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Calculate degrees of freedom in physics and chemistry

In this chapter those topics will be discussed:
freedom degree physics and chemistry definition, quadratic degrees of freedom in mechanics, degrees of freedom mastering physics, how to calculate degrees of freedom chemistry, degrees of freedom in chemical kinetics definition, degrees of freedom for diatomic molecule, and a fast view to degrees of freedom in biology.

Degree of freedom in physics and chemical kinetics is a scientific term used to specify how many independent ways in which an atom or molecule can take up energy?
It may be applied in biology as degree of freedom of knee or hand...etc

How to calculate degrees of freedom in physical chemistry?
To calculate the degree of freedom for a gas we need to specify two parameters:
first: number of parameters to specify system's configuration, i.e. orientation of atoms in the three dimensions of space, on space coordinates "x, y, and z".
second:the number of parameters to define physical phase or state of a system (pressure, and temperature for a monoatmoic gas)
A system of N independent particles, therefore, has the total of 3N degrees of freedom.

In kinetics:
for a diatomic molecule
    3N = 3 + 3 + (3N - 6)
by take in account the parameters:
Translation between (x, y, and z)
Rotation around (x, y, and z)
Vibration "increase degree of freedom"
in addition to Linear and Non-linear movements
which means that an N-atom molecule has 3N − 6 vibrational degrees of freedom for N > 2. In special cases, such as adsorbed large molecules, the rotational degrees of freedom can be limited to only one.

Examples to explain degree of freedom:
The mean energy per atom for each degree of freedom is the same, according to the principle of the equipartition of energy, and is equal to kT/2 for each degree of freedom (where k is the Boltzmann constant and T is the thermodynamic temperature). Thus for a monatomic gas the total molar energy is 3LkT/2, where L is the Avogadro constant (the number of atoms per mole). As k = R/L, where R is the molar gas constant, the total molar energy is 3RT/2.
In a diatomic gas the two atoms require six coordinates between them, giving six degrees of
freedom. Commonly these are interpreted as six independent ways of storing energy: on this
basis the molecule has three degrees of freedom for different directions of translational
motion, and in addition there are two degrees of freedom for rotation of the molecular axis
and one vibrational degree of freedom along the bond between the atoms. The rotational
degrees of freedom each contribute their share, kT/2, to the total energy; similarly the
vibrational degree of freedom has an equal share of kinetic energy and must on average have as much potential energy. The total energy per molecule for a diatomic gas is therefore
3kT/2 (for translational energy of the whole molecule) plus 2kT/2 (for rotational energy)
plus 2kT/2 (for vibrational energy), i.e. a total of 7kT/2.

Calculate freedom degree of correlation:
To calculate the degrees of freedom for a correlation, you have to subtract 2 from the
total number of pairs of observations. If we denote degrees of freedom by df, and the total
number of pairs of observations by N, then:
Degrees of freedom, df=N-2.
For instance, if you observed height and weight in 100 subjects, you have 100 pairs of
observations since each observation of height and weight constitutes one pair. If you want
to calculate the correlation for these two variables (height and weight), your degrees of
freedom would be calculated as follows:
Therefore, df=100-2=98

Calculate the degrees of freedom for the A times B interaction:
The AxB interaction has (nA - 1)*(nB - 1) degrees of freedom where there are nA levels of A
and nB levels of B.

Quadratic degrees of freedom
Also used in Newtonian mechanics to calculate the dynamics of a system. A degree of freedom Xi is quadratic if the energy terms associated to this degree of
freedom can be written as
    E = ai.Xi^2 + Bi.Xi.Y
where Y is a linear combination of other quadratic degrees of freedom.
example: if X1 and X2 are two degrees of freedom, and E is the associated energy:

Resources of degrees of freedom in physics and chemistry:
Calculate degree of freedom sheet.pdf
Gibbs free energy and freedom degree.pdf
Degree of freedom.ppt

Any help just PM me.
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