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# Thermodynamics

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Thermodynamics is the study of energy, its conversions between various forms, the ability of energy to do work, and the spontaneity of processes. It is closely related to statistical mechanics from which many thermodynamic relationships can be derived. It is not concerned with the concept of time, or that of rate of change (derivative in time). As a result, it has been suggested that this science should rather have been called thermostatics.

## The Laws of Thermodynamics

Alternative statements are given for each law. These statements are, for the most part, mathematically equivalent.

• Zeroth law: Considered to be more fundamental than the other three laws, it was not termed a law until after the others were already in use, hence the number 'zero'. There is some discussion about its status. Stated as:
• If each of two systems is in thermal equilibrium with a third system, all must be in equilibrium with each other.

• 1st Law: Is stated as follows:
• Energy can neither be created nor destroyed only changed.
• The heat flowing into a system equals the sum of change in internal energy plus the work done by the system.
• The work exchanged in an adiabatic process depends only on the initial and the final state and not on the details of the process.
• The sum of heat flowing into a system and work done by the system is zero.

• 2nd Law: A far reaching and powerful law, it can be stated many ways, the most popular of which is:
• It is impossible to obtain a process such that the unique effect is the subtraction of a positive heat from a reservoir and the production of a positive work.
• A system operating in contact with a thermal reservoir cannot produce positive work in its surroundings (Kelvin)
• A system operating in a cycle cannot produce a positive heat flow from a colder body to a hotter body (Clausius)
• The entropy of a closed system never decreases (see Maxwell's demon)

• 3rd Law: This law explains why it is so hard to cool something to absolute zero:
• All processes cease as temperature approaches zero.
• As temperature approaches to 0, the entropy of a system approaches a constant.

The three original laws have been humorously summarised as: (1) you can't win; (2) you can't break even; (3) you can't get out of the game.

## Basics

The following is a list of the major concepts in thermodynamics, together with the algebraic symbols used to represent them.

The rest of this discussion is about systems in equilibrium only. For nonequilibrium thermodynamics, see ...

### Substances describable by temperature alone

Blackbody radiation is an example. The reason why this is the case is because photon number isn't conserved. The state is completely described by its temperature except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase. given the internal energy as a function of temperature, we can define F=U-TS.

### Substances describable by temperature and pressure alone

Most "pure" nonmagnetic substances fall into this category. This state is completely described by its temperature and pressure, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase. Given U and V (or the density ρ) as a function of T and P, we can define the Helmholtz energy as before and the Gibbs energy as G=U-TS+PV and the enthalpy as H=U+PV.

### Substances describable by temperature, pressure and chemical potential

If there are more than one kind of atom/molecule, a substance would fall into this category. This state is completely described by its temperature, pressure and chemical potentials, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.

### Substances describable by temperature and magnetic field

If a substance is a ferromagnet or a superconductor, for example, it would fall into this category. It is completely described by its temperature and magnetic field, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.

## Thermodynamic Systems

A thermodynamic system is that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the surroundings. Often thermodynamic systems are characterized by the nature of this boundary as follows:

## Thermodynamic State

A key concept in thermodynamics is the state of a system. When a system is at equilibrium under a given set of conditions, it is said to be in a definite state. For a given thermodynamic state, many of the system's properties have a specific value corresponding to that state. The values of these properties are a function of the state of the system and are independent of the path by which the system arrived at that state. The number of properties that must be specified to describe the state of a given system is given by Gibbs phase rule. Since the state can be described by specifying a small number of properties, while the values of many properties are determined by the state of the system, it is possible to develop relationships between the various state properties. One of the main goals of Thermodynamics is to understand these relationships between the various state properties of a system. Equations of state are examples of some of these relationships.