# What is the molar entropy of a system with 150000 microstates at a certain temperature?

##### 2 Answers

Use the formula

Where

Ω is the number of microstates that is 150,000

Plug in the variables

**Boltzmann's formulation of entropy** is given by:

#S = k_BlnOmega# where

#k_B = 1.38065 xx 10^(-23) "J/molecule"cdot"K"# is the Boltzmann constant.

If the system has

#S = 1.38065 xx 10^(-23) "J"/("molecule" cdot "K") ln(150000)#

#= 1.646 xx 10^(-22) "J/molecule"cdot"K"#

Using units that we're more familiar with...

#color(blue)(S) = 1.646 xx 10^(-22) "J"/(cancel"molecule" cdot "K") xx (6.0221413 xx 10^23 cancel"molecules")/"1 mol"#

#= color(blue)("99 J/mol"cdot"K")#

We don't really know what temperature this is at, but it is on the right order of magnitude. If this was at