At 133.33 K . the RMS velocity of an ideal gas is $\left(\mathrm{M} \equiv 0.083 \mathrm{~kg}…
At 133.33 K . the RMS velocity of an ideal gas is $\left(\mathrm{M} \equiv 0.083 \mathrm{~kg} \mathrm{~mol}^{-1}: \mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$
$200 \mathrm{~ms}^{-1}$
$150 \mathrm{~ms}^{-1}$
$2000 \mathrm{~ms}^{-1}$
$400 \mathrm{~ms}^{-1}$
Solution
Given $\mathrm{T}=133.33 \mathrm{K}$
$\mathrm{M}=0.083 \mathrm{~kg} \mathrm{~mol}^{-1} \Rightarrow \mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol} \mathrm{~K}^{-1}$
To Find the RMS velocity of an ideal gas the formula is-
$v_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
putting the value in the formula.
$v_{\mathrm{rms}}=\frac{\sqrt{3 \times 8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \times 133.33 \mathrm{k}}}{0.083 \mathrm{~kg} / \mathrm{mol}}$
$v_{\mathrm{rms}}=\sqrt{\frac{3323.99}{0.083}} \Rightarrow v_{\mathrm{rms}}=\sqrt{40048.14 \mathrm{~J} \mathrm{~kg}^{-1}}$
$v_{\mathrm{rms}}=200.12 \mathrm{~m} / \mathrm{s}$