BASIC CONCEPTS OF THERMODYNAMICS 17dharm
M-therm/th2-1.pm5
or pV= m NC
1
3(^2) ...(2.2)
This equation is the fundamental equation of kinetic theory of gases and is often referred to
as kinetic equation of gases.
Equation (2.2) may be written as
pV = 2/3 × 1/2 m NC^2
where^12 mNC^2 is the average transmission or linear kinetic energy of the system of particles.
Equation (2.1) can be written as
p = 1/3 ρ C^2 ...(2.3)
where ρ is the density. LQ ρ=
N
M
O
Q
P
mN
V
,,i.e. Total mass
Total volume
This equation expresses the pressure which any volume of gas exerts in terms of its density
under the prevailing conditions and its mean square molecular speed.
From equations (2.2) and (2.3),
C==^33 ρppVmN
Kinetic interpretation of Temperature :
If Vmol is the volume occupied by a gram molecule of a gas and N 0 is the number of moles in
one gram molecule of gas,
M = molecular weight = mN 0. ...(i)
Since p Vmol = R 0 T ......Molar gas equation ...(ii)
From equations (2.2) and (ii),
1/3 m (^) NC 0 = R 0 TR 0 = Universal gas constant
or 2/3 ×^12 m (^) NC 0 2 = R 0 TN 0 = Avogadro’s number
or^12 mC^2 = 3/2 KT ...(2.4)
R
N
0
0 = K (Boltzman’s constant)
(i.e., K.E. per molecule = 3/2 KT)
or C =
3 KT
m
or C =^3 RTM^0 Q K
m
R
Nm
R
M
==^0
0
0
or CRT= 3 ...(2.5) QR=RM^0
where R is characteristic gas constant.
From equation (2.4) it is seen that temperature is a measure of the average kinetic energy
of translation possessed by molecule. It is known as the kinetic interpretation of temperature.
Hence, the absolute temperature of a gas is proportional to the mean translational kinetic energy
of the molecules it consists. If the temperature is fixed, then the average K.E. of the molecules
remains constant despite encounters.