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)

$819{}^\circ C$

Answer 2

${{c}_{rms}}\propto \sqrt{T}$
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
$\sqrt{\frac{273}{T'}}=\frac{1}{2}$
$\frac{273}{T'}=\frac{1}{4}$
$T'=1092K=819{}^\circ C$