Share
Notifications

View all notifications
Advertisement

Prove that Root Mean Square Velocity of Gas Molecule is Directly Proportional to the Square Root of Its Absolute Temperature. - Physics

Login
Create free account


      Forgot password?

Question

Prove that root mean square velocity of gas molecule is directly proportional to the square root of its absolute temperature.

Solution

Expression for r.m.s velocity:

a.   Let, P = pressure exerted by one mole of an ideal gas
V = volume of one mole of the gas
T = absolute temperature
b.   Pressure exerted by gas is given by,

`P=1/3(Mc^2)/V`

where M = mass of one mole (molecular weight) of the gas.

`PV=1/3(Mc^2)` .....................(1)

c.  But for one mole of an ideal gas, PV = RT

`therefore RT=1/3 MC^2`        [From Equation 1]

`therefore c^2=(3RT)/M`

`therefore c=sqrt((3RT)/M)`........................(2)

Equation (2) represents expression for r.m.s velocity of gas molecules.

d.   As R and M in equation (2) are constant,

`therefore c prop sqrtT`

`therefore c_1/c_2=sqrt(T_1/T_2)`

 

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 2016-2017 (March) (with solutions)
Question 2.2 | 2.00 marks
Advertisement

Video TutorialsVIEW ALL [1]

Solution Prove that Root Mean Square Velocity of Gas Molecule is Directly Proportional to the Square Root of Its Absolute Temperature. Concept: Kinetic Theory of Gases- Assumptions.
Advertisement
View in app×