How do you find the degree of freedom for energy

[Storm Butler]

How do you find the "degree of freedom" for energy

how can you find the degree of freedom for energy? would it always be the same or would it constantly be different according to where you are, if so then how do you find it or is it normally given to you (that is if you are doing a problem).

 

[maverick_starstrider]

I'm afraid I don't understand what you're asking. Energy has only one degree of freedom, it's a scalar. Perhaps you're referring to something like the equipartition theorem of statistical mechanics which dictates how energy IS A FUNCTION of the degrees of freedom of the system (i.e. translational, vibrational, rotational, etc)?

 

[Storm Butler]

im not sure all i know is that while reading a brief synopsis on energy and quantum mechanics i came across a formula that described energy density as frequency times the degrees of freedom, when i asked my teacher what this me and he told me it was the a number that when you add one to it you get all of the possible states or positions that it could be in(or something similar to that) and this wasn't very clear to me so i jwas just trying to get a better explanation and feel for the concept.

 

[maverick_starstrider]

If you could provide a link to where you saw this it would be helpful but your teacher's explanations seems to describe a MICROSTATE not a degree of freedom.

 

[Storm Butler]

ok ill try to find one and ill ask my teacher again and try writting down his explination

 

[ZapperZ]

im not sure all i know is that while reading a brief synopsis on energy and quantum mechanics i came across a formula that described energy density as frequency times the degrees of freedom, when i asked my teacher what this me and he told me it was the a number that when you add one to it you get all of the possible states or positions that it could be in(or something similar to that) and this wasn't very clear to me so i jwas just trying to get a better explanation and feel for the concept.

Take note that when a member mentioned anything about "reading something" or "hearing something" or "watched something", in this forum, we require full and complete reference to the source. Members of this forum will tell you that that is one of the first lessons they learn on PhysicsForums, which is to pay attention to the source so that they can make complete citation to it. Otherwise, we are going by hearsay from you, and there's no guarantee that what you interpret was done correctly.

Zz.

 

[Storm Butler]

o well the book that i was reading was Quantum Mecahnics Demystified, the equation came up in the first couple pages when talking about the Ultra violet catastrophe. I believe it was something similar to U(V,T) (v is frequency and t is temperature) where U is energy density and it is found by multiplying the average energy per degree of freedom by number of degrees for the frequency V.

 

[maverick_starstrider]

Oh, I actually have that book. What it's talking about is the equipartition of energy in a non-interacting gas (which is what I initially suspected you were talking about). A perfectly good explanation can be found here http://en.wikipedia.org/wiki/Equipartition_theorem. Basically the energy of a non-interacting gas is proportional to the number of degrees of freedom (for example a diatomic gas which consists of a bunch of particles each of which are 2 atoms joined by a spring have 7 degrees of freedom because the barbell looking atoms can move in 3 directions (x,y,z), rotate in 3 directions, and can also compress/extend the spring in between them. Thefore the energy of such a system is 7*(1/2nkT)

 

[Storm Butler]

o thank you for the link. Also, since you have the book, did you think that it did a good job of getting a general over view of the subject expressed properly as well as cover a decent amount of the basic math involved. Or do you think that it does a poor job trying to summarize the basic concepts of quantum mechanics.

 

[maverick_starstrider]

To be honest I can't really say. I only really picked it up after I already learned what it taught. It's great as a reference though although it may not be indepth enough for a first learning