How Does Black-Body Radiation Affect Thrust in a Two-Plate System in Vacuum?

[Methavix]

hi all,
i have this problem to solve.

there are 2 parallel plates in the vacuum, the first one (the secondary plate, for example on the left) is mechanically connected to the second one (the metal plate, on the right) with a little very hot cylinder in the center (it heats the second plate because are attached each other and emits photons in any direction for the black-body law). the second plate is very hot too (thank to the cylinder) and emits photons (black-body radiation) from both of its faces. i want to know the final thrust (o final momentum) of the structure (the component parallel to the central axes), considering all faces perfectly reflecting.

besides, if the left face of the second plate (that is the face in front of the first plate) is covered by a material perfectly absorbing what does it happen? what is the thrust or momentum? the second plate in that side doesn't emits photons? or it emits photons but when come back from the first plate it absorbs them?

at this address there is a simple scheme of the structure http://www.associazionemicene.it/reactor.jpg

thanks
--
Luca

 

[Jhero]

Dear Luca,

Thank you for sharing your problem with us. From your description, it seems like you are trying to determine the final momentum of a two-plate structure in a vacuum, where one plate is heated by a hot cylinder and both plates emit black-body radiation from their faces. You are also interested in what would happen if the left face of the second plate is covered by a perfectly absorbing material.

To solve this problem, we need to consider a few factors. First, we need to take into account the energy transfer between the two plates. As the hot cylinder heats the second plate, it will emit photons in all directions according to the black-body radiation law. This means that some of the photons will be directed towards the first plate, while others will be directed away from it. The photons that are directed towards the first plate will transfer some of their energy to it, resulting in a force acting on the first plate.

Next, we need to consider the effect of the perfectly absorbing material on the left face of the second plate. If the material is perfectly absorbing, it will absorb all the photons that hit it, resulting in a decrease in the total energy of the system. This means that the force acting on the first plate will be reduced compared to the case where the left face is perfectly reflecting.

To determine the final momentum of the structure, we can use the principle of conservation of momentum. This states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the only external force acting on the system is the force resulting from the energy transfer between the two plates. Therefore, we can calculate the final momentum by considering the initial momentum of the system (before the energy transfer) and the change in momentum due to the energy transfer.

In summary, to solve this problem, we need to consider the energy transfer between the two plates, the effect of the perfectly absorbing material, and the principle of conservation of momentum. I hope this helps you in your research. Best of luck!