Latent Heat and Kinetic Energy
Latent heat isn't heat, it is energy released or absorbed during a constant temperature phase change. The kinetic theory of gasses has little to say about phase changes. (Which by definition involve liquids or solids and may or may not involve gasses, most often "not".) Claiming a phase change releases latent heat is false, an error of comprehension (or articulation). If I slowly accelerate a tank of gas, its kinetic energy increases with no increase in temperature. Temperature is a measure of kinetic energy, not the only measure of kinetic energy. (Which is obvious since you know that temperature doesn't increase as most solids at their melting point do not increase in temperature as heat energy is added to them.) In the broadest (most general) sense, latent energy is the energy difference between the two phases. So where it goes (or where it comes from) is in converting one phase to the other. The assumption here is one phase is lower in potential energy than the other. You may know that entropy is defined in terms of heat and temperature. In classical thermodynamics energy and entropy are two fundamental concepts, they are on equal footing. In statistical thermodynamics, energy is still fundamental, while entropy can be derived from the ensemble of possible states that a system can be in. Whoops! Too much! In the case of ice melting, the intermolecular bonds (mostly hydrogen bonding) are 'broken' (which means there are a lot fewer of them and they are (on average) weaker). The energy that was potential energy of the bonds becomes "kinetic" energy as chemists understand the term in this context. In this context (as contrasted with the kinetic energy of a bullet or a ballistic electron), the kinetic energy includes all of the energy of translation, rotation and vibration: the rotation of a molecule doesn't change its speed, nor do the movements of the two hydrogen atoms with respect to the oxygen atom - their bond to the central O atom can be looked at as a (coil) spring and they can stretch and bend that spring. Faster and greater spring movement occurs during melting. (The rotation of the H atoms also occurs but the energy required to spin a H atom about its bond is very small as bond energies go, so is generally neglected with little loss of accuracy; this wouldn't be true for bonds between larger groups, where rotation around the bond could require quite a bit of energy). So, in the isothermal melting of ice, the place where the energy is going is in these intramolecular movements. (intra = inside). And in the isothermal freezing of water, the place where the energy is coming from is these same intramolecular motions. There is no one unique definition of kinetic energy and another for potential energy. In a group of atoms or molecules, the 'potential' energy is 'internal' and kinetic is 'external' and yet if one focuses in on a single molecule, some of its potential energy is due to its movement (or movements of its parts), so what is and what is not k.e. or p.e. may change with the context. In fact, the basic laws of energy conservation may be K.E. + P.E = constant or K.E. = P.E. (which is often expressed as K.E. - P.E. = 0. These two approaches are embodied in Hamiltonian and LaGrangian Mechanics which are the two related but complimentary ways modern physics is expressed. The LaGrangian is L = T-V (where T is k.e. and V is p.e.) and the Hamiltonian is H = T + V. These are used in both classical Physics and in quantum Physics.