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Q.

The root mean square velocity of the molecules in a sample of helium is(5/7) times the root mean square velocity of the molecules in a sample of hydrogen at temperature 0^oC The temperature of helium is

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a

234^oC

b

6^oC

c

273^oC

d

100^oC

answer is B.

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Detailed Solution

V_He= $\frac{5}{7} V_{H_{2}}; T_{H_{2}} = 0^{o} C$
To find T_He=? We Know that
$V_{rms} = \sqrt{\frac{3 RT}{M}}$
$\frac{V_{He}}{V_{H_{2}}} = \frac{5}{7} \sqrt{\frac{3 {RT}_{He}}{M_{He}}} x \sqrt{\frac{M_{H_{2}}}{3 {RT}_{H_{2}}}} = \frac{5}{7} \frac{3 {RxT}_{{He}_{}}}{M_{{He}_{}}} x \frac{M_{H_{2}}}{3 {RT}_{H_{2}}} = \frac{25}{49} \frac{T_{{He}_{}}}{4} x \frac{2}{273.15} = \frac{25}{49} T_{{He}_{}} = \frac{25 x 2 x 273.15}{49} = 278.72 K = {(278.72 - 273.15)}^{o} C = 5 . 57^{o} C ≅ 6^{o} C$

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