Question

I have been taught in chemistry that, the energy of a vibrational freedom is RT (ie, twice that of rotational/translational) The degree of freedom which I found in chemistry, for the vibrational degree of freedom was given by this - fvib=3N−frot−ftrans (where N is the number of atoms in the molecule) Now I was taught in Physics that...- Energy of ALL (including vibrational) degrees of freedom is (1/2)RT, BUT that the number of degrees of freedom FOR vibration to be fvib=2∗(3N−frot−ftrans) Now this is shocking and confusiong- Both seem to be implying the same when it comes to Internal energy calculation, In the case of calculations of Cv, Cp, and gamma

I am now really confused as I was taught that Cv=fR2,Cp=(f+2)R2
(They give different ans in the "phy"/"chem " interpretations.) Can anyone help me with this? Also, my thought on this was that it is energy that is twice and not degree of freedom, Though I still find plenty of sites with agreement on both these ideas Any help will appreciated.

Answer 1

The confusion arises from the different interpretations and approaches used in both Chemistry and Physics to calculate the energy and degrees of freedom in a molecule.

Both interpretations have their own valid uses depending on the context. When calculating internal energy and specific heat capacities, the Chemistry interpretation is used.

Step-by-step explanation:

The confusion arises from the different interpretations and approaches used in both Chemistry and Physics to calculate the energy and degrees of freedom in a molecule.

In Chemistry, the energy of a vibrational freedom is considered to be RT, which is twice that of rotational and translational energy. The number of degrees of freedom for vibration in Chemistry is given by fvib = 3N - frot - ftrans, where N is the number of atoms in the molecule.

On the other hand, Physics considers that the energy of all degrees of freedom, including vibrational, is (1/2)RT. The number of degrees of freedom for vibration in Physics is given by fvib = 2(3N - frot - ftrans).

Both interpretations are valid depending on the context and purpose of the calculation. When calculating internal energy and specific heat capacities (Cv, Cp), the Chemistry interpretation is used.

Cv = fR/2 and Cp = (f + 2)R/2, where f is the total number of degrees of freedom.