Page 47 - Mechanical Engineers Reference Book

1/36 Mechanical engineering principles

achieved by a process which is idealized as reversible with no transfer, but unfortunately the second law places restraints on
losses. Reversible processes can be described by mathematical the achievement of this desirable situation. The restraint takes
equations and enable analysis to be made to give answers for the practical form of demanding that some of the heat transfer
ideal situations. Real processes have losses and are described to the cycle must be rejected as a heat transfer to a lower
as irreversible, and the ideal results are multiplied by a temperature. Thus when we build a heat engine it has to
coefficient or efficiency (based on measurement or expe- exchange heat with (at least) two reservoirs in order to
rience) to predict real performance. produce work (Figure 1.49). Since work is the objective, the
amount produced per unit heat input is vital information and
we define the thermal efficiency of a heat engine as
1.6.2 The laws of therrnodynarnic~~~~~ Net work transfer from the cycle W
“?thermal = -
-_.
1.6.2.1 The first law of thermodynamics Heat transfer to the cycle Qi
This is a law of energy conservation. When applied to a Since the first law states Ql - Qz = W we see that efficiency
process we write is less than unity.
The second law makes further investigations and determines
Q - W = AEorq - w = Ae the maximum possible efficiency of a heat engine using
where Q is the heat transfer (kJ) or q is the specific heat reversible isothermal processes to transfer heat from two
transfer (kJlkg), W is the work transfer (kJ) or w is the specific reservoirs as
work transfer (kJ/kg), and AE is the energy change (kJ) or Ae ”?thermal maximum 1 - (TmiJ%ax)
is the specific energy change (kJ/kg).
This efficiency is known as the Carnot efficiency and is not
The change symbol A means final value minus initial value. attainable due to losses. It is also found that constant tempera-
AE embraces all forms of energy but in the non-flow process it ture processes, except during phase change, are not practical
is usual to find that the only significant change is in the internal and real processes of heat transfer take place at approximately
energy (U, u) and we write the non-flow energy equation constant volume or constant pressure. One positive product of
the second law is that it tells the engineer that thermal
Q-W=AU or q-w=Au efficiency will be increased by making the maximum cycle
For the steady flow system we write temperature as high as possible (a materials constraint) and by
making the minimum cycle temperature as low as possible
(ambient conditions)
The losses in a real cycle are due to internal fluid friction
and the necessity of having a temperature difference to cause a
heat transfer. The larger the temperature difference, the
greater the losses. The fluid friction losses in a work-producing
where e and Wx are the energy transfer rates and & is the process are defined by the process efficiency
steady mass flow rate across the boundary (in and out), Ah is Actual work produced
the change in specific enthalpy (h = u + pv), AV2/2 is the “?process =
change in specific kinetic energy and Agz is the change in Ideal work produced
specific potential energy. The suffix x is used on the work which is inverted for work-absorbing processes (compression).
transfer to denote that this is the useful work from the system The most common application of this efficiency is in steady
as the flow work is included in the enthalpy term. In flow flow adiabatic processes. Ideally, these are processes with no
problems it will also be necessary to use the continuity heat transfer which are often used as models for real processes
equation in which the heat transfers are negligible compared with the
work transfers (turbine expansion). In such processes the
m = pAV *
where p is the density and A is the area normal to the velocity
V. Analysis of non-steady flow may also be made, in which
case energy terms to allow for the storage of energy in the Hot reservoir
system will be added.
Warning: A sign convention for work and heat is built into
the equations above. Positive work means work obtained from
the system and positive heat means heat put into the system.
Care should be taken to be clear about the symbol V, which
may appear as velocity or volume in many equations.
In order to allow continuous energy transfers a cycle is
defined in which a series of processes brings the working
substance back to the initial state so that the cycle can be
repeated continuously. If we apply the first law to a cycle it
ill
follows that AE is zero and

1.6.2.2 The second law of thermodynamics Cold reservoir
It might be thought that the first law of thermodynamics
permits all the heat transfer to a cycle to be returned as work Figure 1.49 A heat engine