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From: hertz778@gmail.com (rhertz)
Newsgroups: sci.physics.relativity
Subject: Re: Want to prove =?UTF-8?B?RT1tY8KyPyBVbml2ZXJzaXR5IGxhYnMgc2hvdWxkIHRy?=
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Date: Wed, 20 Nov 2024 17:35:09 +0000
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On Wed, 20 Nov 2024 15:57:23 +0000, ProkaryoticCaspaseHomolog wrote:

> On Wed, 20 Nov 2024 14:46:05 +0000, rhertz wrote:
>
>> As I wrote before, the cavity NEVER reaches a steady state (thermal
>> equilibrium is just one possible goal to reach a steady state).
>>
>> 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).
>
> No, because the temperature of the foil rises until the power emitted
> equals 5 watts. Once that happens, no further increase of stored
> energy occurs.
>
> P = ε * σ * T^4
>
> Let us assume a 10x10x10 cm cube with surface area 0.06 m^3
> So 5 watts total power emitted means 83 watts/m^2
> Assume ε = 0.13
>
> Let T_i be 273 K
>
> 83 = ε * σ * (T_f^4 - T_i^4)
> 11,260,344,593 = (T_f^4 - 5,554,571,841)
> T_f = 274.8 K
>
> In other words, the temperature of the foil rises to 1.8 degrees
> above room temperature.
>
>> In physics, a steady state is a condition in which a system or process
>> does not change over time, or any changes are balanced out. This means
>> that the variables that define the system's behavior remain constant.
>> Some examples of steady states include:
>>
>> Bathtub with a running tap: After a while, the water level stabilizes
>> and the system is in a steady state.
>>
>> Thermal equilibrium: Two systems are in thermal equilibrium when they
>> are at the same temperature and there is no heat flow between them.
>>
>> In 72 hours none of these conditions are reached: No steady state nor
>> thermal equilibrium. The inner temperature increase constantly, due to
>> the accumulation of energy within the cavity.
>>
>> Regarding the orifice used to inject the laser beam, I always thought of
>> using a directional micro-glass window that reflects, internally, laser
>> hits.


I'm very surprised that you used the Stefan-Boltzmann law here.

I studied the history of quantum physics until the Planck's
breakthrough, and in 2019 I wrote this entry on my blog (which I only
used one more time):


Thermal Radiation, Black Body Theory and the Birth of Quantum Physics

https://physictheories.blogspot.com/2019/

**************************************************

EXCERPT:

Stefan-Boltzmann Law of Thermal Radiation

The experimental studies of Tyndall (1863) translated to German by A.
Muller in his 1865 book, and the work of the French physicists Dulong
and Petit, inspired in 1879 to Joseph Stefan, who derived his law
stating that the heat radiation from a body is proportional to T⁴, with
T being its absolute temperature in Kelvin degrees.

The Stefan's law is:

j = 𝜎T⁴

where j is the emitted power per unit area, 𝜎  a the Stefan's constant
and T the temperature of the surface of the body, measured in Kelvin
degrees (273.15 + ºCelsius). The transformation of ºK in ºC was a
critical step of Stefan's theory, when using the experimental data of
Tyndell.

Stefan estimated the constant 𝜎 value as 4.5E-08 Watt/m²/K⁴, using
available rates of emission of energy (cal.cm-2.min-1) and emissivity
(which had a wide dispersion), and used it to calculate the temperature
of the Sun's surface, obtaining an average of 5,700 K, close to the
current value of 5,778 K. Modern value of  𝜎 is 5.67E-08 Watt/m²/K⁴.

Stefan's law has been applied to a wide range of problems, in particular
at astrophysics, where it's used to calculate the temperature of stars
based on their luminosity and stellar radius, treating them as black
bodies.

Even when proved to be very useful, even today, it didn't solve the
Kirchoff's theorem about J(λ,T) because his formula only depends on the
absolute temperature T.
************************************************

The Stefan-Boltzmann Law can be derived from Planck's Law of Spectral
Intensity, by using the following integral:


      ∫x³/(eˣ-1) dx = π⁴/15  , between 0 and infinity

by making x = (hʋ/kT)

************************************************


This law has been used for almost 160 years to calculate the temperature
of star's surfaces, ASSUMING that they behave as a black body IN THERMAL
EQUILIBRIUM (ironically).

This IS NOT the case of the cavity under discussion, because its
temperature increase with the permanent supply of energy, until it's
destroyed, partially or entirely.

And it could take months before the above situation happens.