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(A) The $r.m.s.$ velocity of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This shows that $v_{rms} \propto \sqrt{T}$.The pre

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$\frac{400}{\sqrt{3}}$

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(A) The $r.m.s.$ velocity of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This shows that $v_{rms} \propto \sqrt{T}$.The pressure does not affect the $r.m.s.$ velocity of an ideal gas.Given $T_1 = 27^o C = 300 \,K$ and $v_1 = 200 \,m s^{-1}$.Given $T_2 = 127^o C = 400 \,K$.Using the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.$\frac{v_2}{200} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Therefore,$v_2 = 200 	imes \frac{2}{\sqrt{3}} = \frac{400}{\sqrt{3}} \,m s^{-1}$.

The molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is

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