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.