Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 4

is that the difficulty lies not in the third law itself, as now stated, but
in the lack of knowledge sometimes existing as to the true internal
condition of the crystals on which low-temperature heat-capacity
measurements are made. Fortunately, the number of substances
with which there has been difficulty so far is only a small fraction of
the total number that have been studied.
The increase in entropy in warming a substance from 00 to T{K.,
is, by definition,
AS=TSTSo fT dQ (4)
Here, ST1 is the entropy at T1, So is the entropy at 00, and dQ is the
increment of heat absorbed at the temperature T. If the substance
has been cooled and the measurements made under conditions of com-
plete equilibrium, then So=O, and
Consider first a crystalline substance in complete equilibrium
whose change in heat content,f dQ, and the first derivative of heat
content are continuous in the range 00 to TI. In such a case, dQ=
C,dT or dQ=C,dT, depending on whether the substance is heated at
constant pressure or at constant volume. The symbol C, represents
the true or "instantaneous" heat capacity at constant pressure, and
C,, the true heat capacity at constant volume. The integral (5) gives
the entropy either at constant pressure or constant volume, depend-
ing on which heat capacity is employed. We shall be concerned here
only with the calculation of entropies for a constant pressure of 1
atmosphere. Returning to equation (5), then
S T1 -oT1 C,d T
S T (6)
In such a simple case, specific-heat measurements down to very low
temperatures are all that is required for computing St1. Discussion
concerning evaluation of this integral will be given later.
Suppose now a more complicated state of affairs and assume a
substance in equilibrium crystalline condition as 0o is approached,
but which undergoes a transition at some temperature, T', melts at
temperature T", and boils under 1 atmosphere pressure at tempera-
ture T"' (T', T", and T"' all lying in the range 00 to T1). The
integral in equation (5) may now be separated into several constituent
parts as
s T1' C, (crystals II)dTAH' T" C, (crystals I)dT H
STI=J0 T T1rs T T1 1
T'" C . (liquid) AH"' +T' C, (gas)
S,, d T+ , + ,,, d T, (7)
in which AH', AH", and AH"' are, respectively, the heats of transition,
fusion, and vaporization.

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Kelley, K. K. Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation, report, 1950; Washington D.C.. ( accessed May 27, 2019), University of North Texas Libraries, Digital Library,; crediting UNT Libraries Government Documents Department.

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