The r.m.s. velocity of a certain gas is v at | vedclass

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(A) The formula for $r.m.s.$ velocity is $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constant,$V_{rms} \propto \sqrt{T}$.Given $V_1 = v$ at

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$1200$

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(A) The formula for $r.m.s.$ velocity is $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constant,$V_{rms} \propto \sqrt{T}$.Given $V_1 = v$ at $T_1 = 300 \ K$ and $V_2 = 2v$ at $T_2 = ?$.Using the ratio: $\frac{V_1}{V_2} = \sqrt{\frac{T_1}{T_2}}$.Substituting the values: $\frac{v}{2v} = \sqrt{\frac{300}{T_2}}$.Squaring both sides: $(\frac{1}{2})^2 = \frac{300}{T_2} \implies \frac{1}{4} = \frac{300}{T_2}$.Therefore,$T_2 = 300 	imes 4 = 1200 \ K$.

The $r.m.s.$ velocity of a certain gas is $v$ at $300 \ K$. The temperature,at which the $r.m.s.$ velocity becomes double,is ............... $K$.

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