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Translational partition function

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Title: Translational partition function  
Author: World Heritage Encyclopedia
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Subject: Rotational partition function, Statistical mechanics topics, Open statistical ensemble, Isoenthalpic–isobaric ensemble, Conformal field theory
Collection: Partition Functions
Publisher: World Heritage Encyclopedia

Translational partition function

In statistical mechanics, the translational partition function is that part of the partition function resulting from the movement (translation) of the center of mass. It is derived in the same way as the partition function for the canonical ensemble.

The translational component of the molecular partition function, q_T, of a molecule in a container may be described by q_T = \frac{V}{\Lambda^3} = V\frac{(2\pi mkT)^{\frac{3}{2}}}{h^3}, where \Lambda=h\sqrt{\frac{\beta}{2\pi m}} and \beta=\frac{1}{kT}.

Here, V is the volume of the container holding the molecule, \Lambda is the thermal wavelength, h is the Planck constant, m is the mass of a molecule, k is the Boltzmann constant and T is the temperature (in Kelvin).

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