Given data: Temperature of Methane Gas T2 = 27 degree celcius = 27 + 273 = 300K At temperature T1, Vrms of Oxygen and Methane are equal. To find: Temperature T1. Solution: We know that, Root mean square velocity Vrms = sqrt(3RT/M) Here, M is the molecular mass of the gas. R the gas constant. T is the absolute temperature. Now, if Vrms of oxygen and methane are equal, then sqrt(3RT1/M1) = sqrt(3RT2/M2) T1 = (M1/M2) T2 We know that, Molecular mass of oxygen M1 = 32 g/mol Molecular mass of methane M2 = 16 g/mol So, T1 = (32/16 ) * 300 = 600K answer is 600 Kelvin or 327 degree Celcius.
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At what temperature is the $\mathrm{rms}$ velocity of hydrogen molecule equal to that of an oxygen molecule at $27^{\circ} \mathrm{C} ?$ (a) $10 \mathrm{~K}$ (b) $20 \mathrm{~K}$ (c) $18.75 \mathrm{~K}$ (d) $19.75 \mathrm{~K}$ Answer VerifiedVerified Open in App Suggest Corrections 1 |