At T K temperature,the average speed of O_2 w | vedclass

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(A) The average speed of $O_2$ is given by $V_{av} = \sqrt{\frac{8RT}{\pi M_{O_2}}}$,where $M_{O_2} = 32 	imes 10^{-3} \, kg/mol$.The $rms$ speed of

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$1320$

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(A) The average speed of $O_2$ is given by $V_{av} = \sqrt{\frac{8RT}{\pi M_{O_2}}}$,where $M_{O_2} = 32 	imes 10^{-3} \, kg/mol$.The $rms$ speed of $N_2$ is given by $V_{rms} = \sqrt{\frac{3RT'}{M_{N_2}}}$,where $T' = 47 + 273 = 320 \, K$ and $M_{N_2} = 28 	imes 10^{-3} \, kg/mol$.According to the problem: $\sqrt{\frac{8RT}{\pi 	imes 32}} = \frac{7}{4} \sqrt{\frac{3R 	imes 320}{28}}$.Squaring both sides: $\frac{8RT}{32\pi} = \frac{49}{16} 	imes \frac{3R 	imes 320}{28}$.Simplifying the equation: $\frac{RT}{4\pi} = \frac{49 	imes 3R 	imes 320}{16 	imes 28}$.Solving for $T$: $T = \frac{49 	imes 3 	imes 320 	imes 4\pi}{16 	imes 28} \approx 1320 \, K$ (taking $\pi \approx \frac{22}{7}$ for calculation).

At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

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