Physics Asked on May 14, 2021
Let’s take water for example. How can we calculate the heat (enthalpy) of vaporization from first principles?
The enthalpy of vaporization $ Delta H_v$ is
$$ Delta H_v = Delta U_v + pDelta V$$
where $Delta U_v$ is the increase in internal energy of the vapor phase over the liquid phase; in essence it is the energy required to overcome interatomic interactions when evaporating water. So the question becomes, how to calculate $Delta U_v$? Should we use something with the stiffness of water molecules or strength of hydrogen bonds?
Alternatively, you can view the enthalpy of vaporization as the heat that must be absorbed to accommodate the increase in entropy between the liquid and vapor states:
$$ Delta H_v = TDelta S_v$$
where the entropy of vaporization $Delta S_v$ is the increase in entropy of the vapor state over the liquid state. Using this approach, could we calculate $Delta S_v$ using approximations of entropy for the liquid and vapor state?
Are there any useful statistical mechanics equations to calculate entropy changes between a liquid and vapor state, especially from first principles? I imagine something like a partition function written for the liquid and vapor states would be a good starting point.
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