For 10 points, identify this quantity, the sum of probabilities that a statistical mechanics system will be in a certain state that exists in 'canonical' and 'grand canonical' forms.
A. A. Zaitsev utilized a variational method to calculate this quantity for a lattice-gas model which was an improvement over the non-linear 'cavity method' developed by Bethe and Peirels. Â For dissociated species in solution, the ratio of the number of particles of the original species to the product of the numbers of ions is equal to the similar ratio of this quantity for the respective species by the(*) Saha equation. The van der Waals equation can be derived by multiplying together this quantity for each particle and then taking the volume derivative of the logarithm of that product. The internal energy of a system is given as the negative derivative of the log of this quantity with respect to the Boltzmann factor and the Helmholtz free energy is directly proportional to the log of this quantity. Â For 10 points, identify this quantity, the sum of probabilities that a statistical mechanics system will be in a certain state that exists in 'canonical' and 'grand canonical' forms.
A. A. Zaitsev utilized a variational method to calculate this quantity for a lattice-gas model which was an improvement over the non-linear 'cavity method' developed by Bethe and Peirels.
partition function