Question

Calculate the most probable speed, average speed and the root mean square speed for
gas molecules at 300 K. The mass of gas molecule is 5 × 10−26 kg and
kB = 1.38 × 10−23 JK

Answer 1

Answer on Question #65325, Physics Molecular Physics Thermodynamics

Calculate the most probable speed, average speed and the root mean square speed for gas molecules at 300 K. The mass of gas molecule is $5 \times 10^{-26} \mathrm{~kg}$ and $\mathrm{kB} = 1.38 \times 10^{-23} \mathrm{JK}$

Solution:

Data:

$$T = 300{}^{\circ}K$$ $$m = 5 * 10^{-26} \mathrm{kg}$$ $$k = 1.38 * 10^{-23} \frac{\mathrm{J}}{\mathrm{K}}$$ $$(v) = \sqrt{\frac{8kT}{\pi m}} = \sqrt{\frac{8 * 1.38 * 10^{-23} * 300}{3.1415 * 5 * 10^{-26}}} = 459.19 \frac{\mathrm{m}}{\mathrm{s}}$$ $$v_{\text{most probable}} = \sqrt{\frac{2kT}{m}} = \sqrt{\frac{2 * 1.38 * 10^{-23} * 300}{* 5 * 10^{-26}}} = 406.94 \frac{\mathrm{m}}{\mathrm{s}}$$ $$\sqrt{(v^2)} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3 * 1.38 * 10^{-23} * 300}{* 5 * 10^{-26}}} = 498.4 \frac{\mathrm{m}}{\mathrm{s}}$$

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