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The velocity of 4 gas molecules are given by $1 \mathrm{~km} / \mathrm{s}, 3 \mathrm{~km} / \mathrm{s}, 5 \mathrm{~km} / \mathrm{s}$ and $7 \mathrm{~km} / \mathrm{s}$. Calculate
the difference between average and RMS velocity.
Options:
the difference between average and RMS velocity.
Solution:
2994 Upvotes
Verified Answer
The correct answer is:
$0.583$
The average velocity
$$
\begin{aligned}
v_{\mathrm{av}} &=\frac{v_{1}+v_{2}+v_{3} \ldots v_{n}}{N} \\
&=\frac{1+3+5+7}{4}=4 \mathrm{~km} / \mathrm{s}
\end{aligned}
$$
Root mean square velocity
$$
v_{\mathrm{rms}}=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+\ldots+v_{n}^{2}}{N}}
$$
$$
\begin{array}{l}
=\sqrt{\frac{1+(3)^{2}+(5)^{2}+(7)^{2}}{4}} \\
=\sqrt{21}=4.583 \mathrm{~km} / \mathrm{s}
\end{array}
$$
Difference between average velocity and root mean square velocity $=4.583-4$
$$
=0.583 \mathrm{~km} / \mathrm{s}
$$
$$
\begin{aligned}
v_{\mathrm{av}} &=\frac{v_{1}+v_{2}+v_{3} \ldots v_{n}}{N} \\
&=\frac{1+3+5+7}{4}=4 \mathrm{~km} / \mathrm{s}
\end{aligned}
$$
Root mean square velocity
$$
v_{\mathrm{rms}}=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+\ldots+v_{n}^{2}}{N}}
$$
$$
\begin{array}{l}
=\sqrt{\frac{1+(3)^{2}+(5)^{2}+(7)^{2}}{4}} \\
=\sqrt{21}=4.583 \mathrm{~km} / \mathrm{s}
\end{array}
$$
Difference between average velocity and root mean square velocity $=4.583-4$
$$
=0.583 \mathrm{~km} / \mathrm{s}
$$
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