The rms speed of gas molecules at a temperature 27 K and pressure 1.5 bar is 1 x 10⁴ cm/sec. If both temperature and pressure are raised three times, the rms speed of the gas will be:

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$\approx$ 1 x 10⁴ cm/sec

1 x 10⁴ cm/sec

9 X 10⁴ cm/sec

3 X 10⁴ cm/ sec

answer is D.

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Detailed Solution

$u_{rms} = \sqrt{[\frac{3 RT}{M}]}; rms speed depends on temp. \frac{1 \times 10^{4}}{u_{2}} = \sqrt{\frac{27}{3 \times 27}} u_{2} {=1×10}^{4} × \sqrt{3} {= 1.73×10}^{4} {≈1×10}^{4} {cm s}^{- 1}$

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