Why? (HINT: consider what happens for a large system).

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