Thermodynamics
No TL;DR found
Abstract
Thermodynamics is the study of heat and temperature. One thing that makes thermodynamics hard (and generally unpopular) is all the damn variables. Everything is related and it's often tough to keep straight what is an independent and what is a dependent variable. We will do our best to write the dependent variables explicitly whenever possible. Another thing that makes thermodynamics hard is that we give new definitions to common words. Words like system, energy, work, heat, temperature, etc. have precise meanings in physics that do not always agree with their everyday meanings. For example, we defined temperature in terms of the number of states, not what you measure with a thermometer. So learning thermodynamics means unlearning some of your associations. Let's start by defining some concepts we will use a lot. We define a system as the thing we are observing or calculating properties of. The system is separated from the surroundings by a barrier. The barrier could be open, so matter and energy can pass through, or closed. For example, when we talk about doing work on a gas by moving a piston, the piston is usually part of the surroundings and the gas is the system. We could alternatively treat the whole gas/piston complex as the system, and our arm that pushes the piston as the surroundings. Or we could attach the piston to a weight, put a box around the whole thing and call the everything together the system. In such a case, where the surroundings have no influence on the system, we say the system is isolated. Energy we take to mean the internal energy of the system, stored in chemical bonds, or kinetic motion of the atoms. Generally, we won't include in energy the gravitational energy from the earth or nuclear energy within the atoms. We use the symbol E for energy, although sometimes U is used for internal energy. Quantum mechanically, energy is the expectation value of the Hamiltonian; classically it is the value of the (classical) Hamiltonian. I like to use " for energies for individual molecules (microscopic energy) and E for macroscopic energy. An important constraint on energy is