'
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.)