Quantum approach to latent heat

[Bassalisk]

Hello,

I am just curious. Latent heat and its characteristics are classical approach right? Its by all means classical?

Does quantum approach or something like that exists? Can anybody give me directions, or some terms...


Thanks

 

[marcusl]

Latent heat of fusion depends critically on chemical bond breaking and formation, and therefore is ultimately coupled to the quantum theory of bonding. I'm not much of an expert in this area but quantum chemistry books would be a good place to look.

Walter Harrison (a physicist) wrote a book called "Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond" that might be helpful.

 

[alxm]

I am just curious. Latent heat and its characteristics are classical approach right? Its by all means classical?

Only in the sense of "classical thermodynamics", but that's as-opposed-to statistical thermodynamics (which isn't at odds with classical thermo). It's got no particular dependence on mechanics, whether they be classical or quantum. So long as it's got energy.

Does quantum approach or something like that exists? Can anybody give me directions, or some terms...

Depends on what you mean by 'quantum'. You can just take the energy levels that you determined from solving the Schrödinger equation and stick that into the Boltzmann/Fermi-Dirac/Bose-Einstein distribution, or use it to construct a partition function, and use the tools of statistical thermodynamics without problems. There's of course the issue of fermion vs boson statistics, but that's about as far as it goes.

In practical terms, ΔH for a chemical reaction, at 0 K, is the electronic change in energy ΔE, plus the changes in zero-point vibrational energy, which you can approximate well enough from the second derivatives (Hessian) of the reactant/product energy with respect to nuclear coordinates and finding the fundamental vibrational frequency. (In simpler terms: Treating the interatomic bonds as a harmonic oscillator potential as far as vibrations are concerned) For finite temperature you need to calculate Cp, which you can do from a partition function constructed with a harmonic-oscillator+rigid rotor+ideal gas type partition function. That's usually accurate enough considering the typical errors in your quantum-mechanical calculation of ΔE (the S.E. not being analytically solvable and all that).

At higher temperatures you need a better potential function for your vibrational energies, and you also start to have to take into account vibrotational coupling, as well as vibronic coupling to the electronic states and all that. But that ultimately just means a more complicated partition function, nothing particularly quantum-mechanical about it.

 

[Bassalisk]

Wow, one weekend and will give this a thought with Hessian and second derivatives of multivariable calculus. Thank you VERY much for this info, I like challenges.

 

[marcusl]

alxm, I have to disagree. I think your view of vibrating bonds is off mark here. For a phase change (melting, for instance) to occur, bonds must be broken and reformed into a different substance--a solid ice crystal into individual H20 molecules, that is. This is a more complicated topic than you describe. Bonding at a microscopic level is the topic of quantum chemistry and statistical mechanics.