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 $v_{ rms }=\sqrt{\frac{3 R T}{M}} ;$ at $T=T_{0}$ (NTP)
$v_{ rms }=\sqrt{\frac{3 R T_{0}}{M}}$
But at temperature $T, v_{ rms }=2 \times \sqrt{\frac{3 R T_{0}}{M}}$
$\Rightarrow \sqrt{\frac{3 R T}{M}}=2 \sqrt{\frac{3 R T_{0}}{M}}$
$\Rightarrow \sqrt{T}=\sqrt{4 T_{0}}$
or $T=4 T_{0}$
$T=4 \times 273\, K =1092\, K$
$\therefore T=819^{\circ} C$