- Home
- Standard 11
- Physics
The average translational energy and the rms speed of molecules of a sample of oxygen gas at $300\ K$ are $6.21 \times 10^{-21}\ J$ and $484\ m/s$ respectively. The corresponding values at $600\ K$ are nearly (assuming ideal gas behaviour)
$12.42 \times {10^{ - 21}} J;$ $968\ m/s$
$8.78 \times {10^{ - 21}}J;$ $684\ m/s$
$6.21 \times {10^{ - 21}}J;$ $968\ m/s$
$12.42 \times {10^{ - 21}}J;$ $684/ m/s$
Solution
Average translation energy $\mathrm{E} \propto \mathrm{T}$
and rms speed ${v_{rms}} \propto \sqrt T $
If temperature is doubled, average energy is also
doubled and rms speed becomes $\sqrt{2}$ times.
Hence, $\mathrm{E}=2 \times 6.21 \times 10^{-21} \mathrm{\,J}$
$=12.42 \times 10^{-21} \mathrm{\,J}$
and $\mathrm{v}_{\mathrm{rms}}=\sqrt{2} \times 484 \mathrm{\,m} / \mathrm{s}=684 \mathrm{\,m} / \mathrm{s}$
