The density of a gas at 100 , kPa pressure is | vedclass

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(B) The formula for $rms$ speed is $u_{rms} = \sqrt{\frac{3RT}{M}}$.Since $PV = nRT = \frac{m}{M}RT$,we have $\frac{RT}{M} = \frac{PV}{m} = \frac{P}{d

Vedclass · Accepted Answer

$1732$

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(B) The formula for $rms$ speed is $u_{rms} = \sqrt{\frac{3RT}{M}}$.Since $PV = nRT = \frac{m}{M}RT$,we have $\frac{RT}{M} = \frac{PV}{m} = \frac{P}{d}$,where $d$ is the density.Therefore,$u_{rms} = \sqrt{\frac{3P}{d}}$.Given $P = 100 \, kPa = 100 	imes 10^3 \, Pa$ and $d = 0.1 \, g \, cm^{-3} = 0.1 	imes 10^{-3} \, kg 	imes (10^{-2} \, m)^{-3} = 100 \, kg \, m^{-3}$.$u_{rms} = \sqrt{\frac{3 	imes 100 	imes 10^3}{100}} = \sqrt{3000} \approx 1732 \, m \, s^{-1}$.

The density of a gas at $100 \, kPa$ pressure is $0.1 \, g \, cm^{-3}$. What will be its $rms$ speed in $m \, s^{-1}$?

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