Pressure/volume diagram

FIG. 11 83 Pressure-volume diagram of an ideal (thin line) and actual (thick hne) reciprocating compressor. 

Figure 4-22. Pressure-volume diagram of the compression cycle of a sliding vane compressor.

The horizontal line at the bottom of the pressure-volume diagram of Figure 4 traces the other tv o strokes of the four-stroke cycle. On the exhaust stroke, from 5 to 6, the rising piston expels most of the remaining combustion products from the cylinder. On the intake stroke, from 6 to 7 (= 1), the descending piston inducts a fresh charge for repetition of the cycle. The net thermodynamic work developed in this cycle is proportional to the area enclosed by the pressure-volume diagram. In the ideal case, both the exhaust and intake strokes occur at atmospheric pressure, so they have no effect on the net output work. That justifies their exclusion from the thermodynamic representation of the ideal Otto... 

Pressure-volume diagram for ideal Otto cycle (1-2-3-4-5), with exhaust and intake of four-stroke cycle (5-6-7) added. ... 

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula is... 

Figure 1.5 Pressure-volume diagram for water around the supercritical region.

Such a cycle is represented as a pressure-volume diagram in Figure 6.2. The representation of a temperature-volume diagram in Figure 6.3 emphasizes the isothermal nature of Steps I and III. 

The results of the process described in Figure 2-2 may be presented in the form of a pressure-volume diagram. Figure 2-9 shows two isotherms of a typical pressure-volume diagram for a pure substance. Processes 1-3 and 4-5 correspond to the processes indicated in Figure 2-3. 

Fig. 2-9. Typical pressure-volume diagram of a pure substance showing two isotherms 13 below critical temperature, 45 above critical temperature.

Figure 2-10 shows a more nearly complete pressure-volume diagram.2 The dashed line shows the locus of all bubble points and dew points. The area within the dashed line indicates conditions for which liquid and gas coexist. Often this area is called the saturation envelope. The bubble-point line and dew-point line coincide at the critical point. Notice that the isotherm at the critical temperature shows a point of horizontal inflection as it passes through the critical pressure. 

Fig. 2-10. Pressure-volume diagram of ethane. (Data from Brown et al., Natural Gasoline and the Volatile Hydrocarbons, NGAA, Tulsa, 1947.)...

We will first consider phase diagrams. Then we will define the critical point for a two-component mixture. This will be the correct definition for multicomponent mixtures. Also, we will look at an important concept called retrograde condensation. Then the pressure-volume diagram will be discussed, and differences between pure substances and two-component mixtures in the two-phase region will be illustrated. Finally, the effects of temperature and pressure on the compositions of the coexisting liquid and gas will be illustrated. 

Fig. 2-20. Pressure-volume diagram of a mixture of 47.6 weight percent n-pentane and 52.4 weight percent n-heptane. (From Volumetric and Phase Behavior of Hydrocarbons, Bruce H. Sage and William N. Lacey. Copyright 1949, Gulf Publishing Co., Houston. Used with permission.)...

Already we have seen that the critical temperature isotherm on a pressure-volume diagram for a pure substance has a horizontal point of inflection as it passes through the critical pressure. The data of Figure 2-10 clearly show this. Thus, for a pure substance at the critical point... 

Pressure is plotted against total volume, as in Figure 10-2. The plot reproduces part of an isotherm of a pressure-volume diagram. The shape is similar to that shown in Figure 2-20. 

Phase Diagram for a Pure Substance — Use of Phase Diagrams — Vapor Pressure of a Pure Substance Pressure-Volume Diagram for a Pure Substance -Density-Temperature Diagram for a Pure Substance Two-Component Mixtures 61... 

Phase Diagrams of Two-Component Mixtures — Pressure-Volume Diagram for a Two-Component Mixture — Composition Diagrams... 

The effect of preignition on engine efficiency can be illustrated by the pressure-volume diagram shown in Figure 1 (52). In the ideal engine process, ABCD, combustion... 

Figure 1. Pressure-volume diagram illustrating effect of preignition...

The temperature-entropy diagram for the Camot cycle, corresponding to the pressure-volume diagram is shown in Fig. 2. 

Since as far back as the time of the classical works on gasdynamics only compression shock waves were known, while rarefaction occurred without discontinuities. Rarefaction waves are continuous in space. This is stated by Zemplen s theorem and is related to the fact that in a rarefaction discontinuity the entropy would decrease, which is impossible. But this is so only if the adiabate in the pressure-volume diagram is convex down. This fact was also known. The thermodynamic properties of practically all substances satisfy this condition. 

The thermodynamic process can be indicated both on a P-V (pressure-volume) diagram and on a h-S(enthalpy-entropy) diagram as shown in figure n. A. 2. The propellants enter the chamber at point i and are gasified. They react as a constant pressure, pc, and then they are expanded isentropically through the nozzle to the exhaust pressure pe. The throat conditions are noted with the subscript t. 

Figure 11.l. Pressure-volume diagram for carbon dioxide. 

The Pressure-Volume Diagram for a One-Companent System. Another way of describing the phase behavior of a system is by means of a pressure-volume diagram. Pressure is plotted as a function of the volume and the behavior of the system at constant temperature is described. Consider a fixed quantity of a pure fluid at a fixed tern-... 

It is customary to include several isotherms on a pressure-volume diagram. Such a diagram is shown in Figure 21. The isotherm at the critical temperature To gives an inflectimi at ihe point C. C represents the critical point and Pe is the critical pressure. If the system... 

Fw. 21. Typical pressure-volume diagram for a single-component system showing... 

Fig. 7.3.1. Pressure-volume diagram (schematic) for a fluid near its critical point. See text for details.

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