At which temperature is the r.m.s. velocity o | vedclass

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(D) The root mean square (r.m.s.) velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas

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$20$

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(D) The root mean square (r.m.s.) velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature in Kelvin, and $M$ is the molar mass of the gas.Given, the r.m.s. velocity of hydrogen $(H_2)$ at temperature $T_H$ is equal to the r.m.s. velocity of oxygen $(O_2)$ at temperature $T_O = 47^{\circ} C = 47 + 273 = 320 \,K$.The molar mass of hydrogen $M_H = 2 \,g/mol$ and the molar mass of oxygen $M_O = 32 \,g/mol$.Equating the velocities: $\sqrt{\frac{3RT_H}{M_H}} = \sqrt{\frac{3RT_O}{M_O}}$.Squaring both sides: $\frac{T_H}{M_H} = \frac{T_O}{M_O}$.Substituting the values: $\frac{T_H}{2} = \frac{320}{32}$.$T_H = 2 	imes 10 = 20 \,K$.

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $\,K$)?

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