EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES.
169
If we denote by
and
the volumes (determined under standard conditions of temperature and pressure) of the quantities of the gases
and
which are contained in a unit of volume of the gas
, we shall have
and
|
(306)
|
and (302) will reduce to the form
|
(307)
|
Moreover, as by (277)
|
(308)
|
we have on eliminating
|
(309)
|
where
|
(310)
|
It will be observed that the quantities
will always be positive and have a simple relation to unity, and that the value of
will be positive or zero, according as gas
is formed of
and
with or without condensation. If we should assume, according to the rule often given for the specific heat of compound gases, that the thermal capacity at constant volume of any quantity of the gas
is equal to the sum of the thermal capacities of the quantities which it contains of the gases
and
, the value of
would be zero. The heat evolved in the formation of a unit of the gas
out of the gases
and
, without mechanical action, is by (283) and (257)
|
|
or
|
|
which will reduce to
when the above relation in regard to the specific heats is satisfied. In any case the quantity of heat thus evolved divided by a
will be equal to the differential coefficient of the second member of equation (307) with respect to
. Moreover, the heat evolved in the formation of a unit of the gas
out of the gases
and
under constant pressure is which is equal to the differential coefficient of the second member of (309) with respect to
, multiplied by
.
It appears by (307) that, except in the case when
, for any given finite values of
and
(infinitesimal values being excluded as well as infinite), it will always be possible to assign such a finite value to
that the mixture shall be in a state