# Entropy as number of microstates

1. Dec 19, 2014

### avito009

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?

2. Dec 19, 2014

### Staff: Mentor

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. Dec 19, 2014

### Khashishi

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.