Question

At what temperature is the root mean square speed of $N_2$ gas equal to that of propane gas at STP?

• A. ${173.7}^{\circ }C$
• B. $173.7K$
• C. $273K$
• D. $-{40}^{\circ }C$

Answer 1

The correct option is B $173.7K$

According to formula of rms speed,

$U_{rms}=\sqrt{\frac{3RT}{M}}$

$U_{rms}\left(N_2\right)=U_{rms}\left(He\right)$

$\sqrt{\frac{3RT}{28}}=\sqrt{\frac{3R\times 273}{44}}$

$T=\frac{273\times 28}{44}=173.7K$

Temeperature is $173.7K.$