The assumption made in statistical mechanics for quasi static changes is that a small quantity of work done on the system results in a small upward shift in energy levels, but a small amount of heat flowing into the system results in a small change in populations of (unchanged) energy levels.

A simple example: A particle (modelling an ideal gas) in a cuboidal box of side lengths 𝑎, 𝑏, 𝑐 can only have energies given by

$$E=\frac{h^2}{2m}\left(\frac{n_x^2}{a^2}+\frac{n_y^2}{b^2}+\frac{n_z^2}{c^2}\right)$$

$n_x, n_y, n_z$ are integers. If we do work slowly on the gas by pushing in a piston we reduce 𝑎, 𝑏 or 𝑐, so we increase the energy of any given level, as identified by a given set of integers $n_x, n_y, n_z$. We don't – according to a theorem of Ehrenfest – alter the populations of the levels.

But if we feed in heat we don't alter the shape of the box, so we don't alter the energy levels. But we do alter the distribution of particles in the various energy levels.

The assumption made in statistical mechanics for quasi static changes is that a small quantity of work done on the system results in a small upward shift in energy levels, but a small amount of heat flowing into the system results in a small change in populations of (unchanged) energy levels.

A simple example: A particle (modelling an ideal gas) in a cuboidal box of side lengths 𝑎, 𝑏, 𝑐 can only have energies given by

$$E=\frac{h^2}{8m}\left(\frac{n_x^2}{a^2}+\frac{n_y^2}{b^2}+\frac{n_z^2}{c^2}\right)$$

$n_x, n_y, n_z$ are integers. If we do work slowly on the gas by pushing in a piston we reduce 𝑎, 𝑏 or 𝑐, so we increase the energy of any given level, as identified by a given set of integers $n_x, n_y, n_z$. We don't – according to a theorem of Ehrenfest – alter the populations of the levels.

But if we feed in heat we don't alter the shape of the box, so we don't alter the energy levels. But we do alter the distribution of particles in the various energy levels.

The assumption made in statistical mechanics for quasi static changes is that a small quantity of work done on the system results in a small upward shift in energy levels, but a small amount of heat flowing into the system results in a small change in populations of (unchanged) energy levels.

The assumption made in statistical mechanics for quasi static changes is that a small quantity of work done on the system results in a small upward shift in energy levels, but a small amount of heat flowing into the system results in a small change in populations of (unchanged) energy levels.

A simple example: A particle (modelling an ideal gas) in a cuboidal box of side lengths 𝑎, 𝑏, 𝑐 can only have energies given by

$$E=\frac{h^2}{2m}\left(\frac{n_x^2}{a^2}+\frac{n_y^2}{b^2}+\frac{n_z^2}{c^2}\right)$$

$n_x, n_y, n_z$ are integers. If we do work slowly on the gas by pushing in a piston we reduce 𝑎, 𝑏 or 𝑐, so we increase the energy of any given level, as identified by a given set of integers $n_x, n_y, n_z$. We don't – according to a theorem of Ehrenfest – alter the populations of the levels.

But if we feed in heat we don't alter the shape of the box, so we don't alter the energy levels. But we do alter the distribution of particles in the various energy levels.