Question

The temperature of the gas is raised from $27^\circ C\, to\, 927^\circ C$ the root mean square velocity is

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

Answer 1

The Correct Option is D

Root mean square velocity-at $T_1$ temperature
$\, \, \, \, \, \, \, U_1=\sqrt{\frac{3RT_1}{M}}=\sqrt{\frac{3R(27+273)}{M}}\, \, \, \, \, \, \, \, \, ...(ii)$
Root mean square velocity at $T_2$ temperature,
$\, \, \, \, \, \, \, U_2=\sqrt{\frac{2RT_2}{M}}=\sqrt{\frac{3R(927+273)}{M}}\, \, \, \, \, \, \, \, \, ...(ii)$
E (i) divided by E (ii)
$\, \, \, \, \, \, \, \frac{U_1}{U_2}=\sqrt{\frac{27+273}{927+273}}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =\sqrt{\frac{300}{1200}}=\frac{1}{2}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, U_2=2U_1$