Pressure-volume graph

Static compliance is usually higher than dynamic compliance because there is time for volume and pressure equilibration between the lungs and the measuring system. The measured volume tends to increase and the measured pressure tends to decrease, both of which act to increase compliance. Compliance is often plotted on a pressure-volume graph. 

The line plotted on a pressure-volume graph that describes the relationship between filling status and systolic pressure for an individual ventricle (ESPVR). 

This pressure-volume graph shows an inverse relationship as pressure increases, volume decreases. 

In a pressure-volume graph, we have previously seen that the area between the abscissa and the line representing a process is proportional to the external work (W=jpdV). See Fig. 4-3. If we wish to represent heat energy as a similar area, with temperature T as the ordinate, the abscissa will be dQ/T. (See Fig. 4-6.)... 

The purpose of the graph is to demonstrate the effect of airway and tissue resistance on the pressure-volume relationship within the chest. 

Fig. 19.5. Equilibrium curve, heatup path and heatup path-equilibrium curve intercept for after-intermediate-FESOj-making catalyst bed. Attainment of equilibrium in the catalyst bed gives 98.9% oxidation of the bed s input S02. The lines apply only to the graph s specified inputs and bed pressure. This graph is a blowup of Fig. 19.6. Its intercept is confirmed by a Goal Seek calculation in Appendix T. The S02 and 02 inputs are equivalent to 0.234 volume% S02 and 7.15 volume% 02.

Suppose 1 mol of gaseous sulfur dioxide is compressed at a temperature fixed at 30.0°C. The volume is measured at each pressure, and a graph of volume against pressure is constructed (Fig. 10.18). At low pressures, the graph shows the inverse dependence (V 1/F) predicted by the ideal gas law. As the pressure increases, deviations appear because the gas is not ideal. At this temperature, attractive forces dominate therefore, the volume falls below its ideal gas value and approaches 4.74 L (rather than 5.50 L) as the pressure approaches 4.52 atm. 

If we examine a pressure vs. volume graph for each case, the work done is given by the area under the curve. Notice that the area is different for each case. 

In graph (a) below, isotherms for water are plotted against pressure and volume. Graph (b) is a phase diagram of water with pressure vs. temperature. 

Figure 2-4 Pressure-temperature graph of pure fluid showing the solid, liquid, vapor and supercritical regions. Dotted lines are lines of eonstant molar volume.

Isotherm Ts9- th9rm [F isotherme, adj (1859) n. Constant temperature line used on graphs of climatic conditions or thermodynamic relations, such as pressure-volume relations at constant temperature. Ready RG (1996) Thermodynamics. Plenum Publishing Co., New York. 

The P-V Relationships movie eChapter 10.3) illustrates Boyle s law and points out that this law holds only when temperature is constant, (a) Reproduce the pressure versus volume graph presented in the movie, (b) Using the ideal-gas equation, deduce and superimpose on your graph from part (a) the line you would expect on the P-V plot at a temperature higher than the original and at a temperature lower than the original, (c) Do the same for the V versus 1/P plot. 

Figures 2-17 and 2-18 show plots of both these functions vs pressure for molten high-density polyethylene. The pressure-volume-temperature data for these graphs were obtained from Refs. 5 and 8. Graphically integrating the appropriate curve gives the enthalpy or entropy correction due to pressure change. This correction applied to the value of enthalpy or entropy at atmospheric pressure will, in turn, yield the appropriate thermodynamic function at the pressure and temperature. Figures 2-19-2-29 give enthalpy and entropy data as functions of temperature and pressure for various polymers.

Figure 1. Schematic explanation of coupling the left ventricular contraction with the systemic arterial tree. In the middle left panels, left ventricular contraction is represented by its end-systolic pressure-volume relationship. Given a particular end diastolic volume (EDV), this relationship can be converted into ventricular end-systolic pressure P s) stroke volume (5Vj relationship, which is shown by the rectilinear curve coursing from the lower left to upper right corner in the graph at the bottom. In the right middle panel, the aortic input impedance property is represented by a rectilinear arterial end-systolic pressure fF, )-stroke volume SV) relationship curve (Eq. (5)). See the text for the explanation of this representation. This arterial Pes-SV relationship is transcribed in the bottom panel in superposition with the ventricular Pe -SV relationship. The intersection of the two Pes-SV relationship curves indicates the end-systolic pressure and stroke volume which should result from coupling a left ventricle with the given EDV and the slope parameter with a systemic arterial tree with the slope parameter...

In the previous cases the external work is often called pressure-volume work. In a graph of the process, with volume as the abscissa and pressure as the ordinate, the external work is the area between the process line and the v axis. (See Fig. 4-3.)... 

The bottom graph shows the pressure-volume product of one mole of various gases at 0°C and at different pressures.The top graph shows values at low pressure. For an ideal gas, the pressure-volume product is constant. 

Volume vs. Pressure Tiie graph of volume versus pressure shows an inversely proportional relationship. The curve is called a hyperbola. Note the difference between the shape of this graph and that of the graph in Figure 3.7. 

In reality, the performance curve is easy to understand. It isn t rocket. science. The performance curve indicates that the pump will discharge a certain volume or flow (gpm) of a liquid, at a certain pressure or head (H), at an indicated velocity or speed, while consuming a specific quantity of horsepower (BHP). The performance curve is actually four curves relating with each other on a common graph. These four curves are ... 

Another important objective which must be considered is to provide adequate cyclone capacity for the application. The volume of feed slurry that a given cyclone can handle is related to the pressure drop across the cyclone. The relationship between flow rate and pressure drop for several different sizes of standard cyclones is shown in Figure 56. As shown, the flow rate increases as the pressure drop increases. In order to utilize this graph, the pressure drop used for calculating the separation is used to determine the flow rate for the cyclone diameter which was... 

This subject has received little attention in the context of pressure vessel bursts. Pittman (1976) studied it using a two-dimensional numerical code. However, his results are inconclusive, because the number of cases he studied was small and because the grid he used was coarse. Baker et al. (1975) recommend, on the basis of experimental results with high explosives, the use of a method described in detail in Section 6.3.3. That is, multiply the volume of the explosion by 2, read the overpressure and impulse from graphs for firee-air bursts, and multiply them by a factor depending on the range. 

To use a thermodynamic graph, locate the fluid s initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure py) Read the enthalpy hy volume v, and entropy from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state , with Eq. (6.3.23). 

Volume is inversely proportional to pressure. Figure 5.4 shows a typical plot of volume (V) versus pressure (P). Notice that Vdecreases as P increases. The graph is a hyperbola. The general relation between the two variables is... 

The [H+H0H-] relationship. A graph of [OH-1 versus [H+] looks veiy much like a graph of gas volume versus pressure. In both cases, the two variables are inversely proportional to one another. When [H+] gets larger, [OH-] gets smaller. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

Charles and Gay-Lussac carried out a number of experiments with the hope of improving the performance of their balloons. They found that, provided the pressure is kept constant, the volume of a gas increases as its temperature is raised. In this case, a straight-line graph is obtained when the volume is plotted against the temperature (Fig. 4.10). This result implies... 

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