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Question

Question: At what temperature r.m.s. speed of air molecules doubles of that at N.T.P. is...

At what temperature r.m.s. speed of air molecules doubles of that at N.T.P. is

A

819°C

B

719°C

C

909°C

D

None of these

Answer

819°C

Explanation

Solution

vrmsTv_{rms} \propto \sqrt{T}Ž v12v22=T1T2\frac{v_{1}^{2}}{v_{2}^{2}} = \frac{T_{1}}{T_{2}}Ž v24v2=273T2\frac{v^{2}}{4v^{2}} = \frac{273}{T_{2}}

ŽT2=1092K=819CT_{2} = 1092K = 819{^\circ}C