Question

The r.m.s. speed of the molecules of a gas at ${100}^o$C is . The temperature at which the r.m.s. speed will be $\sqrt{3v}$ is

• A. ${546}^{o}C$
• B. ${646}^{o}C$
• C. ${746}^{o}C$
• D. ${846}^{o}C$

Answer 1

Answer: (D)

${846}^{o}C$

The rms speed of a gas is given by $c_{rms}=\sqrt{\frac{3RT}{M_0}}$.

Hence $c_{rms}\propto \sqrt{T}$.

Hence when the speed of molecules becomes $\sqrt{3}v$, the tempearture of gas must becomes thrice of the initial value.

Thus $T^{\prime }=3\times (100+273)$

$=1119K$

$={846}^{\circ }C$