Untitled - Aerobib - Universidad Politécnica de Madrid

16 CHAPTER 1. THERMOCHEMISTRY
As in the previous cases, f can be expressed in the form
( ) p
f = f 0 + R m T ln + T ∑ p 0
j
R gj Y j ln X j , (1.61)
where
f 0 = u − T s 0 . (1.62)
Chemical Potentials
The chemical potential µ i of species A i in the mixture is G i
( )
( )
µ i = G i = G 0 pi
p
i + RT ln = G 0 i + RT ln + RT ln X i . (1.63)
p 0 p 0
1.4 Calculation of the thermodynamic functions
The preceding formulas show that all thermodynamic functions of a gas can be determined
provided that one of them and the standard values for the others are known. For
example, the heat capacity, either at constant pressure or at constant volume, and the
formation enthalpy and entropy of the gas determine all other thermodynamic functions.
The law of variation of heat capacity as function of T is generally complicated.
Fig. 1.5, for example, obtained from the tables in Ref. [10], shows the curves of c p
versus T for some gases. These curves are usually approximated with empirical formulae.
For example, the following Table 1.3, taken from Ref. [4] p. 28, gives some
of these parabolic formulae as well as their maximum deviations within the range
300 < T < 2 000K. The use of linear formulas is advisable for smaller ranges of T .
Gas c p (cal gr −1 K −1 ) Max. error (%)
H 2 3.440 + 0.033 × 10 −3 T + 0.1395 × 10 −6 T 2 1
N 2 0.225 + 0.065 × 10 −3 T - 0.0123 × 10 −6 T 2 2
O 2 0.196 + 0.086 × 10 −3 T - 0.0241 × 10 −6 T 2 1
CO 0.223 + 0.075 × 10 −3 T - 0.0164 × 10 −6 T 2 2
NO 0.207 + 0.081 × 10 −3 T - 0.0204 × 10 −6 T 2 2
H 2 O 0.383 + 0.182 × 10 −3 T - 0.0191 × 10 −6 T 2 2
CO 2 0.156 + 0.194 × 10 −3 T - 0.0562 × 10 −6 T 2 3
NH 3 0.348 + 0.527 × 10 −3 T - 0.1040 × 10 −6 T 2 1
C 2H 2 0.318 + 0.404 × 10 −3 T - 0.1020 × 10 −6 T 2 2 (for T > 400 K)
CH 4 0.211 + 1.119 × 10 −3 T - 0.2620 × 10 −6 T 2 2
Table 1.5: c p(T ) correlations for several gases.