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P 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. - Physics

Sum

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

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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

\[\sqrt{\frac{3 \times 8 . 3T}{0 . 002}} = 2 \times 1932 . 6\] 

\[ \Rightarrow T = 1200 \text {  K }\]

Concept: rms Speed of Gas Molecules
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 12 | Page 34
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