Question 8

Number of molecules in a volume of $$4\,\text{cm}^3$$ of a perfect monoatomic gas at some temperature T and at a pressure of $$2\,\text{cm}$$ of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is $$4 \times 10^{-14}\,\text{erg}$$, $$g = 980\,\text{cm s}^{-2}$$, density of mercury $$= 13.6\,\text{g cm}^{-3}$$)

$$P = \rho g h = 13.6 \times 980 \times 2 = 26656\ \text{dyn cm}^{-2}$$

$$k_B T = \frac{2}{3}E_{\text{avg}} = \frac{2}{3} \times 4 \times 10^{-14} = \frac{8}{3} \times 10^{-14}\ \text{erg}$$

$$N = \frac{PV}{k_B T} = \frac{26656 \times 4}{\frac{8}{3} \times 10^{14}} = 39984 \times 10^{-14} \approx 4.0 \times 10^{18}$$

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