Question

At what temperature is rms speed of air molecules double of that at NTP?

• A. $ 819{}^\circ C $
• B. $ 719{}^\circ C $
• C. $ 909{}^\circ C $
• D. None of these

Answer 1

Answer: (A)

$ {{c}_{rms}}\propto \sqrt{T} $
Or $ {{c}_{rms}}\propto \sqrt{273} $ ..(i)
Now consider that at temperature $ T', $ rms speed gets dubled,
therefore $ 2({{c}_{rms}})\propto \sqrt{T'} $ ... (ii)
From Eqs. (i) and (ii), we get
$ \sqrt{\frac{273}{T'}}=\frac{1}{2} $
$ \frac{273}{T'}=\frac{1}{4} $
$ T'=1092K=819{}^\circ C $