Spontaneous process; reverse would never be observed, why ?? Entropy and disorder Consider an isothermal, free expansion of an ideal gas; V1  2V1 Spontaneous process; reverse would never be observed, why ?? Consider the statistical probabilities of final states

(a) Case 1: only 2 gas molecules Probability that both molecules are on left side:

(b) Case 2: 3 gas molecules 1 2 1 1 3 3 2 2 1 1 Probability that all molecules are on left side:

(c) Case 3: 4 gas molecules 1 3 4 1 2 3 6 1 2 3 4 1 3 2 4 2 4 1 1 Probability that all molecules are on left side:

For 1 mole of gas, probability that all molecules are on left side: Equal numbers of molecules in each half is the most probable Boltzmann: “microstates” ratio of probabilities