#### Astro commander

##### 2nd Lieutenant

In another thread it was questioned if Kilrah would still be so glowing hot if it exploded. This was brought up based on a painted planet I did which had a glowing core.

I showed the planet to my wife and she said it should be brighter at the core, more white, but I argued it exploded and was cooling so a nice yellow should be hot enough (blackbody yelloow is around 4000K depending on your eye's interpretation of blackbody spectra charts) But she countered that it exploded, which is absurd, but accepting that the core had to have gotten really hot and so thats a lot of thermal energy to dissapate. Then in this thread, it was questioned again.

So first to a chat on this topic

Yet I wanted to play and do a back of the napkin calc however woefully inadequat it would be.

If we assume

Mass Kilrah = mass earth = 6x10^24 Kg

Core is iron

Mass iron 55.8g/mol

heat capacity is 25.1J/mol*k or 450J/kg*K

Thermal mass of kilrah is 2.68 10^27 J/K

Area earth=area Kilrah = 5 10^8 km^2

boiling point of iron is 3134K so we assume that is the hottest Kilrah could be after it exploded.

Then we calcuate the energy necessary to chagne 1 degree kelvin

Q(J)=C(3x10^27 J/K)*DeltaT(1degree K)

Q=3 10^27 J to cool 1 deg Kelvin

Then using stefan-boltzman we calculate power radiated at a given temprature say T=3000K due to some explosive cooling, this is below the boiling point and we will assume no boiling or other mechanism for cooling, also ignore the suns minimal heating.

Power(W)=sigma(5.67 x10^-8 W/m2 K4) *T^4 *Area

Power(W)~8 x 10^17 Watts or J/s

Then 3x10^27 J / (8 10^17 J/s) = 3.7billion seconds or => 118 years to cool 1 degree Kelvin.

If I made a math error in there please correct.

But yea Billions of years to cool seems reasonable.

And yes there are lots of caveats as the link above points out since they look at a lot more factors. But basic blackbody suggests this will take a long time to cool in vacuum. That was fun, I hope it isnt too innacurate.