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Second law of thermodynamics, entropy

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 η=1.0⋅10−3.\eta=1.0 \cdot 10^{-3} . What is the average number of molecules inside such a sphere?

Reveal Answer
 2.158. d=6/πn0η23=0.4μm, where n0 is Loschmidt’s num-  ber; ⟨n⟩=1/η2=1.0⋅106\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}
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