Environmental Engineering Reference
In-Depth Information
Closely related to the internal energy
U
and enthalpy
H
are the terms heat capacity
at constant volume
C
v
and heat capacity at constant pressure
C
p
. The concept of
temperatureresultingfromthethirdlawstatesthatthetemperaturedifferencesprovide
the driving force for heat flow between bodies. The ratio of the amount of heat
transferredtothebodyandtheresultingtemperaturechangeiscalledthe
heatcapacity
.
For an infinitesimal change the ratio is given by
d
q
d
T
;
C
=
(2.25)
∂U
∂T
∂H
∂T
C
v
=
;
C
p
=
.
(2.26)
V
P
Heat capacities are tabulated for several compounds in the literature usually as empir-
ical equations. These are given as polynomial fits with temperature as the dependent
variable and are valid only within the given range of temperature.A short compilation
for some important compounds is given in Table 2.2. Note that for very small ranges
of temperature, the heat capacity can be assumed to be a constant. For solids and liq-
uids the heat capacities are similar in magnitude, but for gases there is a relationship
between the two given by
C
P
−
C
V
=
nR
.
(2.27)
2.2.6 T
HERMODYNAMIC
S
TANDARD
S
TATES AND
E
NTHALPIES OF
R
EACTION,
F
ORMATION, AND
C
OMBUSTION
Thermodynamic quantities are estimated at the so-called
standard states
. The defini-
tion of the standard state is to be noted whenever
U
or
H
or any other thermodynamic
quantities are used in a calculation. For convenience, we choose some arbitrary state
of a substance at a specified temperature
T
, standard pressure
P
0
, standard molality
m
0
, or standard concentration
C
0
. Although the choice of
P
0
,
m
0
,or
C
0
will depend
TABLE 2.2
Empirical Equations for Specific Molar Heat Capacities at Constant
Pressure
C
p
=
cT
2
dT
3
Applicable for 273
a
+
bT
+
+
≤
T
≤
1500 K
(Units: cal/K/mol)
Compound
10
2
10
5
10
9
a
b
×
c
×
d
×
H
2
6.95
−
0.045
0.095
−
0.208
O
2
6.08
0.36
−
0.17
0.31
H
2
O
7.70
0.046
0.25
−
0.86
CH
4
4.75
1.2
0.30
−
2.63
CHCl
3
7.61
3.46
−
2.67
7.34
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