THE THERMODYNAMICS O F COMPRESSIBILITY AND EXPANSION
"
1 In
It
c t3Isothermal AB=c
BC =c/e
Volumes
mean of the areas representing the heat energies in Section 2 and Section 3 , that is, equal t o
Thermodynamics of Compressibility and Expansion 875
+
%&g(t,--t,)
~v(4-t3)l*
By the “First Law of Thermodynamics” we have the work done the heat expended
-
76 X d X 981 X c
+ s&z
% eg { S p ( 4 - 4 )
- 11) 1
(Joule’s equivalent) = constant; =J
whence C
eg { s g ( 4 -4 ) + -4 ) I = J/76 X d X 981 X 2
constant. For the sake of simplicity put =
z = sp(4
--I>
+ s,(4-
t3),
then constant. Sac. 5 . In the case of solids and liquids sg and s, are equal so that on simplification z = s(t, - t3), where s is the specific heat as ordinarily understood. SEC.6 . It can be very easily shown that c/egz
=
t,-tl
1°C
=
and
t3 = I O c. ( I ) Imagine a substance, of unit volume compressed isothermally t o volume I - c under a compressing force of c/e atmospheres; now heat it I O C, and its volume a t (t, + I ) O C becomes I -c c = I = initial (original) I “)C = t,, volume; but ( t , theref ore t,-
+
+
t,
- t,
=
I O
c.
Consider the body a t temperature tl” C, volume I - c, and under a compressing force equal to c/e atmospheres. Now t o reduce the initial ( = I ) volume by the amount c (to I - c) and maintain it thus requires’the force (2)
Philip Blackman
876
c / e . But if the volume is maintained a t I - c by some other means the force to do this becomes unnecessary or c / e may be put equal to 0. To effect this let the substance be cooled I O C, i. e., to (t - I ) O C, which of itself would tend to reduce the volume from I to I - c; hence (t, - I ) O C = t,, or t, - t3 = I O c. Therefore the expression z = S&, - 4) S V ( t , - t,) simplifies to
+
z =
sb
+ s,
(for gases),
and z =
2s
(for solids and liquids).
SEC.7. In the cases of gases the coefficient e is obtainable very simply by physical determination, but for solids and liquids this is a matter of very great difficulty. The formula c/egz = constant
may, with the above limitations for solids and liquids, be written c / e g ~ s = constant,
or c/cgs = constant.
If we designate a number of bodies by the symbols a, p, etc., and the corresponding quantities for the coefficients of cubical expansion, coefficients of compressibility, specific gravities, and specific heats by the symbols c,, cp, etc., ea, ep, etc., g,, g,, etc., and s, s, etc., respectively, we have c, c, --e, g, s, ep gp sp - . . . . . . .~
whence
a result which admits of the comparison of the coefficients of compressibility of all solids and liquids. Lolzdon
