THERMODYNAMICS OF RADIATION 
35 
(27*4) 
» 
...(27-5). 
temperatures and 
ases according to 
ature and density 
>re generally from 
3 the intermediate 
le route and back 
bility no entropy 
crease of entropy 
7 number of times 
i infinite decrease 
r erse. 
e depend only on 
satisfies this; and 
es be independent 
all be a constant. 
age of volume the 
s possible to vary 
de to the integral 
E the intermediate 
temperature the 
(27-6). 
e of a perfect-gas 
)und is applicable 
3 f material in ac- 
(27*7). 
28 . Reverting to the monatomic gas, we obtain from (27-5) and (27*6) 
#2 - #i = $91 log (TJTj) + 91 log (vjvj) 
= 91 {log (v t Tf) - log K7Y 1 )}, 
so that the entropy of a gram-molecule of the gas is 
S = 91 log (vT*) + C, 
where C is a constant which may depend on the nature but not on the 
state of the gas. If the gas expands or contracts adiabatically, i.e. without 
transference of heat from or to the surroundings, the entropy remains 
constant since energy received or given up as mechanical work has zero 
entropy. Accordingly for adiabatic changes 
vT - = const (28-1), 
an equation which can also be obtained directly by setting dQ = 0 in (27*3). 
More generally for a gas in which the whole heat energy is e times the 
translatory energy of the molecules, the pressure is 2/3e times the energy- 
density, and the adiabatic law is 
v T* e — const (28-2), 
which gives 
pocT? e , poz T l + ¥ , pozp l+2/3e (28-3). 
The last equation is usually written p oc pv, so that the adiabatic constant 
y is given by 
y = 1 + 2/3e (28-4). 
It can easily be shown that y is equal to the ratio of the specific heat at 
constant pressure to the specific heat at constant volume. 
Equilibrium of Radiation. 
29 . The spontaneous flow of heat from a hot body to a cooler body 
is a net transfer. Actually heat is flowing in both directions so that each 
receives heat from the other; but the hot body loses more than it gains 
and the cool body gains more than it loses. The inequality tends to right 
itself because a body as it loses heat will fall in temperature and the rate 
at which it sends out heat to the surroundings will decline; eventually it 
will reach a condition in which the loss of heat is just equal to the gain. 
This “theory of exchanges” applies to flow of heat both by conduction 
and by radiation, but we are most concerned with radiation. 
Consider an enclosure surrounded by walls maintained at a constant 
temperature. Radiation will be emitted from the walls into the enclosure, 
and radiation in the enclosure which falls on the walls will be wholly or 
partially absorbed by them. The greater the quantity of radiation inside 
the enclosure the greater will be the amount falling on the walls and the 
greater the amount absorbed. The quantity in the enclosure will thus 
3-2 
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