The absolute entropy of a system at a given temperature is its entropy at that temperature relative to its entropy at absolute zero.
The consequence of eq300 is that we can calculate the absolute entropies of substances at any temperature. From eq119,
For a system at constant volume, (see Q&A below for derivation), so
For ideal and real gases, is a function of temperature and is proportional to
at low temperatures according to the Debye formula. At higher temperatures,
can be approximated as a function described by eq43, where
. Since,
, eq301 becomes
Having computed eq302, we can use the value to calculate the absolute entropy of the same substance at other temperatures, for instance,
Using the same logic, a system at constant pressure is given by
If eq301 or eq304 has a temperature range that includes phase transitions, which result in points of discontinuity in or
(see diagram above), we have to modify the equation (e.g. eq304) as follows:
Finally, just as the change of standard reaction enthalpy is , the change of standard reaction entropy is:
Question
Show that and
for an isobaric process.
Answer
The change in enthalpy for an isobaric process that involves only pV work is given by
For an isobaric process, , so
or
. Hence,
.
The change in entropy of a constant pressure system at a transition temperature is:
Both and
are exact differentials and therefore,
.