12.2Entropy
Section · module m68817Read §12.2 at OpenStax ↗
Study this section
Written from the section, each card quoting the span it came from. The ones you miss come back sooner.
What this needs
Learn these first — this section will not make sense without them.
S = k ln W, and ΔS = k ln(Wf/Wi), require evaluating a natural log of a microstate count; the ‘Determination of ΔS’ example computes k·ln(6/1) directly, which is meaningless arithmetic to a student who has not met what ln does to a ratio.
What this touches
Algebra that turns up here. Not a blocker, but this is where you will see it used.
- Applies9.5Counting Principles
Counting the microstates available to N particles in n boxes as nᴺ (2⁴=16 for four particles in two boxes), then grouping them into distributions (six of the sixteen put two particles in each box), is the multiplication and combination counting the algebra course names — chemistry is where ‘how many arrangements are there’ turns into a physical entropy.
- Applies9.7Probability
The probability of a given distribution (6/16, i.e. 3/8, for the even split of four particles) is a plain favorable-outcomes-over-total-outcomes probability computed from the microstate counts just derived — the same ratio definition taught abstractly for coins and cards.