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...
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...
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...
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...
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...
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?
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...