From this we can begin to guess at some of the properties of Tritanium. The equation which describes the energy needed to increase the temperature of a material is :
E = (specific heat capacity x mass x temperature increase) + (heat of fusion/kg x mass) + (heat of vapourization/kg x mass)
Unfortunately, in the case of Tritanium we know almost none of these numbers! For comparison, let's look at a block of Aluminium :
Density : 2,700 kgm-3
Specific Heat : 900 Jkg-1K-1
Melting Point : 933 K
Boiling Point : 2,740 K
Heat of Fusion : 399,903 JKg-1
Heat of vaporization : 10,874,101 JK-1
Room temperature assumed to be 293 K, the energy to boil a cubic metre of Aluminium would therefore be :
E = (900 x 8,100 x 2,447) + (399,903 x 8,100) + (10,874,101 x 8,100)
= 1.784 x 1010 + 3.239 x 109 + 8.808 x 1010
= 1.092 x 1011 Joules
Which is some 65.96 times lower than the energy required for Tritanium!
So, Tritanium must therefore have a much higher density, boiling point, heat of vaporization, heat of fusion, or specific heat than aluminium - or some combination of the five. Since we have never been given figures for these numbers, we can never know which it is. Assuming only one factor differed there are five possible answers :
Assuming that only the boiling point was different, Tritanium would have a boiling point of about 975,420 K.
Assuming the only the density was different, Tritanium would have a density of about 178,090 kg/m3. Over fifteen times the density of lead.
Assuming the only the specific heat was different, Tritanium would have a specific heat of about 358,650 J/kg/K.
Assuming the only the heat of fusion was different, Tritanium would have a heat of fusion of about 2.654 x 109 J/kg.
Assuming the only the heat of vaporization was different, Tritanium
would have a heat of vaporization of about 2.664 x 109 J/kg.
Boiling point is a potential candidate to be responsible for the higher energy, but the episode "The Arsenal of Freedom" indicates that the hull of the Enterprise-D can only withstand a few thousand degrees before sustaining serious damage. While I guess it's possible for a substance to melt at, say, 5,000 K and not boil until near 1,000,000 K, it doesn't seem very likely.
The remaining three are probably the best candidates - it seems fairly certain that Tritanium has a high specific heat, heat of fusion, or heat of vaporization. More likely, a combination of the three.
The above treats Tritanium as a single substance, but Michael Voelker
has pointed out that the episode "Rascals" confirms that Tritanium is an
alloy of some sort. The episode also reveals that the "molecular structure"
of some Tritanium had broken down, indicating that either one or more of
the elements exists in molecular form, or that there is a compound in there
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