Question

The R.M.S. velocity of hydrogen is $\sqrt{7}$ times the R.M.S. velocity of Nitrogen. If T is the temperature of the Gas, then

• A. $T_{H_2}=T_{N_2}$
• B. $T_{H_2}>T_{N_2}$
• C. $T_{H_2}<T_{N_2}$
• D. $T_{H_2}=\sqrt{7}\times T_{N_2}$

Answer 1

The correct option is C

$T_{H_2}<T_{N_2}$

$\sqrt{\frac{T_{H_2}\times M_{N_2}}{T_{N_2}\times M_{H_2}}}=\frac{\sqrt{7}}{1}=\frac{\mu H_2}{\mu N_2}$

$\Rightarrow \frac{T_{H_2}\times 28}{T_{N_2}\times 2}=7$ Or, $T_{H_2}=\frac{1}{2}{T}_{N_2}Hence{T}_{H_2}<T_{N_2}$