Page 93 - Advanced Thermodynamics for Engineers, Second Edition

4.7 AVAILABILITY BALANCE FOR A CLOSED SYSTEM 79

Example 4.7.2: change of availability for a closed system in which the volume changes
An internal combustion engine operates on the Otto cycle (with combustion at constant volume)
and has the parameters defined in Table 4.1; it is based on one in Heywood (1988).
Calculate the variation in availability of the gases in the cylinder throughout the cycle from start of
compression to the end of expansion. Assume the compression and expansion processes are adiabatic.
Solution:
This example introduces two new concepts:
1. The effect of change of volume on the availability of the system and
2. The effect of ‘combustion’ on the availability of the system.
Equation (4.24) contains a term which takes into account the change of volume ( p 0 ðV 2 V 1 Þ), but
it does not contain a term for the change in availability which occurs due to ‘combustion’.
Equation (4.24) gives the change of availability of a system of constant composition as an extensive
property. This can be modified to allow for combustion by the addition of a term for the availability of
reaction. Chapter 10 contains a further discussion of the application of the energy equation to com-
bustion processes, but it should be possible to understand this example without reading the whole of
that chapter. This is defined as

DA R ¼ DF R ¼ U P ðT s Þ U R ðT s Þ T 0 ðS R ðT s Þ S P ðT s ÞÞ (4.30)
where F R is the Helmholtz energy of reaction of the fuel at the standard temperature, T s and T s is the
temperature at which the energies of reaction are evaluated. Hence,

DA R ¼ DF R ¼ DU R T 0 ðS R ðT s Þ S P ðT s ÞÞ
(4.31)
¼ðQ v Þ T 0 ðS R ðT s Þ S P ðT s ÞÞ
s
This term can be added into Eqn (4.24) to give

A 2 A 1 ¼ DA R þðU 2 U 1 Þ T 0 ðS 2 S 1 Þþ p 0 ðV 2 V 1 Þ (4.32)

Table 4.1 Operating Parameters for Otto Cycle
12
Compression ratio, r c
0
Calorific value of fuel, Q (kJ/kg) 44000
v
1.0286
Ratio, x a ¼ DA R /Q 0 v
Pressure at start of compression, p 1 (bar) 1.0

Temperature at start of compression, T 1 ( C) 60
Airefuel ratio, ε 15.39
Specific heat of air at constant volume, c v (kJ/kg K) 0.946
Ratio of specific heats, k 1.30
Temperature of surroundings, T 0 (K) 300
Pressure of surroundings, p 0 (bar) 1.0