By what ratio does the average velocity of a | vedclass

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(A) The average velocity $(V_{av})$ of gas molecules is given by the formula $V_{av} = \sqrt{\frac{8RT}{\pi M}}$.Since $R$,$\pi$,and $M$ are constant,

Vedclass · Accepted Answer

$1.21$

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(A) The average velocity $(V_{av})$ of gas molecules is given by the formula $V_{av} = \sqrt{\frac{8RT}{\pi M}}$.Since $R$,$\pi$,and $M$ are constant,$V_{av} \propto \sqrt{T}$.Convert temperatures to Kelvin: $T_1 = 50 + 273 = 323 \ K$ and $T_2 = 200 + 273 = 473 \ K$.The ratio of average velocities is $\frac{(V_{av})_1}{(V_{av})_2} = \sqrt{\frac{T_1}{T_2}} = \sqrt{\frac{323}{473}} \approx \sqrt{0.6828} \approx 0.826$.However,the question asks for the ratio of the final velocity to the initial velocity: $\frac{(V_{av})_2}{(V_{av})_1} = \sqrt{\frac{473}{323}} \approx \sqrt{1.464} \approx 1.21$.Re-evaluating the provided options,the ratio $\frac{V_2}{V_1} = 1.21 : 1$ corresponds to option $A$.

By what ratio does the average velocity of a gas molecule change when the temperature is raised from $50^{\circ}C$ to $200^{\circ}C$ (in $: 1$)?

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