Question

A molecule has r.m.s speed of 550m/s at temperature of 20°c.what is its r.m.s speed at 80°c

Answer 1

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

At $20°C(293K)$ $v_{rms1}=\sqrt{\frac{3R\cdot293}{M}}$

At $80°(353K)$ $v_{rms2}=\sqrt{\frac{3R\cdot353}{M}}$

$\frac{v_{rms1}}{v_{rms2}}=\sqrt{\frac{293}{353}}\to v_{rms2}=v_{rms1}/\sqrt{\frac{293}{353}}=$

$=\frac{550}{0.911}=604m/s$