CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 90
3.5 Changes of thermodynamic quantities.
Only two of the three state variablesp,V,Tare independent at a constant amount of substance
n, while the third is determined by an equation of state [see equations (2.12)]. The thermody-
namic quantitiesCV, U, F are usually considered to be functions of temperature and volume,
while the quantitiesCp, H, Gare considered to be functions of temperature and pressure. En-
tropy is considered to be the function ofT, V orT, p. When deriving the function dependence
of thermodynamic quantities, we proceed from the knowledge of the equation of state and of
the dependence of heat capacity (CporCV) on temperature.
If a phase transition occurs during a change of state variables [see7.1.3], the corresponding
changes of thermodynamic functions have to be considered. During phase transitions, changes
of enthalpies and volumes are usually known experimentally while the changes of other ther-
modynamic functions are calculated from them.
3.5.1 Heat capacities
3.5.1.1 Temperature dependence.
A number of empirical relations are applied in calculating the temperature dependence of the
heat capacities of gases, liquids and solids, e.g.
Cpm(T, p) = a+bT+cT^2 , [p], (3.60)
CVm(T, V) = a′+b′T+c′T^2 , [V], (3.61)where the constantsa,b,c,a′,b′,c′are determined using the measured data.
Note:This and other similar empirical relations can be used reliably only in the temper-
ature interval for which the constants were determined.For crystalline substances in the vicinity of absolute zero,T∈(0, T 1 ), whereT 1 ≈15 K, the
Debye relationapplies
CVm=Cpm= constT^3. (3.62)