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

Answer: (D)

We have $v_{rms}=\sqrt{\frac{3RT}{M}};$ at $T=T_0$ (NTP)
$v_{rms}=\sqrt{\frac{3R{T}_0}{M}}$
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 $T=4T_0$
$T=4\times 273K=1092K$
$\therefore T=819^{\circ }C$