Question

The RMS velocity of H2 molecule at 27°C is 1930m/s the RMS velocity of O2 molecule at 1200K will be

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Rms Velocity of ${\sf H_2=1930\:m/s}$ temperature ${\sf (T_1)=27°C}$
• Temperature of ${\sf O_2}$ molecule 200K

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Rms Velocity of ${\sf (O_2)}$

$\color{darkblue}\underline{\underline{\sf Solution-}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\Large\color{violet}\bullet\underline{\boxed{\sf v\:\:\propto\:\:\sqrt{T}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\implies{\sf \dfrac{V_{H_2}}{V_{O_2}}=\sqrt{\dfrac{T_{H_2}}{T_{O_2}}}}$

$\implies{\sf \dfrac{1930}{V_{o_2}}=\sqrt{\dfrac{300}{1200}}}$

$\implies{\sf \dfrac{1930}{V_{O_2}}=\sqrt{\dfrac{1}{4}}}$

$\implies{\sf \dfrac{1930}{V_{O_2}}=\dfrac{1}{2}}$

$\implies{\sf V_{O_2}=2×1930}$

$\color{red}\implies{\sf V_{O_2}=3860\:m/s}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Rms Velocity of ${\sf O_2}$ is $\color{red}{\sf 3860\:m/s}$.