What Are Black Body Assumptions in Deriving Spectrums?

[spaghetti3451]

To derive the blackbody spectrum, we set up the situation by assuming that a cavity is in thermodynamic equilibrium with a heat bath.

My questions are:

1) Is the heat bath the black body?

2) Why is it called a blackbody?

3) Why does the cavity have to be in thermal equilibrium with the heat bath?

4) Where in the derviation of the spectrum are the assumptions of a heat bath and thermodynamic equilibrium and cavity incorporated?

 

[Drakkith]

I can't answer it all, but I believe they call it a black body because the object absorbs all electromagnetic radiation. There isn't actually something in real life that is a perfect black body, but it's useful to think of for the theory.

 

[Andy Resnick]

To derive the blackbody spectrum, we set up the situation by assuming that a cavity is in thermodynamic equilibrium with a heat bath.

My questions are:

1) Is the heat bath the black body?

2) Why is it called a blackbody?

3) Why does the cavity have to be in thermal equilibrium with the heat bath?

4) Where in the derviation of the spectrum are the assumptions of a heat bath and thermodynamic equilibrium and cavity incorporated?

It's important to know that blackbody radiation refers to the thermal equilibrium of an electromagnetic field; not a physical object. As a practical matter, the cavity is held at a fixed temperature, and the radiation is in thermal equilibrium with the cavity.

NIST has a lot of information about blackbodies:

http://www.google.com/url?sa=t&sour...sg=AFQjCNHQP5im9pBuWnK2S7Y_0Ys_AFkpJw&cad=rja

http://www.google.com/url?sa=t&sour...sg=AFQjCNEbsxOeLSV1gEse7GUJx_D3JCoTUQ&cad=rja

 

[Amok]

To derive the blackbody spectrum, we set up the situation by assuming that a cavity is in thermodynamic equilibrium with a heat bath.

My questions are:

1) Is the heat bath the black body?

No

2) Why is it called a blackbody?

A perfect black body absorbs all wavelengths of electromagnetic radiation.

3) Why does the cavity have to be in thermal equilibrium with the heat bath?

So you get constant temperature I would guess. You are working in a grand-canonical ensemble (it can't be canonical because the number of photons is not constant). I think you consider the cavity to be a closed thermodynamic system.

 

[spaghetti3451]

No

What then is the black body? And why would we need a heat bath?

A perfect black body absorbs all wavelengths of electromagnetic radiation.

So, how does that the body is black? Is the body black in reality?

So you get constant temperature I would guess. You are working in a grand-canonical ensemble (it can't be canonical because the number of photons is not constant). I think you consider the cavity to be a closed thermodynamic system./QUOTE]

Ok, I see! We use a heat bath so that the temperature of the cavity remains constant.
Further, how can the cavity be a closed thermodynamic system if it is absorbing and releasing matter and energy continuously. And why do can't we deal with the general case of non-uniform temperature?

 

[Amok]

What then is the black body? And why would we need a heat bath?

So, how does that the body is black? Is the body black in reality?

I guess it would be really black, the blackest of blacks. A body that doesn't absorb everything is usually referred to as a 'gray body'.

Ok, I see! We use a heat bath so that the temperature of the cavity remains constant.
Further, how can the cavity be a closed thermodynamic system if it is absorbing and releasing matter and energy continuously. And why do can't we deal with the general case of non-uniform temperature?

When you poke a hole in the ''box'' in order to see the black body emission, I guess the system isn't closed anymore and that's why you should poke only a very small hole in it. Honestly though, there's only so much I remember about statistical mechanics, but this subject is treated very thoroughly in most good statistical mechanics book.

 

[kloptok]

So, how does that the body is black? Is the body black in reality?

I guess it would be really black, the blackest of blacks. A body that doesn't absorb everything is usually referred to as a 'gray body'.

Not really, the "blackest" bodies we know of are probably stars, and they are not really black (the color black, that is). Just because it absorbs all incoming radiation doesn't mean that it doesn't emit any radiation, quite the contrary.

 

[epenguin]

When I googled for back body once I found there are companies that sell them.
I don't know how buoyant the market fr them is.

 

[Amok]

Not really, the "blackest" bodies we know of are probably stars, and they are not really black (the color black, that is). Just because it absorbs all incoming radiation doesn't mean that it doesn't emit any radiation, quite the contrary.

Now that you mention it a black body is supposed to absorb and then re-emit all radiation that falls upon it.