Page 48 - Mechanical Engineers Reference Book

Principles of thermodynamics 1/37
efficiency is known as the isentropic efficiency because the 1.6.4.4 Process laws
ideal adiabatic process has constant entropy (qv).
Lossles due to fluid friction and losses due to heat transfer This is a particularly important step in thermodynamic analysis
across :finite temperature differences are found to result in an because an idealized reversible process has to be chosen to
increase in the value of the entropy that would be expected in represent as closely as possible the real process in order to
a reversible process. Thus an expected increase would be calculate energy changes. When the working substance is a gas
larger ;and an expecred decrease would be smaller. It is not it is convenient in an elementary analysis to use perfect gas
easy to define entropy except mathematically. In practical use laws with the process calculation. These are
as the abscissa of charts it enables work transfers in ideal pv = RT or pV = mRT
adiabafic processes to be represented as vertical lines if
enthalpy is used as an ordinate, and in this guise is a valuable u = c,AT and h = cFAT
visual method of presentation. where c, and cF are the specific heat capacities at constant
volume and constant pressure, respectively, which are related
as follows:
1.6.3 Thermoeconomics"J2
cF - c, = R and cdc. = y
When (a more detailed study of a flow process is made by the
second law of thermodynamics is is found that specific entropy where R is the specific gas constant and y is the isentropic
(kJ.kg-lK-') appears as part of a property known as availabil- index.
ity. In a flow process we write b = h - To s, in which b is the Ideal processes commonly used are constant pressure, con-
specific availability function, h is the specific enthalpy, To is stant volume, constant temperature (which for a perfect gas
the temperature (absolute) of the surroundings and s is the becomespv = constant) together with two other more general
specific entropy. The second law shows that the maximum relations: the adiabatic process, pvk = constant (which for a
work potential or exergy of any state in surroundings at state 0 perfect gas becomes pvy = constant) and the polytropic pro-
is given by b - bo. Thus for a change of state in a flow process cess, pv" = constant. The last process is a general relation
from 1 to 2 the maximum specific work obtainable is given by between pressure and volume which is used if none of the
the exergy change, wxmax = (bl - bo) - (b2 - bo) = (b, - other clearly special cases are considered valid. Usually
b2) = -Ab. If we measure or predict by analysis the actual 1 < n < 1.4.
work achieved it is possible to determine numerically the lost It is possible (by using the gas laws) in adiabatic and
work or irreversibility in the process. If engineering plant is to polytropic gas processes to rearrange the relations to involve
be designed to the best advantage it is clear that processes pressure and temperature or temperature and volume to yield
should be chosen to minimize this loss. The lost work may be very useful relations:
associated with costs and we move into the developing field of
thermoeconomics. Cleariy, this is a compiex subject but it is
important in that it unites thermodynamics with costs and can
help in the design of long-life expensive plant.

1.6.4 Work, heat, property values, process laws and
cornbustion9Jo Processes may be represented on property diagrams to enable
cycle visualization (Figures 1.5G1.54).
To deploy the laws of thermodynamics outlined above we
need more information. To perform simple cycle analysis the 1.6.4.5 Combustion
data below is vital.
To avoid involving complex chemical equations, engineers
1.6.4.1 Work often use the calorific value of a fuel coupled with a combu-
stion efficiency to estimate the energy transfers in combustion
In a non-flow process work transfer can be determined from processes. Thus the rate of energy input by combustion is
w = Jpdv. The mathematical relation for the process is known
as the process law (qv). In most flow processes used in E = mf ' Cv.r)comb
engineering cycles the adiabatic approximation is used so that where mf is the fuel mass flow rate, CV the calorific value of
the steady flow energy equation, neglecting changes in kinetic the fuel and qcomb the cornbustion efficiency.
and potential energy, gives
w, = Ah 1.6.5 Cycle analysis
One example will be given of the simple analysis of the ideal
1.6.4.2 Heat Joule cycle for a gas turbine plant (Figure 1.55). The cycle
consists of four flow processes described in Table 1.7 and
This is usually an unknown quantity and is found by the
application of the energy equation. As stated earlier, many analysed by the steady flow energy equation.
From the data in the table it can be seen that the specific
processes are approximately adiabatic so that heat transfer is work w = cF(T3 - T4) - cF(Tz - TI) and the thermal effi-
zero anid in others heat transfer is obtained from combustion ciency
data or, if a heat exchange process, by heat exchanger
efficiency. In heating plant such as boilers which do no useful
work the steady flow energy equation shows q = Ah.
1.6.4.3 Property valuesi3 If allowance is made for the isentropic efficiency of the
compression and expansion processes the cycle diagram is
These are found in tables or from charts €or common changed to show the associated entropy increases but the
substances. Computer formulations are also available. expressions for work and efficiency above are still valid with