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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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Translational partition function