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Question

Find the temperature at which molecules of oxygen gas have the same rms speed as that of Helium atoms at 240 K.
{Molecular mass of O2=32 g/mol & He=4 g/mol}


A
1920 K
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B
2400C
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C
24 K
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D
758.95 K
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Solution

The correct option is A 1920 K
RMS speed of a molecule of mass M is given by
Vrms=3RTM
RMS speed of oxygen is given by (VO2)=3RTO2MO2 ......(1)
RMS speed of helium gas (VHe)=3RTHeMHe ......(2)
Given that, RMS speed of oxygen gas and helium gas are same.
So, equating (1) and (2), we get
3RTO2MO2=3RTHeMHe
TO2MO2=THeMHe
TO2=THe×MO2MHe=240×324=1920 K
Thus, option (a) is the correct answer.

Physics

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