olute temperature of the
auxiliary medium. When divided by that temperature the quotient is
called the change of "entropy" associated with the given change (see
THERMODYNAMICS). Thus if a body at temperature T receives a quantity
of heat Q, and if T0 is the temperature of the auxiliary medium, the
quantity of work which could be obtained from Q by means of ideal
thermodynamic engines would be Q(1 - T0/T), and the balance, which is
QT0/T, would take the form of unavailable or waste energy given to the
medium. The quotient of this, when divided by T0, is Q/T, and this
represents the quantity of entropy associated with Q units of heat at
temperature T.

Any irreversible change for which a compensating transformation of
energy exists represents, therefore, an increase of unavailable
energy, which is measurable in terms of entropy. The increase of
entropy is independent of the temperature of the auxiliary medium. It
thus affords a measure of the extent to which energy has run to waste
during the change. Moreover, when a body is heated, the increase of
entropy is the factor which determines how much of the energy imparted
to the body is unavailable for conversion into work under given
conditions. In all cases we have

increase of unavailable energy
------------------------------- = increase of entropy.
temperature of auxiliary medium

When diffusion takes place between two gases inside a closed vessel at
uniform pressure and temperature no energy in the form of heat or work
is received from without, and hence the entropy gained by the gases
from without is zero. But the irreversible processes inside the vessel
may involve a gain of entropy, and this can only be estimated by
examining by what means mixed gases can be separated, and, in
particular, under what conditions the process of mixing and separating
the gases could (theoretically) be made reversible.

9. _Evidence derived from Liquefaction of one or both of the
Gases._--The gases in a mixture can often be separated by liquefying, or
even solidifying, one or both of the components. In connexion with this
property we have the important law according to which "The pressure of a
vapour in equilibrium with its liquid depends only on the temperature
and is independent of the pressures of any other gases or vapours which
may be mixed with it." Thus if two closed vessels be taken containing
some water and one