(1.75)
The kinetic energy of the fluid leaving the diffuser is usually ignored due to the low velocity at the exit, C2 (Figure 1.11b). The energy equation is then reduced to
(1.76)
Reciprocating internal combustion engine. Figure 1.12 shows a schematic diagram of the engine as a single steady‐flow system. Assuming negligible pressure work and potential and kinetic energies, energy Eq. (1.62) can be written as follows:
(1.77)
The energy equation is often used for the combined combustion/expansion (power) stroke in reciprocating engines in order to assess the process of heat release by the burning fuel. As both inlet and exhaust valves are closed during this process, it is a non‐flow closed system with no added mechanical work. Applying the energy Eq. (1.58) written in terms of specific values, we obtain
(1.78)
Both the volume and pressure change as the gases expand in the cylinder, producing work w = ∫ pdv. There is no work addition to the process, but there is a heat loss to the surroundings (unless it is assumed that the process is adiabatic); hence, the energy equation then becomes
(1.79)
This simple and convenient form of the energy equation equates the energy input as heat from the combustion of the fuel to the sum of the change of internal energy of the gases as their temperature changes, work done by the gases as they expand in the cylinder during the power stroke, and the heat loss to the surroundings.
Gas turbine. The expansion process is steady‐state, steady‐flow with heat exchange with the surroundings and negligible potential and kinetic energy changes (Figure 1.13).
Figure 1.13 Schematic diagram of a turbine.
From Eq. (1.61)
(1.80)
If the expansion process in the turbine is adiabatic, the output power is simply
(1.81)
Air compressor. The potential energy, input heat, inlet velocity, and output mechanical work can be ignored in the case of the compressor shown in Figure 1.14. Equation (1.61) is then reduced to
(1.82)
Figure 1.14 Schematic diagram of air compressor.
If the velocity of the gas is reduced at the exit from the compressor so that the kinetic energy of discharge is negligible and there is no appreciable heat loss, Eq. (1.82) is reduced to
(1.83)
For a perfect gas, Eq. (1.83) can be written as
(1.84)
Heating gas at constant pressure or constant volume. When a gas is heated at constant volume without work or heat transfer, Eq. (1.58) is written as
(1.85a)
For a perfect gas,
(1.85b)
When the gas is heated at constant pressure under steady flow conditions, Eq. (1.60) is reduced to
(1.86)
For a perfect gas with negligible heat losses, q2 = 0 and Eq. (1.86) becomes
(1.87)
1.3.6 Second Law of Thermodynamics
The first law of thermodynamics states that energy cannot be created or destroyed but it can be converted from one form to another; and when heat is converted to work, the latter can never be greater than the former. However, it does not state how much of the heat energy, for example, can be converted to work and how efficiently. The second law, in its various statements, gives the answers to these questions. A clear statement of the second law (Rogers and Mayhew, 1992) that is relevant to the subject matter of this book and based on Planck's statement is as follows:
“It is impossible to construct a system which will operate as a cycle, extract heat from a reservoir and do an equivalent amount of work on the surroundings.”
It follows that part of the extracted heat must be rejected to another reservoir at a lower temperature. Two cases can be identified:
Heat transfer will occur down a temperature gradient as heat from high‐temperature source, such as combustion chamber in a gas turbine, is partly converted to mechanical work with the balance rejected to a low‐temperature reservoir (sink) such as the atmosphere (Figure 1.15a). This system is known as a heat engine.