At what temperature, RMS speed of air molecules is doubled of that at NTP?

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At what temperature, RMS speed of air molecules is doubled of that at NTP?

PhysicsKinetic Theory of GasesNEET

Options:

A $819 ° C$
B $719 ° C$
C $909 ° C$
D none of these

Solution:

2279 Upvotes Verified Answer

The correct answer is:

819 ° C

v_{rms} \propto \sqrt{T}

\Rightarrow \frac{v_{1}^{2}}{v_{2}^{2}} = \frac{T_{1}}{T_{2}}

\Rightarrow \frac{v^{2}}{4 v^{2}} = \frac{273}{T_{2}}

\Rightarrow T_{2} = 1092 K = 819 ° C

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