B.4 · IB Physics
Entropy and microstates
Start with every particle in the left half, remove the partition and watch the gas spread. The chart shows how many microstates W belong to each left/right split, and the entropy S = k ln W of each.
W = N! / (n_L! (N − n_L)!)
S = k ln W
k = 1.38×10⁻²³ J K⁻¹
P(n_L) = W / 2ᴺ
Try this
- Set N = 4 and use the inspect slider: confirm W = 1, 4, 6, 4, 1, so the 2–2 split is six times as likely as all-left.
- Set N = 100, remove the partition and watch n_L settle and fluctuate near 50. Read off P for n_L = 100 to see why the gas never returns on its own.
- Compare S at the most probable split for N = 10 and N = 100 with N k ln 2: the agreement improves as N grows.
Exam tip: S = k ln W uses the natural logarithm, so an entropy change is ΔS = k ln(W_final / W_initial); when every microstate is equally likely, the most probable macrostate is simply the one with the largest W.