Question

At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

• A. ${273}^{\circ }\text{C}$
• B. ${514}^{\circ }\text{C}$
• C. ${819}^{\circ }\text{C}$
• D. ${1012}^{\circ }\text{C}$

Answer 1

The correct option is C ${819}^{\circ }\text{C}$

Let $v_1$ be the r.m.s velocity at $\text{S.T.P}$ and $v_2$ be the r.m.s. velocity at unknown temperature $T_2$.
$\because v\propto \sqrt{T}$
$\Rightarrow \frac{v_1^2}{v_2^2}=\frac{T_1}{T_2}$
$\Rightarrow T_2=\left(T_1\right){\left(\frac{v_2}{v_1}\right)}^2$
$\Rightarrow T_2=\left(273\right)(2{)}^2$
$\Rightarrow T_2=1092\text{K}$
$\therefore T_2=(1092-273)={819}^{\circ }\text{C}$