P-V diagram

Figure 16-2. Idealized P-V diagram for a 4-cycle, spark-ignited engine.

The area contained within the P-V diagram represents the total mechanical work performed by the piston. Some of this work is required to sustain the cycle and must be subtracted from the work calculated tiom the P-V diagram to determine the total external work available from ilie piston. 

Figure 6.12. p-V diagram showing actuai and assumed path process for a bursting sphere (Adamczyk 1976). 

Enthalpy is a properly of the system independent of the path selected. Processes can be conveniently represented graphically. For example, a P-V diagram can be used to illustrate the work done when a system undergoes a change in state (see Figure 2-31). In each of the cases depicted in Figure 2-.31, the work is equal to the shaded area under the P-V curve as shown. 

Plots of the properties of various substances as well as tables and charts are extremely useful in solving engineering thermodynamic problems. Two-dimensional representations of processes on P-V, T-S, or H-S diagrams are especially useful in analyzing cyclical processes. The use of the P-V diagram was illustrated earlier. A typical T-S diagram for a Rankine vapor power cycle is depicted in Figure 2-36. 

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

Figure 2-80. Typical P-V diagram for a pure substance showing isotherms and saturation (phases) envelope.

Quality of a Wet Vapor, in the vapor-liquid region of a pure substance, the composition of a two-phase system (at given T and P) varies from pure saturated liquid at the bubble jjoint M to pure saturated vapor at the dew point N along the line MQN on the P- V diagram (Figure 2-80). For a wet vapor represented by an intermediate... 

In Chapter 2 (Section 2.2a) we qualitatively described the Carnot cycle, but were not able to quantitatively represent the process on a p— V diagram because we did not know the pressure-volume relationship for a reversible adiabatic process. We now know this relationship (see section 3.3c), and in Figure 3.3, we compare a series of p-V adiabats with different starting temperatures for an... 

On the P — T diagram, at right, each of the mixed-phase regions is represented by a single co-existence line. The value of the chemical potential must be the same for the two phases at any point on a co-existence line. The lines meet at the triple point where all three phases are in equilibrium. The triple-point line on the P — V diagram is marked TP. 

Figure 5 P — V diagram of the Van der Waals equation of state. The solutions to these simultaneous equations are...

Energy can cross the boundary of a system without mass transfer in either macroscopic form called work (W) or microscopic form called heat (Q). Boundary work is due to a pressure difference and causes a system volume displacement (d V). The boundary work of a process is given by the expression W = fpdV. On a p-V diagram, the boundary work of a process is the area underneath the process path. Heat is due to a temperature difference and causes a system entropy displacement (d5). The heat of a process is given by the expression Q = f TdS. On a T-S diagram, the heat of a process is the area underneath the process path. 

Considering the concepts of reversible processes, a reversible cycle can be carried out for given thermal reservoirs at temperatures and Tl. The Carnot heat engine cycle on a p-V diagram and a T-S diagram, as shown in Fig. 1.4 is composed of the following four reversible processes ... 

Which area represents cycle net work of an Otto cycle plotted on a T-s diagram and p-v diagram ... 

The combustion process in internal combustion engines as an isobaric or isometric heat-addition process is oversimplistic and not realistic. A real cycle p-v diagram of the Otto or Diesel cycle looks like a curve (combination of isobaric and isometric) rather than a linear line. Are the combustion processes in the dual cycle more realistic ... 

By the way, Mikhel son was the physicist who, accdg to Rus sources, gave the definition and proposed the use in p,v diagram of the line known in Europe US as Rayleigh Line [See Cook (1958), pp 67 79], but called in Russia Liniya MikbeTsona [See under Detonation (and Explosion) of Gases, etc]... 

It was stated on p 73 of Ref 55 that for stationary motion of the gas Eq 6 for D2 should be fulfilled for any reference surface which is constructed inside the reaction zone, since the process cannot be stationary if the propagation velocity, D, is different at different points. Therefore, D is identical for all reference surfaces. If we illustrate the processes which are taking place in the detonation wave, which has specified velocity D, in a p,v diagram, then they will... 

Equation (4) represents a curve in the p - v diagram, the Hugoniot curve. 

The p(V) diagram shows the shock adiabat of the explosive, which is also called the Hugoniot curve or Hugoniot adiabat (see Fig. 1.22). The shock adiabat can be calculated for both the non-reacted explosive as well as for the reaction products (see Fig. 1.22). The C-J point, which represents the point where the C-J conditions are fulfilled, is therefore the point where the shock adiabat of the reaction products touches the Raleigh line (tangent), which is described by the following equation ... 

Maxwell, Theory of Heat, 1897, 113, 121 (emphasising the different p v diagrams for steam and carbon dioxide), 134. 

There will be an isotherm similar to ABCD for each temperature. The complete P-V diagram for the i-pentane, w-heptane S3retem containing 52.4 weight per cent w-heptane is shown in Figure 24. The critical point is the point where the bubble-point line and dew-point line meet. This is equivalent to the statement that the intensive properties of the coexisting liquid and vapor phases are identical at the critical point. Consequently, the liquid and tiie vapor are indistinguishable at the critical pressure and temperature, The critical... 

The phase behavior of multicomponent hydrocarbon systems in the liquid-vapor region is very similar to that of binary systems. However, it is obvious that two-dimensional pressure-composition and temperature-composition diagrams no longer suffice to describe the behavior of multicomponent systems. For a multicomponent system with a given overall composition, the characteristics of the P-T and P-V diagrams are very similar to those of a two-component system. For systems involving crude oils which usually contain appreciable amounts of relatively r on-volatile constituents, the dew points may occur at such low pressures that they are practically unattainable. This fact will modify the behavior of these systems to some extent. 

The P-V Diagram for a Multicomponent System. For a relatively volatile multicomponent system, a gasoline for example, an isotherm on the P-V diagram is similar to its counterpart for a binary system (Figure 23). However, it is commonly found that at the dew point the break in the P-V isotherm is not very pronounced in multi-component systems. Consequently, for systems of this type, it may be very difficult to fix the dew point in this manner. This experimental difficulty can be overcome by using a windowed cell and observing the pressure and volume when traces of liquid appear in the system. 

Figure 19.2 P-V diagram showing two rarefaction wavelets jumping down the Hugoniots.

Assuming mechanical leversibihty, calculate W, Q, AC/, and AH for each process. Sketch each path on a single P V diagram. 

Figure 5.3 P V diagram showing Carnot cycle for an ideal gas...

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