At what temperature T will the average speed | vedclass

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Question

(C) The formula for average speed is $\overline{v} = \sqrt{\frac{8RT}{\pi M}}$.Given: $\overline{v} = 9.0 	imes 10^4 \ cm \ s^{-1}$,$M = 44 \ g \ mol

Vedclass · Accepted Answer

$1684$

Vedclass · Answer

(C) The formula for average speed is $\overline{v} = \sqrt{\frac{8RT}{\pi M}}$.Given: $\overline{v} = 9.0 	imes 10^4 \ cm \ s^{-1}$,$M = 44 \ g \ mol^{-1}$,$R = 8.314 	imes 10^7 \ erg \ K^{-1} \ mol^{-1}$ (in $CGS$ units).Substituting the values: $9.0 	imes 10^4 = \sqrt{\frac{8 	imes 8.314 	imes 10^7 	imes T}{3.14159 	imes 44}}$.Squaring both sides: $81 	imes 10^8 = \frac{8 	imes 8.314 	imes 10^7 	imes T}{3.14159 	imes 44}$.Solving for $T$: $T = \frac{81 	imes 10^8 	imes 3.14159 	imes 44}{8 	imes 8.314 	imes 10^7} \approx 1684 \ K$.

At what temperature $T$ will the average speed of $CO_2$ gas be $9.0 \times 10^4 \ cm \ s^{-1}$ (in $K$)?

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