All Problems Second law of thermodynamics, entropy
Problem 2.154
\(N\) atoms of gaseous helium are enclosed in a cubic vessel of volume \(1.0 \mathrm{~cm}^{3}\) at room temperature. Find: (a) the probability of atoms gathering in one half of the vessel; (b) the approximate numerical value of \(N\) ensuring the occurrence of this event within the time interval \(t \approx 10^{10}\) years (the age of the Universe).
2.154. (a) \(P=1 / 2^{N}\) (b) \(N=\frac{\log (t / \tau)}{\log 2} \approx 80,\) where \(\tau \approx 10^{-5} \mathrm{~s}\) is the mean time which takes a helium atom to cover distances of the order of the vessel's dimensions.