Question

The average energy and the rms speed of molecules in a sample of oxygen gas at $300\text{K}$ are $6.21\times {10}^{-21}\text{J}$ and $484{\text{ms}}^{-1}$ respectively. The corresponding values at $600\text{K}$ are nearly

• A. $12.42\times {10}^{-21}\text{J},968{\text{ms}}^{-1}$
• B. $8.78\times {10}^{-21}\text{J},684{\text{ms}}^{-1}$
• C. $6.21\times {10}^{-21}\text{J},968{\text{ms}}^{-1}$
• D. $12.42\times {10}^{-21}\text{J},684{\text{ms}}^{-1}$

Answer 1

The correct option is D $12.42\times {10}^{-21}\text{J},684{\text{ms}}^{-1}$

Average energy $\propto T$
Let we denote the average energy by $E$ then
$\frac{E_1}{E_2}=\frac{T_1}{T_2}$
$E_2=E_1\times \frac{T_2}{T_1}$
$E_2=6.21\times {10}^{-21}\times \frac{600}{300}$
$E_2=12.42\times {10}^{-21}\text{J}$
$v_{rms}\propto \sqrt{T}$
$\frac{v_{rm{s}_2}}{v_{rm{s}_1}}=\frac{\sqrt{T_2}}{\sqrt{T_1}}$
$v_{rm{s}_2}=\sqrt{2}{v}_{rm{s}_1}$
$v_{rm{s}_2}=\sqrt{2}\times 484=684{\text{ms}}^{-1}$