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2. Show that the rms speed of molecules in a gas is given by `v_(rms) = sqrt(3P//ρ)`, where `P` is the pressure in the gas, and `ρ` is the gas density.
2. Show that the rms speed of molecules in a gas is given by v_(rms) = sqrt(3P//ρ), where P is the pressure in the gas, and ρ is the gas density. `PV = NkT`
`v_(rms) =sqrt((3kT)/m)`
`ρ = M/v`
Equations:
`PV = NkT`
`v_(rms) =sqrt((3kT)/m)`
`ρ = m/V`
Solution:
Total mass `M = Nm`
`ρ = M/V => V = M/ρ =(Nm)/ρ`
`PV = NkT => T = (PV)/(Nk) = (P((Nm)/ρ))/(Nk) = (Pm)/(ρk)`
`v_(rms) =sqrt((3kT)/m)`
`v_(rms) =sqrt((3k((Pm)/(ρk)))/m)`
`v_(rms) =sqrt((3P)/ρ)`
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