Entropy: Does Disorder Really Measure Order?

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SUMMARY

Entropy is fundamentally a measure of energy distribution rather than disorder, as illustrated by the comparison between a dirty room and a clean library, both occupying the same number of microstates. The equation S = k ln W demonstrates that while both environments have the same entropy, their perceived order differs. It is crucial to distinguish between total entropy and entropy density, as the library has lower entropy density due to fewer microstates per unit volume. This discussion clarifies that "order" does not equate to "low entropy" in thermodynamic terms.

PREREQUISITES
  • Understanding of the concept of microstates in statistical mechanics
  • Familiarity with the equation S = k ln W for entropy calculation
  • Knowledge of the distinction between total entropy and entropy density
  • Basic principles of thermodynamics and energy distribution
NEXT STEPS
  • Research the implications of entropy in statistical mechanics
  • Explore the relationship between entropy and energy distribution in thermodynamics
  • Study the concept of microstates and their significance in entropy calculations
  • Investigate real-world applications of entropy in various scientific fields
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Students of physics, thermodynamics enthusiasts, and anyone seeking to deepen their understanding of entropy and its implications in energy distribution and statistical mechanics.

Jaccobtw
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Homework Statement
How is entropy a measure of disorder?
Relevant Equations
S = k ln W
Let's say you have a very dirty small room room and a giant clean library (lots of organized books) and let's say these occupy the same number of microstates. The entropy according to this equation is the same for the library and the room. But one is more ordered than the other one. How does it make sense that entropy is a measure of disorder?? I hope this question makes sense.
 
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Jaccobtw said:
Homework Statement:: How is entropy a measure of disorder?
Relevant Equations:: S = k ln W

Let's say you have a very dirty small room room and a giant clean library (lots of organized books) and let's say these occupy the same number of microstates. The entropy according to this equation is the same for the library and the room. But one is more ordered than the other one. How does it make sense that entropy is a measure of disorder?? I hope this question makes sense.
What are your thoughts so far?

Is this question for schoolwork/homework, or a more general question? Thanks.
 
"Order = tidy" is not equivalent to "order = low entropy;" this inevitably comes up/arises in "life = order" arguments, and cannot be further from the actual facts of the matter.
 
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Jaccobtw said:
Homework Statement:: How is entropy a measure of disorder?
Relevant Equations:: S = k ln W

Let's say you have a very dirty small room room and a giant clean library (lots of organized books) and let's say these occupy the same number of microstates. The entropy according to this equation is the same for the library and the room. But one is more ordered than the other one. How does it make sense that entropy is a measure of disorder?? I hope this question makes sense.
Don't confuse total entropy with entropy density.
 
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Jaccobtw said:
Homework Statement:: How is entropy a measure of disorder?
It's better to think of entropy as the spreading of energy.
 
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Bystander said:
"Order = tidy" is not equivalent to "order = low entropy;" this inevitably comes up/arises in "life = order" arguments, and cannot be further from the actual facts of the matter.
Doesn’t life have low entropy?
 
haruspex said:
Don't confuse total entropy with entropy density.
Are you saying the library has lower entropy density than the room?
 
Jaccobtw said:
Are you saying the library has lower entropy density than the room?
Yes. The library has fewer microstates per unit volume.
 
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Jaccobtw said:
Doesn’t life have low entropy?
No.
 

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