So Mr Elementary Considerations

Tin- first and second Laws of Thermodynamics appear to apply to all thermal power machines, including Stirling engines. Unfortunately no way to demonstrate the first and second laws in some simple but irrefutable fashion has been devised. Equally, of course, it is completely outside human experience for a machine to behave in contravention of these fundamental laws, despite the aspirations ol many inventors. Proposals for perpetual motion machines always contravene the fust or second law.

Belief in the Laws of Thermodynamics is closely akin to religious faith. If one has it. all is explainable. II" one doubts, nothing is explainable. An understanding and belief in the laws of thermodynamics is necessary to appreciate the delights of regenerative thermal engines.

The first Law of Thermodynamics

The first Law, a restatement of the Law of Conservation of Energy, denies the possibility of an engine (or some thermodynamic 'black box') to exist, from which power, or work, can be drawn continuously, without replenishment. The first Law requires that at least as much energy (in any form) shall be supplied to the machine as is taken from it. Let us consider air and petrol, supplied to a spark-ignition engine. Firstly, they combine in a combustion process, and the hot gases drive the engine. Of the energy supplied in the fuel, about one-third goes to useful work output from the engine, another third goes to the cooling system, and the remaining third leaves the exhaust as low-grade thermal energy. If the petrol supply is terminated, the engine stops. This is a direct application of the first Law of Thermodynamics, and a matter of common experience.

The second Law of Thermodynamics

The second Law of Thermodynamics is, perhaps, less well understood. One statement of this Law is that it is not possible to construct a system which will operate in a cycle, extract heat from a reservoir anil do an equivalent amount of work on the surroundings. The first Law says that the work produced can never be greater than the supplied heat, while the second Law goes further, and says that it must always be less. In the spark-Ignition engine, it is the second Law which denies the possibility of converting all the energy in the supplied petrol to useful work. Some of the energy must be 'wasted' in the form of heat which is rejected to the cooling system or the exhaust.

These bold statements will suffice for our purpose here. For fuller disrirccirtn rtf ll>r» fiict <»«,4 eomnrl I *n---—-------•— - • ' r • •

follows, the reader is referred to any standard text on engineering thermodynamics, e.g. Wallace and Linningt (1968).

Thermal efficiency

The ratio of the work produced IV to the energy supplied Q is called the thermal efliciency 7f, so that tj = WiQ. In many applications, it is important to maximize the thermal efficiency, since this represents the fraction of 'useful1 energy obtained from that energy which is purchased in the form of gallons of petrol or oil. It is of interest, therefore, to establish the maximum possible value of thermal efficiency, bearing in mind the limitation of the second Law of Thermodynamics that it must always be less than unity.

Carnot efficiency

For any given situation, the theoretical maximum thermal efficiency depends only on the maximum and minimum temperature of the cycle, and is given by

This relationship is so important that it is given the special name 'Carnot efliciency1. It is the highest possible value, and is attained when all heat transfers to. or from, the system occur at the constant temperatures of T,,,« or Tmin respectively.

P-V and l-S diagrams

The processes which occur in the simplest thermal machine are still, however, so complicated that il is not possible to calculate precisely what is happening. Instead, a theoretical model is assumed, in which the various events arc idealized to the extent necessary to make analysis of their operation possible. In this way, the operation of most types oJ machines may be simulated by the assumption of a repeated sequence of thermodynamic processes, called a cycle. Usually, each process is assumed to be one in which changes in the thermodynamic functions are occurring as I he fluid moves from one state to another, but one of the functions is maintained constant. The important thermodynamic functions here arc pressure (P). volume ( V), temperature (T), internal energy (U), enthalpy (YV) and entropy (S).

A cycle, consisting of a sequence of processes in which one of the thermodynamic functions is maintained constant while the others change, can be graphically represented in a variety of ways. Two of these are of importance in aiding the analysis of the operation of thermal machines.

I Wallncc, F. J. ami Uniting, W. A. (1968). Basic engineering thermodynamics, Sii ls;iac I'itmnn and Son l..t«l., London,

These are the pressure-volume (P-V) and the temperature-entropy (7-.S) diagrams.

These two diagrams are important because areas on the P -V diagram represent work done and areas on the T-S diagram represent heat transferred. As an example, consider Fig. 2.1. which shows a piston in a closed-ended cylinder. Some gas is trapped in the volume contained between the end of the cylinder and the piston, ami can he said to be at a stale represented by the point A, shown on the pressure-volume and temperature-entropy planes. If this gas were now heated through the cylinder walls, from some external source, a number of different things might happen. If the piston were fixed, the volume would remain constant, and heating the gas would result in increases in the pressure and temperature, as shown in Fig, 2.1(a). The supplied heat would be the

Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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