Please find the review attached with this message. Eq 84 (along with preceding equations) establish a formula for vibrational entropy but I can't seem to confirm the consistency of units. Please look through it.
I am not sure I understand your problem. The quasiharmonic entropy of Eq. (85) is obtained by differentiating the seond term of Eq. (84) with respect to T.
B has the unit of pressure, V_0 that of volume, and their product is an energy. 𝛼 has the unit of an inverse temperature, so 𝛼 squared times T is an inverse temperature. As a result, S_q has the correct unit of energy over temperature.
I agree with R. Monnier: B : J/m^3 V_0: m^3 alpha: 1/K T: K So, (J/m^3 )*m^3*(1/K)^2 *K= J/K i.e. units of entropy.
The equation of entropy that is shown by equation (85) is already consistent in unit. The unit of entropy is (JK-1). B as bulk modulus has a unit of (Pa = Nm-2) and the alpha = expansion coefficient has a unit of (K-1). Mathematically, we can find: that 9BVo(alpha2)T = (Nm-2)(m3)(K-2)(K) = (Nm)(K-1) = Nm/K. If we remember that Nm is equivalent with joule (J), so : S = 9BVo(alpha2)T has a unit of (JK-1).
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