Today is the birthday of
- Evgeny Lifshitz (1915-1985).
Today’s Problem
The enclosed volume of a Crookes radiometer is spherical with a diameter of 8 cm. At room temperature (20\(^{\circ}\)C), and a typical pressure of 13 Pa, estimate the number of air molecules in the radiometer.
Answer
Using the ideal gas law, \(PV=nRT\) where \(R=8.315\,\text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\), we can get the number of moles, \(n=PV/(RT)\)
\[n = \frac{(13\,\text{J}\cdot\text{m}^{-3})(\frac{4}{3}\pi(0.08\,\text{m})^3)}{(8.315\,\text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1})(273.15\,\text{K}+20\,\text{K})} = 1.14\times 10^{-5}\,\text{mol} = 11.4\,\mu\text{mol}\]
So the number of air molecules is
\[(1.14\times 10^{-5}\,\text{mol})(6.022\times 10^{23}\,\text{molecules/mole})=6.9\times 10^{18}\,\text{molecules}\]
© 2026 Stefan Hollos and Richard Hollos