Chapter 10
Heat and Matter
Abstract Chapter 10 is devoted to kinetic theory of gases, collision cross-section,
mean free path, van der Waal’s equation, thermal expansion of solids, liquids and
gases; gas equation, heat conduction in composite slabs and sphere; Newton’s law of
cooling, radiation problems covering Boltzmann law and Wien’s law, specific heat
and latent heat, thermodynamics, indicator diagrams, the Carnot, Otto and Sterling’s
cycles, thermodynamic relations, elasticity and surface tension.
10.1 Basic Concepts and Formulae
The mean free path λ of a gas molecule is the average distance travelled by the
molecule between successive collisions
λ =
x i /N
(10.1)
The average time of collision T is related to λ and the mean speed by
λ = T = / f
(10.2)
where f = 1/T
(10.3)
is the collision frequency.
N (v) dv = 4π N [m/2π kT ]
3/2
v
2 exp[−mv
2
/2kT ]dv (Maxwell’s law) (10.4)
Assuming Maxwell’s law of velocity distribution,
Most probable speed v p =
2kT
m
=
2RT
M
(10.5)
Average speed < v >=
8kT
π m
=
8RT
π M
(10.6)
Root-mean-square speed
< v 2 > =
8kT
m
=
8RT
M
(10.7)
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