First slide

Rms speed

Question

The root mean square velocity of the molecules in a sample of Helium is 5/7th that of the molecules in a sample of Hydrogen. If the temperature of Hydrogen sample is 0 °C, then the temperature of the Helium sample is about

Moderate

A

6 ⁰C
B

0 K
C

273 ⁰C
D

100 ⁰C

Solution

$\large {\left( {{V_{rms}}} \right)_{He}}\, = \,\frac{5}{7}{\left( {{V_{rms}}} \right)_H}$
$\large \sqrt {\frac{{3R{T_{He}}}}{{{M_{He}}}}} \, = \,\frac{5}{7}\sqrt {\frac{{3R{T_H}}}{{{M_H}}}} \, \Rightarrow \,\frac{{{T_{He}}}}{4}\, = \,\frac{{5 \times 5}}{{7 \times 7}} \times \frac{{273}}{2}$
$T_{He} = \frac{50}{49} \times 273 = 278.57 K ≃ 6 {}^{0}C$

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