How do you find the degree of freedom for energy

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Discussion Overview

The discussion revolves around the concept of "degree of freedom" in relation to energy, particularly in the context of statistical mechanics and quantum mechanics. Participants explore how degrees of freedom relate to energy density and the implications for different systems, such as gases.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to determine the degree of freedom for energy and whether it varies depending on the context.
  • Another participant asserts that energy is a scalar with one degree of freedom, suggesting that the equipartition theorem may be relevant to the discussion.
  • A different participant mentions encountering a formula relating energy density to frequency and degrees of freedom, seeking clarification on the concept.
  • One reply indicates that the teacher's explanation likely pertains to microstates rather than degrees of freedom.
  • Another participant references a specific book, "Quantum Mechanics Demystified," and describes a formula related to energy density, frequency, and degrees of freedom.
  • One participant elaborates on the equipartition theorem, explaining that it applies to non-interacting gases and provides an example involving diatomic gases with multiple degrees of freedom.
  • There is a request for feedback on the referenced book's effectiveness in summarizing quantum mechanics concepts.
  • A later reply notes that the book may serve as a good reference but may not be suitable for initial learning.

Areas of Agreement / Disagreement

Participants express differing views on the definition and implications of degrees of freedom in relation to energy. Some agree on the relevance of the equipartition theorem, while others question the clarity of the initial inquiry and the teacher's explanation. The discussion remains unresolved regarding the precise interpretation of degrees of freedom in this context.

Contextual Notes

Some participants highlight the importance of citing sources when discussing concepts learned from external materials, indicating a limitation in the clarity of the initial inquiry due to a lack of references.

Storm Butler
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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).
 
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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)?
 


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.
 


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.
 


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


Storm Butler said:
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.
 


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.
 


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)
 


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.
 
  • #10


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
 

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