Advertisements
Advertisements
Question
Write the expression for rms speed, average speed and most probable speed of a gas molecule.
Advertisements
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")`
APPEARS IN
RELATED QUESTIONS
The velocity of the three molecules is 2 km s-1, 4 km s-1, 6 km s-1. Find (i) mean square velocity (ii) root mean square velocity.
Which of the following gases will have the least rms speed at a given temperature?
Why moon has no atmosphere?
Calculate the temperature at which the rms velocity of a gas triples its value at S.T.P. (standard temperature T1 = 273 K)
The number of molecules in 100 cc of gas at N.T.P. is ______ if the mass of each molecule is 4.556 x 10-25 kg and R.M.S. speed is 250 m/s.
The root mean square velocity of molecules of a gas is 200 m/s. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?
To what temperature should hydrogen at 227° C be cooled at constant pressure so that root mean square velocity of its molecule becomes half of its previous value?
A container has a mixture of two gases, hydrogen, and oxygen at room temperature. Which one of the following statements is true, if VH and VO are the root mean square velocities of hydrogen and oxygen molecules respectively?
If the absolute temperature of a gas is increased 5 times, then the rms velocity of the gas molecules will be ______.
Which of the following relations is correct for root means square speed of a gas at temperature T?
(m = mass of molecule, K = Boltzmann constant)
