Kinetic Theory of Gases

Ideal Gas
PV = kT ; where k = nkb

Kinetic Energy
Kinetic Energy is directly proportional to Temperature.

Boyle's Law
P1V1 = P2V2 = constant

Charle's Law
V = Vo(1 + T/273.15)

Gay Lussac's Law
V1/ T1= V2/undefinedT2 = constant

Avogadro's Law
V α n

Ideal Gas Equation
PV = nRT

P = dRT / M

P1V1/ T1= P2V2/ T2

Dalton's Law of Partial Pressures
(only for non-reacting gases)

PT = P1+ P2+ P3 + ........ +Pn

Where, P1= x1P1 ; x1= n1/ nT ( x = mole fraction )

When a gas molecule, hits a wall , it transforms momentum equal to 2mv. When a gas molecule hits the walls of an absorbing surface, momentum equal to mv is transformed.

Graham's Law of Diffusion
Rate of diffusion (r) = Volume of Gases Diffused                                                                                                                                 --TIme

r = V/t
r1 / r2 = V1T2/ V2T1 r α 1/√d

... r1/ r2= √ (d2/d1)

... r1/ r2= √ (M2/ M1)

Van der Wahl's Forces or Real Gas Equation
(for real gases)

(P+(a/V2))(V-b) = RT {for 1mole }

(P+(an/V2))(V-nb) = nRT

Maxwell Distribution
Maxwell Distribution is the probability distribution curve of Most Probable Velocity.

Application of Specific Heat
(Cp and Cv for Monoatomic, Diatomic for JEE )

f is the number of degrees of freedom.

PV = kBT ; where kB=n/ N = 1.38 x 10-23 m2kgs-2K-1

P = 1/3 ρC2

kB = 1.38 x 10-23 m2kgs-2K-1

KE = 3/2 PV

KE per mole = 3/2 RT

KE per unit mass = 3/2 RT/M

KE per molecule = 3/2 kBT