Question

Find the rms speed of hydrogen molecules in a sample of hydrogen gas at 300 K. Find the temperature at which the rms speed is double the speed calculated in the previous part.

Answer 1

Here,
Temperature of hydrogen gas, T = 300 K
Molar mass of hydrogen, M_​0 = 2 g/mol=0.002 kg /mol
We know,
$$\begin{gathered} C=\sqrt{\frac{3RT}{M_0}} \\ \Rightarrow C=\sqrt{\frac{3\times 8.3\times 300}{0.002}} \\ \Rightarrow C=1932.6{\mathrm{ms}}^{-1} \end{gathered}$$

In the second case, let the required temperature be T.
​Applying the same formula, we get

$$\begin{gathered} \sqrt{\frac{3\times 8.3T}{0.002}}=2\times 1932.6 \\ \Rightarrow T=1200\mathrm{K} \end{gathered}$$