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Question
Write the expression for rms speed, average speed and most probable speed of a gas molecule.
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Solution
Root mean square speed: (vrms)
vrms = `sqrtbar("v"^2) = sqrt(3"kT")/"m" = 1.73 sqrt("kT"/"m")`
Average speed: `(bar"v")`
`bar"v" = ("V"_1 + "v"_2 + "v"_3 + .... + "v"_"n")/"N"`
`bar"v" = sqrt((8"RT")/(π"M")) = sqrt((8"kT")/(π"m")) = 1.60 sqrt("kT"/"m")`
Most probable speed: (vmp)
vmp = `sqrt((2"RT")/"M") = sqrt((2"kT")/"m") = 1.41sqrt("kT"/"m")`
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