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C Section 5.7
1 Conventional Entropies and
the Third Law
2 Cpf it
3 =$D$2+$E$2*A3+$F$2*A3^2+$G$2*A3^3 Figure 5.8
4 =$D$2+$E$2*A4+$F$2*A4^2+$G$2*A4^3
5 =$D$2+$E$2*A5+$F$2*A5^2+$G$2*A5^3 Some of the formulas in column C
of the Fig. 5.7 spreadsheet.
6 =$D$2+$E$2*A6+$F$2*A6^2+$G$2*A6^3
7 =$D$2+$E$2*A7+$F$2*A7^2+$G$2*A7^3

the polynomial formula into these cells but with the temperature cell A3 in the formula
changed to A4 in cell C4, to A5 in cell C5, etc. Cells C3 to C15 will then contain the
polynomial-fit values. (For an alternative procedure, see Probs. 5.28 and 5.29.)
The $ signs in the formula prevent D2, E2, F2, and G2 from being changed when
the formula is copied from C3 into C4 to C15. A cell address with $ signs is called an
absolute reference, whereas one without $ signs is a relative reference. When a for-
mula is copied from one row to the row below, the row numbers of all relative refer-
ences are increased by 1, while absolute references do not change. When the formula
is copied to the second row below the original row, the row numbers of relative refer-
ences are increased by 2; and so on. Figure 5.8 shows some of the formulas in column
C. [To display all the formulas in their cells, click in the blank rectangle in the upper
left corner of the spreadsheet to select all the cells and then hold down the Control key
(the Command key on the Macintosh) while pressing the backquote (grave accent)
key `. Pressing these keys again will restore the usual display.]
Excel is easy to use and very useful for solving many scientific problems.
However, tests of the “reliability of Excel [97] in three areas: estimation, random num-
ber generation, and statistical distributions” concluded: “Excel [97] has been found
inadequate in all three areas” and recommended that “Excel not be used for statistical
calculations” [B. D. McCullough and B. Wilson, Comput. Statist. Data Anal., 31, 27
(1999)]. Excel 2003 fixed many of the errors in previous versions but did not fix all
errors, and a study concluded that “Excel 2003 is an improvement over previous ver-
sions but not enough has been done that its use for statistical purposes can be recom-
mended” [B. D. McCullough and B. Wilson, Comput. Statist. Data Anal., 49, 1244
(2005)]. A website discussing errors in Excel 2003 and 2007 is www.daheiser.info/
excel/frontpage.html. This site notes that “there were essentially no changes in the
[Excel] 2003 version statistical functions and routines for [Excel] 2007.” McCullough
has praised the willingness of the developers of Gnumeric to fix errors in their spread-
sheet program (www.csdassn.org/software_reports/gnumeric.pdf).

5.7 CONVENTIONAL ENTROPIES AND THE THIRD LAW
Conventional Entropies
The second law of thermodynamics tells us how to measure changes in entropy but
does not provide absolute entropies. We could tabulate entropies of formation S°,
f
but this is not generally done. Instead, one tabulates conventional (or relative)
entropies of substances. To set up a table of conventional standard-state entropies, we
(1) assign an arbitrary entropy value to each element in a chosen reference state, and
(2) find S for the change from elements in their reference states to the desired sub-
stance in its standard state.
The choice of the entropy reference state is the pure element in its stable con-
densed form (solid or liquid) at 1 bar in the limit T → 0 K. We arbitrarily set the molar
entropy S for each element in this state equal to zero:
m
S° lim S° 0 element in stable condensed form (5.22)*
m,0
m,T
TS0