IIT JEE Physics Formula Revision 24. Kinetic theory of Gases

1. p = 1/3*ρ*Mean(v²)


p = pressure of gas
ρ = density of gas
Mean(v²) = mean square speed of molecules of gas

2. pV = 1/3*M*Mean(v²)

V = Volume of gas
M = Total mass of the gas taken

3. pV = 1/3*Nm*Mean(v²)

N = total number of molecules in the sample
m = mass of one molecule

4. Mean(v²) = ΣV²/N
Square root of Mean(v²) is also called root-mean square speed v_rms

Equation 1 can be written as p = 1/3*ρ*v²_rms

So v_rms = SQRT(3p/ρ)

6. In thermal equilibrium in a mixture of two gases, the average kinetic energies of all molecules are equal. If v1 an v2 are rms speeds of the molecules of A and B

½m1v1² = ½m2v2²

7. pV = Nkt

k is known as the Boltzmann constant.
Its value is 1.38*10^(-23) J/K

R = NA*k (NA is Avogadro's number = 6.02*10^23
R = 8.314 J/mol-K

8. pV = nRT

9. RMS spped in terms of temperature
v(rms) = SQRT(3kT/m)

10. v(rms) = SQRT(3RT/M0)

11. Average kinetic energy of a molecule
½mv(rms)² = (3/2) kT

12. Total kinetic energy of all molecules
U = (3/2)nNA kT
or
U = 3/2nRT ( R = NA*k)
n = number of moles of substance

13. maxwells speed distribution law

dN = 4 π[m/2 πkT]^3/2v²e^-(mv²/2kT)dv

14. The speed at which dN/dv is maximum is called the most probable speed.

v_p = SQRT(2kT/m)

15. van der Waals equation for real gases

For an ideal gas
pV = nRT

This is called the equation of state for that substance

For a real gas

[p + a/V²][V-b] = nRT
where a and b are small positive constants.
a is related to the average force of all attracion between the molecules.
bis related to the total volume of the molecules.
This equation is given by van der Waals.

16. Relative humidity = RH =

Amount of water vapour present in a given volume of air at a given temperature
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Amount of water vapour required to saturate the same volume of air at the same tempeture

RH may also be defined as

Vapour pressure of air/SVP at the same temperature

SVP = Saturation vapour pressure: The pressure exerted by a saturated vapour is called saturation vapour pressure.

The RH may also be defined as

SVP at the dew point/SVP at the air temperature

As the vapour pressure of air at the actual temperature is equal to the SVP at the dew point.