CHAPTER
Kinetic Theory of Gases and
16 Thermodynamics
Boyle’s law: If m and T are constant m = mass of each molecule
1 1
V∝ or P= nmv 2
P 3
P1V1 = P2V2 N
n = number density i.e., n =
Charles’s law: If m and P are constant V
Vrms = ( v 2 )
1/ 2
V∝T
V1 V 3 1 2
= 2 K.E. = k BT = mv
T1 T2 2 2
Gay-Lussac’s law: If m and V are constant 3k BT
v2 =
P∝T m
P1 P 3k BT
= 2
⇒ Vrms =
T1 T2 m
Avogadro’s law: If P, V and T are same 8 K BT
N1 = N2 Vav =
πm
where, N1 and N2 are the number of molecules
2 K BT
V ∝ n (no. of molecules of gas) Vmp =
m
V1 V2 1
= Mean free path ( l ) =
n1 n 2 2nπd 2
Graham’s law: If P and T are constant n = number density
1 d = diameter of molecule
rate of diffusion r ∝
ρ Cp
r is density g=
Cv
r1 g = ratio of specific heats
=
r2 Cp = specific heat at constant pressure
Dalton’s law: P = P1 + P2 + P3 ...... Cv = specific heat at constant volume
P = Total pressure Cp – Cv = R
P1, P2, P3 .... = Pressure exerted by each component present R = universal gas constant
in the mixture.
Ideal gas equation: PV = nRT = kBNT No. of
n = number of moles S.No. Atomicity degree of CP Cv g = CP/Cv
N = number of molecules freedom
R = universal gas constant 5 3 5
1 Monoatomic 3 R R
kB = Boltzmann’s constant 2 2 3
Pressure exerted by ideal gas
7 5 7
1 mN 2 2 Diatomic 5 R R
P= v 2 2 5
3 v
2 2 2
v 2 = mean square velocity v 2 = v1 + v2 + v3 + ......
N
Kinetic Theory of Gases and
16 Thermodynamics
Boyle’s law: If m and T are constant m = mass of each molecule
1 1
V∝ or P= nmv 2
P 3
P1V1 = P2V2 N
n = number density i.e., n =
Charles’s law: If m and P are constant V
Vrms = ( v 2 )
1/ 2
V∝T
V1 V 3 1 2
= 2 K.E. = k BT = mv
T1 T2 2 2
Gay-Lussac’s law: If m and V are constant 3k BT
v2 =
P∝T m
P1 P 3k BT
= 2
⇒ Vrms =
T1 T2 m
Avogadro’s law: If P, V and T are same 8 K BT
N1 = N2 Vav =
πm
where, N1 and N2 are the number of molecules
2 K BT
V ∝ n (no. of molecules of gas) Vmp =
m
V1 V2 1
= Mean free path ( l ) =
n1 n 2 2nπd 2
Graham’s law: If P and T are constant n = number density
1 d = diameter of molecule
rate of diffusion r ∝
ρ Cp
r is density g=
Cv
r1 g = ratio of specific heats
=
r2 Cp = specific heat at constant pressure
Dalton’s law: P = P1 + P2 + P3 ...... Cv = specific heat at constant volume
P = Total pressure Cp – Cv = R
P1, P2, P3 .... = Pressure exerted by each component present R = universal gas constant
in the mixture.
Ideal gas equation: PV = nRT = kBNT No. of
n = number of moles S.No. Atomicity degree of CP Cv g = CP/Cv
N = number of molecules freedom
R = universal gas constant 5 3 5
1 Monoatomic 3 R R
kB = Boltzmann’s constant 2 2 3
Pressure exerted by ideal gas
7 5 7
1 mN 2 2 Diatomic 5 R R
P= v 2 2 5
3 v
2 2 2
v 2 = mean square velocity v 2 = v1 + v2 + v3 + ......
N
