Canonical ensemble Definition and 58 Threads

  1. M

    How Can I Calculate Internal Energy Using Grand Canonical Ensemble Method?

    Homework Statement To calculate internal energy for a system of non interacting S.H.O's in 1 dimension at constant T & u(chem potential) using grand partition function The Attempt at a Solution L(Grnd prtition fn)= Summation(z^N)*[Z(TVN)] where z = fugacity , Z = partition fn of...
  2. P

    Canonical Ensemble: Partition Function & Free Energy

    Is it true that partition function for canonical ensemble is Z=\sum_{\{states j\}}e^{-\beta E_j}=e^{-\beta F} where F is Helmholtz free energy?
  3. E

    Canonical Ensemble Homework: Equal Probabilities Postulate

    Homework Statement In the canonical ensemble, the probability that a system is in state r is given by P_i = \frac{g_i \exp (-\beta E_i)}{\sum_i g_i \exp( -\beta E_i)} where g_i is the multiplicity of state i. This is confusing me because I thought P_i = \frac{g_i}{\sum_i g_i} = states...
  4. J

    How Does the Grand Canonical Ensemble Determine Site Atom Occupancy?

    Homework Statement Grand Canonical ensemble problem- A surface of N sites that can have 0,1,2 atoms. It costs no energy to adsorb an atom. Grand canonical problem therefore in contact with particle reservoir. Assume \mu chem potentiol and temp T. What is probability for site to be empty,1,or 2...
  5. T

    Derivation of Grand Canonical Ensemble from scratch?

    I've been studying and thinking about statistical physics for a couple days now... and what bothers me is the grand canonical partition function. Namely that for a system with fixed chemical potential and energy \epsilon_i the probability of having N_i particle in that state is proportional to...
  6. R

    Please help me to derive canonical ensemble

    Hey folks, I really need help setting up a canonical ensemble. I am using the einstein model and have an energy: E_\nu=A + \sum_{i=1}^{2N} \hbar\omega n_i+\sum_{j=1}^{N} \hbarh\omega n_j where A is some constant. Now, I need to build the partition function which I 'think' looks like...
  7. R

    How to Write a Canonical Ensemble for a System Using the Einstein Model

    Hi there, I have a system with the following energy using the einstein model: E_\nu=\sum_{i=1}^{2N} h\omega n_i+\sum_{j=1}^{N} h\omega n_j I need to set up a canonical ensemble for this. How would I write the partition function please?
  8. S

    When Should You Use the Grand Partition Function in Statistical Mechanics?

    I am taking a statictical mechanics course, and one thing bothers me. I am not sure when we should use the normal partition function (Z) and when the grand partition function (twisty Z). In particular, why can we not use grand partition function when we are considering the following system...
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