The r.m.s. speed of gas molecules at 800 K w | vedclass

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(B) The $r.m.s.$ speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this formula,it is clear that $v_{r

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twice the value at $200 \ K$

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(B) The $r.m.s.$ speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this formula,it is clear that $v_{rms} \propto \sqrt{T}$.Let $v_1$ be the $r.m.s.$ speed at $T_1 = 200 \ K$ and $v_2$ be the $r.m.s.$ speed at $T_2 = 800 \ K$.Then,$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the given values: $\frac{v_2}{v_1} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$.Therefore,$v_2 = 2v_1$.This means the $r.m.s.$ speed at $800 \ K$ is twice the value at $200 \ K$.

The $r.m.s.$ speed of gas molecules at $800 \ K$ will be

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