

Fig.1: the Stirling cycle; (a) PV and TS diagrams; (b) piston arrangement at the terminal points of the cycle; (c) timedisplacement diagram Fig. 2(a): Stirling and Carnot PV cycle Fig. 2(b): Stirling and Carnot TS cycle The Stirling cycle is similar, in some respects, to the Carnot cycle, as illustrated in fig.1.
Consider a cylinder containing two opposed pistons, with a regenerator between the pistons. The regenerator (matrix of finelydivided metal) may be thought of as a thermodynamic sponge which alternatively releases and absorbs heat. The volume between the regenerator and a piston maintained at high temperature T_{max} is called the expansion space while the other, maintaned ad low temperature T_{min} the compression space. As in the Carnot cycle, it is assumed that the pistons move without friction or leakage loss of the working fluid. At the beginning, we assume that the compressionspace piston is at the outer dead point and the expansionspace piston is at the inner dead point, close to the face of the regenerator. All the working fluid is then in the cold compression space. The volume is a maximun, so that the pressure and temperature are at their minimun values (point 1). During compression (process 12) the compression piston moves toward the inner dead point, and the expansionspace piston remains stationary. The working fluid is compressed in the compression space and the pressure increases. The temperature is maintaned constant because heat Q_{c} is abstracted from the compressionspace cylinder to the surrounds. In the transfer process 23, both pistons move simultaneously, the compression piston towards (and the expansion piston away from) the regenerator, so that the volume between them remains constant. Therefore, the working fluid is transferred, through the regenerator matrix, from the compression space to the expansion one. In this passage through the regenerator, the working fluid is heated from T_{min} to T_{max} by the heat exchanged from the matrix. The temperature increase at constant volume, causes an increase in pressure. In the expansion process 34, the expansion piston continues to move away from the regenerator towards the outer dead point; the compression piston remains stationary at the inner dead point, close to the regenerator. As the expansion proceeds, the pressure decreases as the volume increases. The temperature remains constant thanks to the heat Q_{e} which is added to the system from an external source. The final process in the cycle is the transfer process 41, during which both pistons move simultaneously, transferring the working fluid from the expansion space to the compression one. In the passage through the matrix, the working fluid releases heat and emerges at T_{min} into the compression space. Heat transferred in the process is contained in the matrix, for transfer to the gas in the process 23 of the subsequent cycle. Therefore, the cycle is composed of four processes: Process 12: isothermal compression at T_{min }Process 23: constant volume Process 34: isothermal expansion at T_{max} Process 41: constant volume If the heat transferred in the process 23 has the same magnitude as in process 41, then the only heat transfers between the engine and its sorroundings are (a) heat supply at T_{max} and (b) heat rejection at T_{min}. This heat supply and heat rejection at constant temperature satisfies the requirement of the second Law of Thermodynamics for maximum thermal efficiency, so that the efficiency of the Stirling cycle is the same as the Carnot cycle, i.e. eta=(T_{max}T_{min})/T_{max }A comparison of the PV diagrams and TS diagrams of a Carnot and Stirling cycle, between given limits of pressure, volume and temperature are shown in fig. 2a and 2b. 

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