' 
THERMODYNAMICS OF RADIATION 33 
3 
sure that the 
rily somewhat 
r to safeguard 
irguments the 
levant. If we 
ks irreversibly 
is works irre- 
} is a limiting 
ction involves 
rneous flow of 
i, cold body in 
lie transfer is 
vision of other 
>n, it may he 
atures T x , T 2 . 
ow from T x to 
s greater than 
ms T 2 = T x is 
mtity of heat 
Hence setting 
( 26 - 1 ). 
9 is a function 
A quantity of 
ure T x to the 
( 26 - 2 ). 
:s only to the 
te quantity of 
3 temperatures 
ent changes of 
riometric*. The 
amic temperature 
principle of thermometry is that a test-body A 2 brought near enough to 
a body A x rises or falls to the temperature of A x ; it therefore requires that 
the spontaneous flow of heat shall be from A x to A 2 or the opposite ac 
cording as T x > T 2 or the opposite—as assumed in our argument. The heat 
referred to (whether molecular motion or radiant energy) is “ordinary” 
heat-energy, that is to say the energy in the states 1 and 2 is assumed to 
have no special organisation beyond that defined by a single physical 
variable, viz. the temperature. It is possible for energy to possess organi 
sation of a more specialised kind, in which case the coefficient 9 will 
not be a function of the thermometric temperature only; for example, 
monochromatic radiation must be considered more highly organised than 
black-body radiation. But when such heat is allowed to flow into a test- 
body as in ordinary thermometry without specialised conditions, the 
excess organisation is inevitably wasted and there is no limiting condition 
of reversible flow with dS = 0. A transfer for which dS — 0 can only 
be arranged with special appliances (e.g. colour-filters), and the coefficient 
6 for such a state of organisation must be found from the behaviour with 
respect to these appliances and not with respect to ordinary thermometry. 
27 . Consider now a gram-molecule of perfect monatomic gas which 
obeys the law 
pv = KT (27-1), 
where 91 is the universal gas constant. 
In an ideal monatomic gas the only heat-energy is kinetic energy of 
molecular motion. Since the pressure is § of the kinetic energy per unit 
volume (§ 23) the heat-energy in the volume v is 
Q = \p . v = f 9 IT (27-2). 
Now let the gas change from a volume and temperature v x , T x to 
v 2 , T 2 . In general it will be necessary to supply or withdraw heat and 
mechanical work will be done by or against the pressure. In a change 
dv, dT the heat supplied must be 
dQ = f 9 IdT + pdv (27-3), 
the first term raising the temperature in accordance with (27-2) and the 
second replacing the energy expended by the pressure in doing mechanical 
work. 
The gas is supposed to have uniform temperature at each stage, and 
the heat dQ is to be added directly at each part of the gas—not poured 
in at one corner and allowed to flow to its destination. With this condition 
there is no limitation on the signs of dT, dv, dQ in (27-3) and the changes 
are therefore reversible. (If the above conditions were not postulated 
irreversible processes would evidently occur.)