Thermodynamics
Table of Contents
1. Introduction
Thermodynamics introduces new physical quantities (namely, temperature and heat). The first thing we need to do: construct an apparatus to measure temperature. A "thermometer", if you will. Towards that end, we need to introduce the zeroth law of thermodynamics.
1.1. Definition: Thermodynamic System, Environment
A Thermodynamic System (or just System) is a collection of matter and/or radiation, confined spatially by some barrier separating it from its Environment.
1.2. Definition: State Variables
We describe a thermodynamic system by means of certain physical quantities called State Variables.
- Extensive state variables are directly proportional to the size of the system. Examples: mass, energy, volume.
- Intensive state variables are not. Examples: density \(\rho\), temperature, hardness.
This division between intensive and extensive state variables make sense within thermodynamics, but clever people may invent quantities which are neither intensive nor extensive (e.g., the squareroot of volume).
1.3. Definition: Thermal Equilibrium
We will say a system is in Thermodynamic Equilibrium if its temperature is approximately the same everywhere within the system.
Different authors give different variations of the definition (e.g., the variance of the temperature is "small" compared to the mean temperature).
1.4. Zeroth Law of Thermodynamics
When two thermodynamic systems are in contact, they will eventually reach thermodynamic equilibrium.
If we have three thermodynamic systems (call them A, B, and C) such that A is in contact with B and B is in contact with C, then eventually they will reach thermodynamic equilibrium with one another. In particular, A will be in thermodynamic equilibrium with C.
Phrased differently, "is in thermodynamic equilibrium with" is a transitive relation.
1.5. Ideal Gas Law
Many physical systems may be approximated by the ideal-gas law:
\begin{equation} pV = nRT \end{equation}where:
- \(p\) is the pressure of the gas
- \(V\) is the volume of the gas
- \(n\) is the number of moles of gas
- \(R\) is the universal gas constant
- \(T\) is the temperature of the gas.
2. Statistical Mechanics
We can derive many results in thermodynamics using a "microscopic" or "molecular" perspective. This is precisely statistical mechanics. (We can also use computers and molecular dynamics nowadays — see, e.g., Rapaport's The Art of Molecular Dynamics Simulation.)
Most books will jump into quantum statistical mechanics, but there are a few which discuss classical derivations: Greiner, Huang, and a few others spring to mind.