Boltman's Constant

[PreMade]

I know what it is, but how would this knowledge be used on the mcat?

Also, in the Khan's video it gives the equation S = k ln(omega), I have no idea what that is.

I'm just trying to tie this conceptually.

https://www.khanacademy.org/test-pr...molecular theory of gas/v/boltzmanns-constant

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[chemist16]

Boltzmann's constant is the molecular version of the ideal gas constant. So PV=nRT reduces to PV=NkT when you're talking about N=number of molecules. It's pretty pervasive and whenever you use a formula where N appears, k also appears. It's also in Boltzmann's distribution, which gives the probabilities associated with different microstates of a system. More rigorously, the Boltzmann constant is the proportionality factor between the temperature a gas molecule is at and its kinetic energy.

The formula you just quoted is Boltzmann's famous equation that gives absolute entropy. However, it's really hard to calculate since omega is the weight associated with a given configuration. In simpler terms, it's the number of microstates accessible to the system. The basis for that equation is given in stat mech but you don't have to know that for the MCAT.

Conceptually, as you increase the number of microstates available to a system, the entropy increases. That's what the formula says.