Relationship between Latent Heat of Fusion and Temperature

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SUMMARY

The discussion centers on the relationship between latent heat of fusion and temperature, specifically in the context of Thorium Dioxide (ThO2) and its application in scramjet combustion chambers. The user seeks to calculate the pressure required to raise ThO2's melting point by 444 Kelvin using the Clausius-Clapeyron Law. The analysis indicates that using a constant heat of fusion leads to impractically high pressure estimates of approximately 1 TPa, which is unfeasible for practical applications. The user emphasizes the importance of maintaining high combustion temperatures for optimal specific impulse while preventing material failure.

PREREQUISITES
  • Understanding of Clausius-Clapeyron Law
  • Knowledge of latent heat of fusion concepts
  • Familiarity with the properties of Thorium Dioxide (ThO2)
  • Basic principles of thermodynamics and combustion chemistry
NEXT STEPS
  • Research advanced applications of the Clausius-Clapeyron Law in material science
  • Investigate the thermal properties of Thorium Dioxide at varying temperatures
  • Explore alternative materials for high-temperature combustion chambers
  • Study the combustion characteristics of Pentaborane in different environments
USEFUL FOR

Engineers, material scientists, and researchers involved in high-temperature applications, particularly those focusing on scramjet technology and advanced propulsion systems.

nlieb
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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.
 
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