Blundell Thermal Physics · Problem 21.2

Statistical mechanics of an ideal gas

Physics — Statistical Mechanics · sackur-tetrode-extensivity-gibbs-paradox

Problem

Show that

S

as given by eqn 21.37 (the Sackur–Tetrode equation) is an extensive quantity, but that the entropy of a gas of distinguishable particles is given by

S = Nk_{\rm B}\left[\frac{3}{2} - \ln(\lambda_{\rm th}^3/V)\right], \tag{21.44}

and show that this quantity is not extensive. This non-extensive entropy provided the original version of the Gibbs paradox.