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where
u = internal energy
T = temperature
In the case of cv the supply of heat to the system occurs at constant volume.
cp and cv are related to each other through the Spencer-Gilmore equation (Equation 2.1):
(2.6)
The numerical values of cp and cv differ by roughly 10%, so that for approximate calculations
cv can be considered equal to cp [2].
Plots of cp as a function of temperature are shown in Figure 2.2 for amorphous,
semicrystalline, and crystalline polymers.
As shown in Figure 2.3, the measured values can be expressed by a polynomial of the
type
a) b) c)
h
Figure 2.2 Specific heat as a function of temperature for amorphous (a), semi crystalline (b),
and crystalline polymers (c) [4]
Specific heat Cp
kg K
measured
polynomial
0
C
Temperature J
Figure 2.3 Comparison between measured values of cp [6] and polynomial for LDPE [1]
/m
(2.7)