Problem 2.158

An ideal gas is under standard conditions. Find the diameter of the sphere within whose volume the relative fluctuation of the number of molecules is equal to \(\eta=1.0 \cdot 10^{-3} .\) What is the average number of molecules inside such a sphere?

Reveal Answer

\begin{aligned} &\text { 2.158. } d=\sqrt[3]{6 / \pi n_{0} \eta^{2}}=0.4 \mu \mathrm{m}, \text { where } n_{0} \text { is Loschmidt's num- }\\ &\text { ber; }\langle n\rangle=1 / \eta^{2}=1.0 \cdot 10^{6} \end{aligned}

Second law of thermodynamics, entropy