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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.
Use R=8.314 JK-1 mol-1
Solution
Here,
Temperature of hydrogen gas, T = 300 K
Molar mass of hydrogen, M0 = 2 g/mol=0.002 kg /mol
We know,
\[C = \sqrt{\frac{3RT}{M_0}}\]
\[ \Rightarrow C = \sqrt{\frac{3 \times 8 . 3 \times 300}{0 . 002}}\]
\[ \Rightarrow C = 1932 . 6 {\text { ms }}^{- 1}\]
In the second case, let the required temperature be T.
Applying the same formula, we get
\[\sqrt{\frac{3 \times 8 . 3T}{0 . 002}} = 2 \times 1932 . 6\]
\[ \Rightarrow T = 1200 \text { K }\]
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