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The velocity of 4 gas molecules are given by1 / \mathrm{km} / \mathrm{s}, 3 \mathrm{~km} / \mathrm{s}, 5 \mathrm{~km} / \mathrm{s} and 7 \mathrm{~km} / \mathrm{s}. Calculate the difference between average and rms velocity-

Option: 1

0.338


Option: 2

0.438


Option: 3

0.583


Option: 4

0.683


Answers (1)

best_answer

The average velocity

\begin{aligned} v & =\frac{v_1+v_2+v_3+\ldots+v_n}{n} \\ & =\frac{1+3+5+7}{4} \\ & =4 \mathrm{~km} / \mathrm{s} \end{aligned}

Root square mean velocity,

\begin{aligned} v_{\text {rms }} & =\sqrt{\frac{v_1{ }^2+v_2{ }^2+v_3{ }^2+v_4{ }^2-\cdots+v_n{ }^2}{n}} \\ & =\sqrt{\frac{1+3^2+5^2+7^2}{4}}=\sqrt{21}=4.583 \mathrm{~km} / \mathrm{s} \end{aligned}

Difference between average velocity and root square velocity=4.583-4=0.583Km/s

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