1.

Calculate the root mean square velocity of nitrogen at `27^(@)C` and `70cm` pressure. The density of `Hg` is `13.6 g cm^(-3)`.

Answer» Volume `V_(2)` at `27^(@)C` and `70 cm` pressure is given by
`(P_(2)V_(2))/(T_(2))=(P_(1)V_(1))/(T_(1))`
`(70 cmxxV_(2))/(300 K)=(70 cmxx0.0224 cm^(3))/(273 K)`
`:. V_(2)=0.026725 cm^(3)`
Pressure `P=((70)/(76))xx1.01325xx10^(5) Nm^(-2)`
`=9.332xx10^(4)Nm^(-2)`
`:. u_(rms)=((3PV)/(M))^(1//2)`
`((3xx9.332xx10^(4) Nm^(-2)xx0.026725 m^(3) mol^(-1))/(28xx10^(-3) kg mol^(-1)))^(1//2)`
`=517 ms^(-1)`


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