Question

At what temperature, rms (root mean square) speed of air molecules is double of that at STP?

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

Answer 1

Answer: (A)

$v_{rms}\propto \sqrt{T}$
$\Rightarrow \frac{v_1^2}{v_2^2}=\frac{T_1}{T_2}$
$\Rightarrow \frac{v^2}{4v^2}=\frac{273}{T_2}$
$\Rightarrow T_2=1092K=819^{\circ }C$