What is the Entropy of a System with Doubly Degenerate Energy Level?

In summary, the conversation discusses an old book on elementary Statistical Mechanics that uses a system with one energy level that is doubly degenerate. However, the author does not provide an example of such a system and one person suggests thinking about spin 1/2 particles. Another person confirms that a spin 1/2 particle has a doubly degenerate energy level in the absence of a magnetic field and would have an entropy of k ln2.
  • #1
Philip Wood
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An old book I have on elementary Statistical Mechanics (Rushbrooke) uses as an especially simple case a system with one energy level. This level is doubly degenerate. The author doesn't give an example of such a system. Can anyone think of one? And would it have entropy [itex]k\ ln 2[/itex]?

[My thoughts turn to spin 1/2 particles but I'd like comment.]
 
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  • #2
Real systems tend to have more than two energy levels, but some are approximated as two level systems in certain situations.
 
  • #3
Philip Wood said:
My thoughts turn to spin 1/2 particles but I'd like comment.
Yes, a spin 1/2 particle has a doubly degenerate energy level in the absence of a magnetic field.
 
  • #4
DrC and TW. Many thanks for replying.

TW: would you, then, say that a spin 1/2 particle, viewed as a system, has an entropy of [itex]k\ ln2[/itex] in the absence of a magnetic field?
 
  • #5
Philip Wood said:
TW: would you, then, say that a spin 1/2 particle, viewed as a system, has an entropy of k ln2 in the absence of a magnetic field?
Yes.
 

What is entropy in a system?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic property that increases as the system becomes more disordered.

What is the significance of k ln 2 in the calculation of entropy?

k ln 2 is a constant term that is used in the calculation of entropy in a system. It represents the Boltzmann constant (k) multiplied by the natural logarithm of 2, which is a conversion factor used to relate energy to temperature.

How does the value of k ln 2 change in different systems?

The value of k ln 2 remains constant, regardless of the system. It is a fundamental constant in thermodynamics and is not affected by the specific characteristics of a system.

Can entropy be negative in a system?

No, entropy cannot be negative in a system. It is always a positive value or zero. A negative entropy value would indicate that the system is becoming more ordered, which goes against the definition of entropy as a measure of disorder.

How is the concept of entropy used in different scientific fields?

Entropy is a fundamental concept in thermodynamics, but it is also used in other scientific fields such as information theory and cosmology. It is a key factor in understanding processes and systems in these fields and plays a crucial role in various equations and calculations.

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