PHY452H1S Basic Statistical Mechanics. Lecture 10: Continuing review of thermodynamics. Taught by Prof. Arun Paramekanti
Posted by peeterjoot on February 14, 2013
Peeter’s lecture notes from class. May not be entirely coherent.
Continuing review of thermodynamics
We have energy conservation split into two types of energy
In fig. 1 we plot changes that are adiabatic processes () and heating and cooling processes (with ).
Given a dimensionality of , a cyclic change is that for which we have
Such a cyclic process could be represented as in fig. 2.
Here we’ve labeled the level curves with a parameter , as yet undefined. We call the thermodynamic entropy, and say that
specifies the state of the system.
Example: Pushing a block against a surface with friction.
Considering two systems in contact as in fig. 3.
- Mechanical equilibrium.
requires balance of the forces
(Note the neglect of the sign here, the direction of the force isn’t really of interest).
- Thermal stability
We must have some quantity that characterizes the state of the system in a non-macroscopic fashion. The identity eq. 1.0.6 is a statement that we have equal temperatures.
We define temperature as
We could potentially define different sorts of temperature, for example, perhaps . Should we do this, we effectively also define in a specific way. The definition eq. 1.0.7 effectively defines this non-macroscopic parameter (the entropy) in the simplest possible way.
Cyclic state variable verses non-state variables
A non-cyclic process changes these, whereas a cyclic process takes back to the initial values. This is characterized by
This doesn’t mean that the closed loop integral of other qualities, such as temperature are necessarily zero
Note that the identification of follows from our definition
so that with we have
Graphically we have for a cyclic process fig. 4.
Irreversible and reversible processes
Reversible means that an undoing of the macroscopic quantities brings us back to the initial state. A counter example is a block on a spring as illustrated in fig. 5.
In such a system the block will hit gas atoms as it moves. It’s hard to imagine that such gas particles will somehow spontaneously reorganize itself so that they return to their initial positions and velocities. This is the jist of the Second law of thermodynamics. Real processes introduce a degree of irreversibility with
but not all