Physical temperature and antenna temperature

[Unconscious]

I have read some documents on the subject, but until now, unfortunately, I still do not have a good understanding of them, most likely due to personal shortcomings that start from physics. In this regard, I would like to try here to expose some doubts that will almost certainly appear very stupid and basic, however I hope that someone has patience in helping me.

I refer to this document (if there is a better one, please tell me): https://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/current_lectures/L07_Noise.pdf

I start slowly, without immediately messing up an infinite number of questions. In the first paragraph I am told that a body at a physical temperature $T_P$, by the mere fact of being at that temperature, has a spectral density of energy (for now it is not even said that it is energy that manifests itself in the form of radiation electromagnetic towards the outside) which is constant and equal to $kT_P$, with k the Boltzmann constant having the value it has surely for deep physical reasons that I would not go into now. From here I immediately asked myself:

1. is it already an approximation? If this were not the case, every body would have infinite energy;

2. up to now, I have always translated in my head "a body is at temperature ..." with the picture "the average kinetic energy of the elementary constituents that compose it is equal to ...". Reading this document I am doubting that this picture is a bit too limited, because if I think of a star (towards which I can point an antenna) it does not seem reasonable to me that the physical quantity temperature should be interpreted as the average agitation of its elementary constituents, but more like something that is directly related to the total power it radiates (which I will have to worry about knowing how to measure, but for now I suppose I can).

If so, it almost seems that the only thing that has real physical significance is the total radiated power, thus saying that the temperature is that physical quantity that I define starting from the radiated power. And this confuses me, because it seems that you could have avoided this artificial construction and immediately speak in terms of power. What is the right way to see things? Thanks to those who want to try to help me on these simple matters.

 

[anorlunda]

It sounds like you should study the blackbody. Especially the part about a cavity with a hole. It starts with the idea of a container with walls at a certain temperature, and then continues with analysis of what happens to radiation bouncing off those walls. Eventually, the energy distribution of the radiation depends on the temperature of the walls. You can say that the energy distribution of light leaking out is an indirect way to measure the temperature.

https://en.wikipedia.org/wiki/Black_body#Idealizations

 

[Unconscious]

Thank you, I will read again with this in mind. Surely, I will come with other questions.

 

[tech99]

I have read some documents on the subject, but until now, unfortunately, I still do not have a good understanding of them, most likely due to personal shortcomings that start from physics. In this regard, I would like to try here to expose some doubts that will almost certainly appear very stupid and basic, however I hope that someone has patience in helping me.

I refer to this document (if there is a better one, please tell me): https://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/current_lectures/L07_Noise.pdf

I start slowly, without immediately messing up an infinite number of questions. In the first paragraph I am told that a body at a physical temperature $T_P$, by the mere fact of being at that temperature, has a spectral density of energy (for now it is not even said that it is energy that manifests itself in the form of radiation electromagnetic towards the outside) which is constant and equal to $kT_P$, with k the Boltzmann constant having the value it has surely for deep physical reasons that I would not go into now. From here I immediately asked myself:

1. is it already an approximation? If this were not the case, every body would have infinite energy;

2. up to now, I have always translated in my head "a body is at temperature ..." with the picture "the average kinetic energy of the elementary constituents that compose it is equal to ...". Reading this document I am doubting that this picture is a bit too limited, because if I think of a star (towards which I can point an antenna) it does not seem reasonable to me that the physical quantity temperature should be interpreted as the average agitation of its elementary constituents, but more like something that is directly related to the total power it radiates (which I will have to worry about knowing how to measure, but for now I suppose I can).

If so, it almost seems that the only thing that has real physical significance is the total radiated power, thus saying that the temperature is that physical quantity that I define starting from the radiated power. And this confuses me, because it seems that you could have avoided this artificial construction and immediately speak in terms of power. What is the right way to see things? Thanks to those who want to try to help me on these simple matters.

kTp is the power per unit bandwidth.
It is an approximation for low frequencies, up to Infra Red say. It does not agree with the spectral curves for optical and shorter wavelengths.