# Deegres of fredom in thermodynamics

1. Mar 18, 2012

### matematikuvol

In thermodynamics heat reservoir has a lot deegres of freedom. Can you tell me some examples of that deegres. Thx

2. Mar 18, 2012

### Alpha Floor

In physics the degrees of freedom of a given system are the set of values (called generalized coordinates, usually angles and/or distances) that uniquely determine the state of the system at any given time.

For example, a double pendulum has 2 degrees of freedom because by giving the angles of both pendulums you know exactly the state of your system at that time.

I don't know how to apply this concept (which is esentially a mechanical concept) to the thermodynamics of a heat reservoir. Maybe you're talking about state functions?

3. Mar 18, 2012

### vanhees71

I think matematikuvol refers to precisely the degrees of freedom you have specified, i.e., the microscopic degrees of freedom. In the most simple case you may consider the classical model of a monatomic gas, where a gas is described by a system of very many (noninteracting or at a higher degree of sophtification weakly interacting) point particles.

To specify the micro state of this system uniquely you need to give a point in a 6N-dimensional space. The most elegant way is to use the Hamiltonian formulation of mechanics, and then these 6N degrees of freedom are the 3N components of positions and 3N components of momenta for the particles.

Of course, nobody can ever write down all these phase-space coordinates, let alone calculate their time evolution since $N = \mathcal{O}(10^{24})$. Thus one uses averaged "macroscopic" variables like various densities (particle number, energy density etc.) to describe the most important observables of the system as a whole. This very roughly is the fundamental idea behind statistical physics.

4. Mar 19, 2012

### Andrew Mason

Thermodynamics uses "degrees of freedom" in the same sense the term is used in mechanics.

In the kinetic theory of gases "degrees of freedom" refers to the number of mechanical degrees of freedom that a molecule can have.

A monatomic gas can have 3 translational degrees of freedom: ie its motion at any given time is completely defined by its velocity in each of the x, y and z directions.

Diatomic and polyatomic molecules can also have vibrational and rotational degrees of freedom. So in addition to the three translational degrees of freedom they can have rotational and vibrational degrees of freedom. A diatomic atom will have one vibrational and two rotational degrees of freedom. However, for most molecules the vibrational mode will not be active at temperatures less than about 1000K (for reasons having to do with quantum mechanics), so most diatomic gases will have 5 degrees of freedom.

AM