Planck's Radiation Law and Stefan's Law

[manofphysics]

I have got 2 questions:
1)In the derivation of Planck's Radiation Law,we assume an enclosure of perfectly reflecting walls which contains diffuse radiations.These are EM waves which reflect from the walls.
Now, in my book(or even http://thermalhub.org/topics/DerivationofPlancksLaw"), it is further said that standing waves are formed which limit the wavelength to
$$\lambda=2l/n_{i}$$.
Now why are ONLY standing waves formed ?Any type of wave can be formed after reflection from the walls.Why are taking the assumption that displacement at the end of walls is zero?

2)In the derivation of Stefan's Law as given by Boltzmann, why can we apply all the thermodynamic relation and thermodyanamic laws ? Does radiation behave exactly like a gas?
I know that pressure of diffuse radiation is similar to that exerted by a ideal gas, but I STILL can't understand how and why thermodyanmics is used in radiations?

 

[manofphysics]

I am disappointed . No reply after over 200 views.

I found out the answer myself.For all the people who didn't know,

1)This is due to Maxwell's boundary conditions at an interface.
$$E_{1}^{||}-E_{2}^{||}=0$$
where $$E_{1}, E_{2}$$ represent fields in air and conductor respectively.

2)As radiation occupies a finite space and exerts finite pressure, and hence can do work,
So we can apply thermodynamics in this case.

 

[astrokreng]

1) The assumption of perfectly reflecting walls and diffuse radiation is made in the derivation of Planck's Radiation Law in order to simplify the problem and make it more manageable. Standing waves are formed because they are the only type of wave that can exist in a confined space, such as an enclosure with reflecting walls. This is due to the boundary conditions at the walls, where the displacement must be zero in order to satisfy the requirement of perfect reflection. While other types of waves may be formed after reflection, they would not be able to exist in this confined space due to the boundary conditions. Therefore, standing waves are the only solution that can exist in this scenario.

2) In the derivation of Stefan's Law, we apply thermodynamic relations and laws because radiation behaves similarly to a gas in some ways. Just like a gas, radiation has properties such as temperature, pressure, and energy. Thermodynamics is used to understand and describe the behavior of radiation in terms of these properties. While radiation may not behave exactly like a gas, the principles and laws of thermodynamics can still be applied to understand its behavior. This allows us to make predictions and calculations about radiation, such as in the case of Stefan's Law which relates the energy emitted by a blackbody to its temperature.