Chemistry Reference
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while keeping another one constant. During this scan, the variation of the (third)
dependable variable (i.e., the mechanical output) and the calorimetric energy
generated (i.e., the thermal output) are recorded simultaneously in situ in the
measuring cell. From these two quantities, associated to a given scan, two thermo-
dynamic derivatives, mechanical and thermal, are thus determined. The derivatives
perfectly characterize the evolution of the thermodynamic potential of the investi-
gated system, particularly any undergone transition or state change induced by the
variable scan. As illustrated in Fig.
3
, making use of the rigorous Maxwell relations
between thermodynamic derivatives, it is possible to directly obtain the ensemble
of the thermophysical properties; undoubtedly this shows the potentiality of the
technique. During measurements, it is essential that the different scans be per-
formed with sufficiently slow rates in order to keep the investigated system at
equilibrium over the entire scan and so that the (Maxwell) thermodynamic relations
remain valid.
The four possible thermodynamic situations (Fig.
3
) are obtained by simulta-
neous recording of both the heat flux (thermal output) and the change of the
dependent variable (mechanical output). Then, making use of the respective related
Maxwell relations, one readily obtains the main thermophysical properties as
follows: (a) scanning pressure under isothermal conditions yields the isobaric
thermal expansivity
a
p
and the isothermal compressibility
k
T
as functions of
pressure at a given temperature; (b) scanning volume under isothermal conditions
yields the isochoric thermal pressure coefficient
b
V
and the isothermal compress-
ibility
k
T
as functions of volume at a given temperature; (c) scanning temperature
under isobaric conditions yields the isobaric heat capacity
C
p
and the isobaric
thermal expansivity
a
p
as functions of temperature at a given pressure; (d) scanning
temperature under isochoric conditions yields the isochoric heat capacity
C
V
and
the isochoric thermal pressure coefficient
b
V
as function of temperature at a given
volume.
In the present work, two different operating modes were used: (
1
) the use of
pressure as scanned variable along different isotherms while recording (versus time
t
)
(
∂V/∂P
)
T
k
T
p
= f(t)
(
∂V/∂T
)
P
T
= cst
a
P
V
= f(t)
Mechanical
(
∂S/∂P
)
T
=
-(
∂V/∂T
)
P
(
∂P/∂T
)
V
T
= f(t)
p
= cst
b
V
(
∂S/∂V
)
T
=
(
∂P/∂T
)
V
T
= f(t)
C
P
C
V
(
∂H/∂T
)
P
V
= cst
Thermal
(
∂U/∂T
)
V
Fig. 3 Thermodynamic scheme of scanning transitiometry showing the four possible modes of
scanning. Each of these modes delivers two output derivatives (mechanical and thermal), which
in turn lead to four pairs of the different thermomechanical coefficients, namely
a
p
,
k
T
,
b
V
,
C
p
,
and
C
V
