Question

The temperature of the gas is raised from ${27}^{o}C$ to ${927}^{o}C$ , the root mean square velocity is:

• A. $\sqrt{927/27}$ times the earlier value
• B. same as before
• C. halved
• D. doubled

Answer 1

Answer: (D)

doubled

We know,

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

Now,

$U_{RMS}\left({27}^{0}C\right)=\sqrt{\frac{3R\times 300}{M}}$

$U_{RMS}\left({927}^{0}C\right)=\sqrt{\frac{3R\times 1200}{M}}$

Hence,

$U_{RMS}\left({927}^{0}C\right)=2\times U_{RMS}\left({27}^{0}C\right)$