Compute the temperature at which the rms speed of nitrogen molecu… - Vidyadip

Question

Compute the temperature at which the rms speed of nitrogen molecules is $831 \mathrm{~m} / \mathrm{s}$. [Universal gas constant, $\mathrm{R}=8310 \mathrm{~J} / \mathrm{kmol} \mathrm{K}$, molar mass of nitrogen $=28 \mathrm{~kg} / \mathrm{kmol}$ ]

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Answer

Data : $v_{\mathrm{rms}}=831 \mathrm{~m} / \mathrm{s}, \mathrm{R}=8310 \mathrm{~J} / \mathrm{kmol} . \mathrm{K}$,
$\mathrm{M}_0=28 \mathrm{~kg} / \mathrm{kmol}$
$
\begin{aligned}
v_{\mathrm{rms}}^2 & =\frac{3 R T}{M_0} \\
\therefore T & =\frac{1}{3} \cdot \frac{M_0 v_{\text {rms }}^2}{R}=\frac{(28)(831)^2}{3(8310)} \\
& =\frac{28 \times 831}{30}=776.5 \mathrm{~K}
\end{aligned}
$
This is the required temperature.

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