The Car Not Cycle

The Carnot cycle is a thermodynamic cycle comprised of four processes, occurring sequentially, as shown in Fig. 2.2.

To consider the operation of an ideal CarnoL-cycle engine, let us assume that we have a cylinder and piston, as shown in Fig. 2.2. We assume that the cylinder is perfectly insulated, and that the piston can move, with no friction and no leakage of the working fluid from the cylinder. The cylinder head is a component that can be perfectly conducting or perfectly insulating, as we choose.

For the start of the cycle we will assume the piston to be at the outer dead point (O.D.P.), so that the volume contained within the piston and cylinder combination is a maximum. The pressure and temperature ( /',„,„) of the working fluid are at their minimum values, and are represented on Fig. 2.2(a) by the point I. We let the piston move towards the cylinder head, so that compression occurs, shown by the process 1-2 on Fig. 2.2(a). For this process, we assume that the cylinder head is perfectly conducting, and that the heat-transfer rate is infinite, so that the process occurs isothermally (constant temperature). Work is done on the gas, represented by the shaded area on the P-V diagram; heat is abstracted from the working fluid, represented by the shaded area on the T-S diagram. In this ease, since the process is isothermal, the amount of the heat transferred is exactly equal to the work done (in comparable units).

I or the second process, isentropic compression, shown in Fig. 2.2(b), the cylinder head is made perfectly insulating. As the piston continues to move towards the cylinder head, heat can no longer be abstracted from the working fluid, and so. ideally, the entropy remains constant. I his process results in a decrease in the volume, and in increases in both the pressure and temperature. The work done on the gas is the shaded area on the P-V diagram, but there is no heat transferred. The remaining two processes, isothermal expansion from 3 to 4 and isentropic expansion from I to I then follow, and arc shown on Pig. 2.2(c) and Fig. 2.2(d), respectively.

II these four diagrams are combined, the resultant P-V and T-S diagrams are as shown in Fig. 2.2(e). The shaded area, enclosed by the

Isontropic

(a) Isothermal compression. 0») Isontropic compression, (c) Isothermal expansion.

the cycle. Similarly, on the T S diagram, the area 3-4 5-6 is the heat supplied I<_» the cycle. The area 1-2-3-4 is the amount converted to work, and the area 1-2-5 6 is the 'waste heat' of the cycle. It is clear, from this diagram, why the Carnot cycle has the highest possible thermal efficiency. Given temperature limits Tiunx and Tni)n, no possible sequence of thermodynamic processes could result in a larger ratio of the areas 1-2-3-4 and 3-4-5-6, so that the efficiency, t? = W/'Q =-- area 1-2-3-4/arca 3-4-5-6 must be a maximum.

Absolute temperatures must be used in thermodynamic analysis. The zero temperature on the T-S diagram is -273CC (»OK) or -460 T ( - tl °R), so that the 'waste-heat' area 1-2-5 6 may be very appreciable.

It is clear that Ihe efiiciency of the Carnot cycle (and litis generally applies to all engines) can be improved by (a) increasing Tmux and (b) decreasing /',„,„. The ultimate maximum value of /„,„, is governed by the materials used lo construct the engine, this is called the 'metallurgical limit'. The lowest possible value of /'„„„ is that temperature at which cooling water or air is available, generally, the ambient atmospheric temperature.

In praclice, it is not possible to construct Carnot-cycle engines. There are no materials which are perfectly insulating or conducting, and all pistons sliding in cylinders do have friction and leakage losses. However, the most serious difficulty arises because isothermal and isentropic processes for a gas (say, air), have slopes that arc so little different, when compared on a P-V diagram, that the area of the P-V diagram shown in Fig. 2.2(e) becomes negligibly small, unless very high pressures and very long piston strokes are used This would result in a tremendously heavy engine, which would be quite unable to produce sufficient work to overcome its own friction losses. Despite this lack of practicality, the Carnot cycle is useful in a preliminary study of the operation of an engine. Furthermore, with some modifications (which change it to the Rankine cycle), the Carnot cycle is representative of the mode of operation of liquid-vapour machines, such as reciprocating steam-engines, steam turbines, or Trcon' refrigerating plants.

Till- STIRI I NCI CYC Lit

I he Stirling cycle is similar, in some respects, to the Carnot cycle. It is illustrated in Fig. 2.3.

Consider a cylindei containing two opposed pistons, with a regenerator between the pistons. The regenerator may be thought of as a thermodynamic sponge, alternately releasing and absorbing heat. It is a matrix of finely-divided metal in the form of wires or strips. One of the

I 1« 4% fAfl«lM.)**Ml^r fit«» niptAMi- Sr flllrtil tllA

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.

Get My Free Ebook


Post a comment