Identify two systems for which it is essential to include a

Identify two systems for which it is essential to include a factor of 1/N! on going from q to Q (molecular to canonical partition function), and two which it is not. Qualitatively, how would you expect Q to \'behave\' with respect to a change in phase (say solid to gas -sublimation). (*Describe the phase transition and how it affects the available molecular motion*)

Solution

The factor is essential when we do not distinguish constituent particles even in classical systems. For example when we take a system of gas particles with smaller particle size this factor is essential. But if we take a system of large particles, for example a colloid, we may or may not distinguish the constituient particles. One can exclude the factor.

If interaction is taken into account in the hamiltonian(phase transition cannot happen if no particle interaction) then all the phases are described by the same partition function.

Phase transition can be of a large variety. For each phase transition one identifies an order parameter, which has a certain value, usually non-zero, in a phase (usually the ordered one, say liquid), and another value , usually zero, in the disordered phase(say gas). The change in this order parameter with the change of external conditions (say, change in temprature) is characterized by the phenomenon of phase transition.

Molecular motion reduces as the system goes to an ordered phase from a disordered one.