Question

At what temperature will the rms speed of air molecules be double that $NTP$?

• A. ${519}^{\circ }C$
• B. ${619}^{\circ }C$
• C. ${719}^{\circ }C$
• D. ${819}^{\circ }C$

Answer 1

The correct option is D ${819}^{\circ }C$

We have $v_{rms}=\sqrt{\frac{3RT}{M}}$; at $T=T_0\left(NTP\right)$

$v_{rms}=\sqrt{\frac{3R{T}_0}{M}}$

But at temperature $T,v_{rms}=2\times \sqrt{\frac{3R{T}_0}{M}}$

$\Rightarrow \sqrt{\frac{3RT}{M}}=2\sqrt{\frac{3R{T}_0}{M}}\Rightarrow \sqrt{T}=\sqrt{4T_0}$

Or $T=4T_0$

$T=4\times 273K=1092K$

$\therefore T={819}^{\circ }C$