TESB Asteroid Vapourization Energy
While pursuing the Millenium Falcon through the Hoth system asteroid field, Star Destroyers were seen casually vaporizing ~40m wide asteroids with their trench-mounted turbolaser batteries. Some Federation cultists have been claiming that these asteroids were not actually being vapourized, but they apparently lack an understanding of Occam's Razor. The visual effects in TESB were completely consistent with vapourization, therefore the simplest theory that fits the facts is the theory that these asteroids were indeed vapourized. The rapidly dispersing gas cloud would quickly become invisible, as do most gases in space (except for those which are kept in a continual state of excitation by outside sources such as enclosed stars or black holes, eg. in a nebula).
Some Federation cultists have attempted to claim that Imperial turbolasers use an NDF reaction similar to the phaser reaction, but again they betray an ignorance of Occam's Razor. The NDF theory is a highly complex theory which is only necessary for phasers because of their extremely anomalous behaviour (see the phaser page). That anomalous behaviour renders conventional energy-transfer mechanisms useless as an explanation for phaser operation. However, blasters and turbolasers do not behave in this way; there are no incidents of turbolaser or blaster operation which are inconsistent with direct energy-transfer mechanisms. The Gra Ploven incident proves that turbolasers do vapourize matter, and there are no discussions of chain reactions or NDF in any of the official literature. Since Occam's Razor demands that we always look for the simplest theory that fits the facts, we are left with the conclusion that Federation phasers work on the NDF principle and turbolasers work on the conventional energy-transfer principle. Anyone who attacks the above distinction as "one-sided" is simply betraying an ignorance of Occam's Razor, and scientific methodology in general.
Now, since we can see the asteroids being vapourized in TESB, we can analyze the weapon layout on a Star Destroyer to see which weapons were used in this scene. The official cutaway diagrams and descriptions in SWICS demonstrate that their trench-mount batteries are actually small point-defense turbolasers, and that a Star Destroyer's heavy weapons are mounted in huge turrets flanking the dorsal superstructure. This incident can therefore be used to determine a conservative lower limit for the firepower of a Star Destroyer's light point-defense turbolasers.
A 40m diameter asteroid has a volume of 33,510 m³, assuming a generally spherical shape. In order to determine the energy required to melt the sphere, we must first know the density, melting point, initial temperature, specific heat, and latent heat of fusion for the asteroid.
Deep inside a typical asteroid field, typical asteroid compositions tend to be silicaceous and stony-iron rather than carbonaceous. Therefore, a reasonable estimate can be made of the energy requirement for vaporizing a typical asteroid by averaging silicon and iron.
It is reasonable to assume (in deep space, in the remote Hoth asteroid belt which was even farther from its sun than Hoth) that the starting temperature is roughly 150K. Therefore, we can derive a formula for melting energy in terms of the following material-specific quantities: density (r), melting temperature (Tmelt), specific heat (Cp), and latent heat of fusion (Hf). The formula follows:
Emelt = 33510·r·[(Tmelt-150)(Cp) + Hf]
Although pressure-shock functions will affect such a rapid phase-change and expansion (the entire process occurs in 1/15 second), they are neglected for the purpose of this analysis simply to be conservative. Therefore, there should be no significant temperature change between melting and boiling because the process occurs in deep space; the vapour pressure is near-zero, so ice will boil at 273.16K, iron will boil at 1810K, etc. (this has been experimentally verified with water in laboratory vacuum conditions, which DOES boil at 0.01 degrees Celsius). Therefore, the vaporization energy can be calculated solely on the basis of the material's latent heat of evaporation:
Evaporization = 33510·r·(Hfg)
Density is 2330 kg/m³, melting point is 1683K, and high-temp specific heat is roughly 650 J/(kg·K). Latent heat of fusion is roughly 1.65 MJ/kg. Latent heat of evaporation is roughly 10.58 MJ/kg. Figures taken from CRC Handbook of Chemistry and Physics 50th Edition and Fundamentals of Heat Transfer 3rd Edition by Incropera and Dewitt. Note that specific heat is not constant, and in fact rises with increasing temperature. The specific heat figures here are an average of the various values at differing temperatures.
Asteroid melt energy = 207 TJ
Asteroid vaporization energy = 826 TJ
Asteroid total energy = 1033 TJ
Density is 7870 kg/m³, melting point is 1808K, and high-temp specific heat is roughly 600 J/(kg·K). Latent heat of fusion is roughly 289 kJ/kg, and latent heat of evaporation is roughly 6.34 MJ/kg. Figures taken from CRC Handbook of Chemistry and Physics 50th Edition and Fundamentals of Heat Transfer 3rd Edition by Incropera and Dewitt.
Asteroid melt energy = 325 TJ
Asteroid vaporization energy = 1672 TJ
Asteroid total energy = 1997 TJ
Density is 900 kg/m³, melting point is 273.16K, specific heat is 2.1 kJ/(kg·K). Latent heat of fusion is roughly 335 kJ/kg. Latent heat of evaporation is roughly 2.25 MJ/kg. All figures taken from Machinery's Handbook 19th Edition.
Asteroid melt energy = 24 TJ
Asteroid vaporization energy = 68 TJ
Asteroid total energy = 92 TJ
By averaging the silicon and iron-based estimates, we can derive a 1500 TJ figure for the minimum energy requirements of vaporizing 40m asteroids which may be either silicaceous or stony-iron. This leads to a lower limit of 22,500 TW for a Star Destroyer's small point-defense trench-mount turbolasers. If size is proportional to power (an unsubstantiated but not unreasonable assumption), then the heavy dorsal turbolasers must therefore output at least 2.8 million TW.
Figures for ice are included only to inform and amuse. The TESB asteroids were clearly not ice. These figures are highly conservative for three reasons:
The fact that the asteroids were vaporized so quickly and completely is indicative of energy input greatly in excess of the minimum. The equations of state for the liquid-gas phase transition mean that significant kinetic energy was added to the mass as well as the aforementioned thermal energy. The fact that the entire energy input occurred in a mere 1/15-second, and that the energy propagated through the asteroid's body in 1/3 to 1/4-second, indicate that this quantity of energy should definitely be significant.
In reality there are a huge variety of process inefficiencies which would raise the energy requirement further. Heat transfer inside the asteroid body is negatively impacted by the non-homogeneous nature of the asteroid's chemical composition (which sets up countless heat transfer boundary conditions). Heat conduction through real-world substances is not instantaneous or even relativistic. The facing side of the asteroid will vaporize first, thus deflecting incoming energy and most likely causing the back half of the asteroid to vaporize through convective heating via contact with the superheated vaporized matter from the front side. All of these factors will tend to increase the actual energy requirement.
In nature, both iron and silicon tend to exist as ceramic compounds (hematite and silicon dioxide) rather than pure elemental metals. These ceramic compounds have much higher specific heats and much lower thermal conductivity than their pure-metal forms. For example, the specific heat for silicon dioxide is more than 60% larger than the specific heat for elemental silicon, and the thermal conductivity for silicon dioxide is 0.9% of the thermal conductivity for elemental silicon. Furthermore, these compounds decompose at high temperatures into their constituent elements, thus the equations governing elemental iron and silicon will still control the latent heats of evaporation.