Relationship between Latent Heat of Fusion and Temperature
Does latent heat of fusion typically go up or down with temperature? I'm trying to calculate the amount of pressure needed to move the melting point of Thorium Dioxide up by 444 degrees kelvin using the Clausius-Clapeyron Law to see whether it would be feasible to line the combustion chamber of a scramjet burning Pentaborane (which burns at 4107°K, or 3834°C, in pure liquid oxygen, so probably a bit less in air, which has a lot of Nitrogen in it to steal Oxygen from the reaction, but this is probably a reasonably valid approximation given high enough pre-compression of the air since Pentaborane is ridiculously combustible) with the stuff to prevent the whole thing from melting. The idea is that at that temperature, anything other than an oxide is going to be oxidized by oxygen. When I use a constant value for Thoria's heat of fusion, I get a pressure on the order of 1 TPa, obviously too much. Lowering the temperature of the reaction is not a solution because that would lower the pressure generated in the combustion chamber and thus the specific impulse, which would be no fun.