Entropy as number of microstates

  • Thread starter avito009
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  • #1
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Main Question or Discussion Point

As we know S=Q/T. And

Entropy is defined as number of microstates of a system. So does that prove that, the lower the temperature the more the microstates available?
 

Answers and Replies

  • #2
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You have to be careful with your equations. ##S=k~\ln(\Omega)## and for a reversible heat transfer ##dS=dQ/T##. So at a lower temperature it requires more transfered heat to make the same change in the log of the number of microstates.
 
  • #3
Khashishi
Science Advisor
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You are missing a derivative in your equation, avito, and also, you left off a logarithm in your definition of entropy.
The correct statement is, at lower temperatures, an increase in energy will generate a larger increase** in microstates than the same increase in energy at higher temperatures.

** because of the logarithm, the increase is measured multiplicatively. e.g., 2 is a bigger (multiplicative) increase over 1, than 3 is over 2.
 

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