Well, if you take 10 Watts in one day, it delivers 864,000 Joules to the body. If you assume that thermal equilibrium is reached in 1 day,
then the equivalent mass:F(energy) would be 9.6*10-9 grams or aprox. 0.01 ugrams.
Assuming that I use Beryllium (emissivity = 0.18) coated with a black polymer (emissivity = 0.999), the body could absorb most of this energy.
With Beryllium melting point at 1,287°C, and assuming that a thermal equilibrium at the isolated system is reached at 27°C (300°K),
and using Stefan's Law:
j = T4 , with = 5.67x10-8 Watt.m-2.K-4
J = 4.59 Watts
So, the body would have a net absorption of 5.41 watts OR 476,424 Joules/day to mantain thermal equilibrium (while the laser is ON).
It gives an amount of 5.19 nanograms (using dm = dE/c2).
I'm wondering if this "gedankeexperiment" has any sense at all.
It's because I introduced a couple of fallacies, starting with "a-priori" assumption that dm = dE/c2 is valid.
This doesn't seem to make much sense at all.
What are you trying to do? If you want to measure the mass gained by a body due to heating, the last thing you want is a radiating system, because you will have a devil of a job working out how much heat has been lost, while you have been putting heat in. You want something that can be thermally isolated: a calorimeter, in fact. Don't you? Why use a laser and futz about with Stefan's Law and all the problem of radiative loss? You can heat it electrically.
And if you think the system comes to equilibrium at only 27C (2C above standard "room temperature"), what temperature are you assuming the block has when you start? Have you made a typo somewhere?
No, the predicted mass gain from thermal effects is too small to measure in practice, so I think you are barking up the wrong tree with this idea. You are far better off to consider the nuclear mass defect. Now that is something that confirms E=mc² in a very obvious and indisputable way.
Edited by exchemist, 06 May 2019 - 09:14 AM.