32
THERMODYNAMICS OF RADIATION
Thus if a process can be shown to be reversible we can be sure that the
entropy is unaltered by it. Reversible processes are necessarily somewhat
idealised because it is scarcely possible in practice entirely to safeguard
the energy from disorganisation. But in thermodynamical arguments the
practicability of the processes considered is not usually relevant. If we
have a process which under certain practical conditions works irreversibly
in one direction, and under very slightly altered conditions works irre
versibly in the opposite direction, we may infer that there is a limiting
intermediate condition for which the process in either direction involves
no alteration of entropy.
An irreversible process of great importance is the spontaneous flow of
heat (by conduction or by radiation) from a hot body to a cold body in
proximity tending to equalise their temperatures. Since the transfer is
spontaneous, i.e. its occurrence is not dependent on the provision of other
sources of energy which might be drained of organisation, it may be
treated as isolated. Consider two bodies A x , A 2 at temperatures T x , T 2 .
If T 2 is slightly less than T x a small quantity of heat will flow from T x to
T 2 \ a slight alteration of the condition so that T 2 is a little greater than
T x causes the process to occur in the reverse direction. Thus T 2 = T x is
the limiting condition for which a transfer of a small quantity of heat
from A x to A 2 or A 2 to A x involves no alteration of entropy. Hence setting
dS = 0 in (25-1) we have
9 2 = 9 X whenever T 2 = T 1 (26-1).
Accordingly when dQ represents heat-energy the coefficient 9 is a function
of the temperature only.
Again, let the temperatures be unequal and T x > T 2 . A quantity of
heat dQ will then flow spontaneously from the temperature T x to the
temperature T 2 \ and by (25-1)
dS = dQ (9 (T 2 ) - 9 {T x )).
Since dS cannot be negative, we have
9 (T 2 ) > 9 (T x ) whenever T x > T 2 (26-2).
Hence 9 decreases as the temperature increases.
It must be understood that the coefficient 9 ( T) refers only to the
transfer of an infinitesimal quantity of heat. When a finite quantity of
heat is transferred from one limited reservoir to another the temperatures
will alter during the progress of the flow and the consequent changes of
9 must be taken into account.
The temperature referred to in this argument is thermometric *. The
* No reference is made in this book to the so-called thermodynamic temperature
introduced in some text-books.