Question 611: Thermodynamics & KTG

Question

Six molecules of a gas in container have speeds $2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$, and $5 \mathrm{~m} / \mathrm{s}$. The r.m.s. speed is

Accepted Answer

$$ v_{	ext {rms }}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+-v_n^2}{n}} $$
r.m.s. speeds of the 6 gas molecules are given as $2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$ and $5 \mathrm{~m} / \mathrm{s}$.
$$ \begin{aligned} & \mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{2^2+5^2+3^2+6^2+3^2+5^2}{6}} \ & \mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}} \ & \mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{106}{6}} \ & \mathrm{v}_{\mathrm{rms}}=\sqrt{18}=3 \sqrt{2}=4.24 \mathrm{~m} / \mathrm{s} \end{aligned} $$

Answer

$4 \mathrm{~m} / \mathrm{s}$

Answer

$1.7 \mathrm{~m} / \mathrm{s}$

Answer

$4.24 \mathrm{~m} / \mathrm{s}$

Answer

$5 \mathrm{~m} / \mathrm{s}$

Thermodynamics & KTG

Six molecules of a gas in container have speeds 2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, and 5 \mathrm{~m} / \mathrm{s}. The r.m.s. speed is

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