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The rms velocity of hydrogen is $\sqrt7$ times the rms velocity of nitrogen. If T is the temperature of the gas, then

$(a)\;T(H_2) = T(N_2)\qquad(b)\;T(H_2) > T(N_2)\qquad(c)\;T(H_2)<T(N_2)\qquad(d)\;T(H_2) = \sqrt7T(N_2)$

Can you answer this question?

$U_{rms} H_2 = \sqrt{\large\frac{3RT_1}{2}}$
$U_{rms} N_2 = \sqrt{\large\frac{3RT_2}{28}}$
$U_{rms} H_2 = \sqrt7\times U_{rms}N_2$
Or $\sqrt{\large\frac{3RT_1}{2}} = \sqrt7\times\sqrt{\large\frac{3RT_2}{28}}$
$\therefore \large\frac{T_1}{2} = \large\frac{T_2}{4}$
Or $T_2 = 2T_1$
$T_{N_2} > T_{H_2}$
Hence answer is (c)
answered Feb 13, 2014