absolute entropy using partition function

The total number of particles in either state is simply the product of these probabilities with the total number of particles, allowing us to make the following sketch for the occupation numbers: We can first calculate the average number of particles in each state. According to the equations describing a closed system, the probability that a particle in the array occupies a state with energy is Meaning the partition function governing the entire array isĪn assertion we established earlier, with the proviso that the particles are distinguishable. What does this tell us about the macrophysical behaviour of the array? The single-particle partition function describing each particle in the web is

The terms up and down are just labels, used to give a pictorial means of telling one state from another the virtue by which the particles have energy needn’t be specified. When pointing upwards, a particle has energy, and when pointing downwards has energy. Imagine an array of particles, trapped in a Cartesian spider web, which can point either up or down. We will calculate how the occupation numbers, mean energy and entropy of the system vary with respect to changes in temperature. We’ll be using the equations describing a closed system of non-interacting, distinguishable particles, whose partition function is simply the single-particle partition function raised to the power of the number of particles in the system. As a gentle introduction to statistical mechanics, let’s consider the simplest possible set of microstates: a pair, with equal and opposite energies:

Absolute entropy using partition function