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md2011-05-note_Part_2

md2011-05-note_Part_2 - C E NVT I In canonical ensemble the...

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Unformatted text preview: C E ( NVT ) I In canonical ensemble the system is closed, but not heat-isolated. I Instead, it is immersed in a large heat bath. I Now the occupation probabilities follow the Boltzmann distribution: p i = 1 Q e- E i / ( k B T ) = e-( E i- A ) / ( k B T ) . (3) I Normalizing factor, Q , is the partition function of the canonical ensemble: Q ( N , V , T ) = e- β A ( N , V , T ) , β ≡ 1 / k B T . (4) Notes I Helmholtz free energy, A , measures the useful work obtainable from an NVT system: A ≡ U- TS . (5) I All other thermodynamic quantities are directly accessible from A . For example: I Entropy is S = - ∂ A ∂ T V , (6) I and pressure is P = - ∂ A ∂ V T . (7) I Gibbs free energy is G = A + PV . Notes G C E ( μ VT ) I In grand canonical ensemble, the constraints are chemical potential μ , volume V and temperature T . I In other words, the system is inside a heat bath with “leaky” walls which let particles through....
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md2011-05-note_Part_2 - C E NVT I In canonical ensemble the...

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