Re: Want to prove E=mc²? University labs should try this!

On Wed, 20 Nov 2024 22:04:22 +0000, rhertz wrote:

On Wed, 20 Nov 2024 19:57:18 +0000, ProkaryoticCaspaseHomolog wrote:
>

On Wed, 20 Nov 2024 18:37:40 +0000, rhertz wrote:

Do you see any error in my interpretation? I just reversed the entry of
power, taking it as power emitted by the reflecting surface. Maybe I'm
wrong, but I don't think so.

>
1) You multiplied to get 0.03927 Wm² (funky units!) instead of
   dividing to get 637 W/m².
2) I was using a cube geometry, not a sphere. So our numbers are going
   to differ by a substantial amount.
3) You should not be starting from absolute zero, but from room
   temperature.
4) Look at my original calculation, where part of my calculation is
   T_f^4 - T_i^4 since I am not starting from absolute zero.

>
I told you that it was the unit area (effective). You can't use 637 W/m²
because a surface of 1 m² doesn't exist. Only a surface 127 times
smaller exist, which is the inner area of the cavity.

A driver can be issued a speeding ticket for driving 80 miles/hour
despite not having driven for an hour. Why should it be impossible
to do the calculation because "a surface of 1 m² doesn't exist"?

Stefan used his formula first to calculate the temperature of the Sun,
with a HUGE effective area. He calculated the "radiant power" by
estimating it in terms of the Sun's luminosity, decades before Planck.
>
In that case (even when I disagree about using Kirchoff's black body
radiation), he obtained a surface temperature that SEEMED TO LET HAPPY
most astronomer of his epoch (and even today). Even IF it's FALSE.
>
But, as in many other things in science, if you had NOTHING, something
seemed to be useful and was adopted by 1870. Using such law, stars
temperatures were calculated using their relative luminosity. But NOBODY
was accountable for the errors, if such equation was/is FALSE.
>
Go close to a star or the Sun and MEASURE its temperature. You can't,
can you? It's THE SAME CRAP as using Planck's equation to measure the
CBR by the COBE/WMAP satellites and (curiously) getting a perfect match.
>
>
I think that it's incorrect to use Stefan's formula in this case. How do
you spread 5 Watts over 0.00785 m²? Using 637 W/m², the formula gives
325.6 K = 52.45 "C. This is not reasonable, because scaling down, it
would represent a STEADY STATE of 41,350 K for such small surface.
>
The Stefan formula is empirical, and doesn't scale down well. It was
developed for big surfaces.
>
Better to use calories, converting the loss of energy in Joules. Then
using an approximation of 1 calorie --> 1"C rise/gram of water, you
could have a better result.
>
>
Now, how do you propose to use Stefan with a surface of 0.00785 m² that
radiates 5 Watts of power?

I shouldn't have trusted *ANY* of your numbers. Where did you get
0.00785 m² as the surface area of your sphere? A 5 cm radius sphere
has a surface area of 0.031 m², so 5 W divided by the surface area
gives 159 W/m².
The question is now, what temperature T_f will result in 159 W/m²
GREATER radiant emittance (radiant flux per unit area) than the
radiant emittance of a room temperature ball?
I'll let you do the calculation. (I have a tendency to key things
wrong in my Windows calculator, as Paul has undoubtedly noticed
and has been kind enough not to point out.)
The important thing is that despite silly computational errors
on _both_ our parts, we can agree that your statement of
Wed, 20 Nov 2024 08:46 is false, where you wrote:
| "The stored energy increases constantly until the temperature of the
| cavity walls (not cancelled by any means) destroy the material that
| form the cavity (either coatings or places on the cavity surface,
| making holes)."
Since once it reaches steady state, the ball radiates as much power as
is being pumped in, there is no danger of the ball being destroyed, as
you claimed in earlier posts.
I have absolutely no idea what this scaling crap is to which you
refer. The Stefan-Boltzmann law is applicable to small surfaces
as well as large. It _DOES_ need to be modified for bodies that
are not black, by application of an empirical emmisivity term.