Appendix Heat Engine Cycles A Definition of Heat Engine Cycles

1. Basic Principles of Heat Engines

A heat engine is a device for converting heat energy into another form of energy. Any substance or system whose physical properties change with temperature can be used as a heat engine. If the temperature of the substance can be made to vary cyclically, then the associated physical properties will vary cyclically. By suitable mechanical, electrical, or other linkages to some one particular physical property, the cyclical changes in temperature of the system can be used to convert heat energy into kinetic or potential energy, for example.

2. Examples of Heat Engines

Among the more common examples of heat engines are steam engines in ships, trains, and electric power generating stations, gasoline engines, diesel engines, jet engines, and rocket engines. All of these have mechanical moving parts. On the other hand, fuel cells and thermoelectric cells, which have no moving parts, and generate electrical energy, are also heat engines.

3. Specification of a Heat Engine

The essential working parts of a heat engine are not always obvious from the external appearances of the overall assembly of the heat engine and its auxiliary apparatus. For example, a complete steam engine such as might be used in a railway locomotive is shown in Fig. 5.10. In terms of size the major components

Figure 5.10. Major components of a steam engine. 1, smokestack; 2, boiler; 3, flywheel; 4, connecting rod; 5, movable piston; 6, steam cylinder; 7, mounting.

are the boiler, the smokestack, and the driving wheel or flywheel. The essential heat engine, however, is the steam cylinder, which is circled in the diagram. The properties that change with temperature are the pressure and volume of the steam in the cylinder. The linkages for converting these property changes into mechanical energy are the movable piston, connecting rod, and flywheel. Not shown in the figure are the condenser and valves for admitting and removing steam.

Figure 5.11 focuses on the basic system involved in the steam engine, the cylinder filled with steam (the working substance) having a variable volume as determined by the movable piston. In oversimplified terms, when the gas (e.g., the steam) in the cylinder is hot and at high pressure, the gas expands, increasing its volume as it pushes the piston outward. When the gas is cool and at lower pressure, it contracts, decreasing its volume as the piston moves inward. It is the expansion and contraction of the volume of the gas that results in the motion of the piston. In fact, the analysis of the heat engine behavior is determined from an analysis of the pressure and volume of the gas in the cylinder as the temperature is varied.

The analysis is done by means of a graph of pressure versus volume. Such a graph is called a P- V graph or alternatively an indicator diagram.

Movable piston

Variable cylinder volume

Figure 5.11. The steam cylinder.

The P-V graph does two things: (1) It makes it possible to specify the thermodynamic state of the working substance (i.e., the value of its parameters P and V—see Section Al) and through the equation of state of the substance, its temperature T\ and (2) it makes it possible to calculate the work done by or on the substance as its state changes. In the case of the cylinder, the force exerted on the piston by the gas is proportional to the pressure of the gas. The distance that the piston moves under the influence of the force is proportional to the change in volume of the gas. Thus a P-V graph is equivalent to a graph of force versus distance; and, as discussed at the beginning of Chapter 4, the area under such a graph is proportional to the work done as the piston moves under the influence of the force.

One additional statement must be made in interpreting the area underneath a P-V diagram. If the pressure is such as to cause the piston to move outward, the work is done by the engine on the piston, and is counted as a positive energy output. If the piston is moving inward, so that the internal pressure is resisting the motion, then the work is done on the engine by the piston, and is counted as a negative energy output, or alternatively an energy input to the system. When a complete cycle is executed, the negative energy outputs must be subtracted from the positive energy outputs, in order to determine the net work done by the engine during the cycle.

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