P-V curves

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. 

The variation of surface pressure with the area available to the spread material is represented by a tt-A (force-area) curve. With a little imagination, tt A curves can be regarded as the two-dimensional equivalent of the p-V curves for three dimensional matter, (n.b. For a 1 nm thick film, a surface pressure of 1 mN m l is equivalent to a bulk pressure of 106 N m-2, or 10 atm.)... 

There are a number of instances in which (with the aid of sensitive measurements) well-defined transitions between gaseous and coherent states are observed as the film is compressed. The tt-A curves show a marked resemblance to Andrews p-V curves for the three-dimensional condensation of vapours to liquids. The tt-A curve for myristic acid, given as an example, has been drawn schematically to accentuate its main features (Figure 4.26). Above 8 nm2 molecule-1 the film is gaseous and a liquid-expanded film is obtained on compression to 0.5 nm2 molecule-1. Fluctuating surface film potentials verify the heterogeneous, transitional nature of the surface between 0.5 nm2 molecule-1 and 8 nm2 molecule-1. 

In order to reduce the contribution of the linear stray capacitor an inverse current compensation is used which directly reduces the influence of this capacitor [11], The optimized results using this method are shown in Figures 17.13 (c) and (d). Now the ferroelectric switching can be seen clearly. The increase in resolution for the P(V) curve is in the range of a factor of 50. 

We can readily extend our discussion to include a pressure-volume, or P-K curve, which has proved useful for analyzing the water relations of plant organs such as leaves. In particular, the earliest calculations of internal hydrostatic pressure and cellular elastic modulus were based on P-V curves. To obtain such a curve, we can place an excised leaf in a pressure chamber (Fig. 2-10) and increase the air pressure in the chamber until liquid just becomes visible at the cut end of the xylem, which is viewed with a dissecting microscope or a hand-held magnifying lens so that water in individual conducting cells in the xylem can be observed. When the leaf is excised, the... 

Figure 2-15. Relation between the reciprocal of leaf water potential determined with a pressure chamber (Fig. 2-10) and the volume of xylem sap extruded as the air pressure in the chamber is progressively increased. The solid line indicates a typical range for data points for material initially at full turgor (TJ, = 0). The reciprocal of the internal osmotic pressure (1/n1) including the value at full turgor (1 /nj,), the internal hydrostatic pressure (P1), the point of incipient plasmolysis and turgor loss, and the volume of symplastic water (VSympiasm) can all be determined from such a P-V curve.

To analyse the complete pressure/volume curve simple statistical methods were applied The p/V curves of every single measurement are linear interpolated and then evaluated on a fixed lattice of points at the logarithmic pressure scale. 

Compared with B2 G2 the dry samples Bl Gl show p/V curves with a greater slope. Their pore size distribution is shifted to smaller pressures (i.e. greater pore radii). They have the highest values for the total pore volume and the median pore radius. 

P-V curves of the type shown in Fig. 2.3.2 are very common and are well simulated by the van der Waals equation of state for n moles of fluid (already introduced earlier)... 

The section BC of the van der Waals isotherm cannot be realized experimentally. In this region the slope of the p-V curve is positive increasing the volume of such a system would increase the pressure, and decreasing the volume would decrease the pressure States in the region BC are unstable slight disturbances of a system in such states as B to C would produce either explosion or collapse of the system. 

FIGURE 10.6 (a) Heart cycles with varying preload and afterload (b) The end-systolic P-V curve with increasing... 

Here, PVR (pressure-volume relationship) is the active P-V curve, and PVRgs and PVRd are the end systolic and diastolic P-V curves, respectively. Using this approach, the PVRgs curve would be parameterized in terms of the inotropic state of the myocardium, and fmax would be a function of inotropic state and heart rate. 

Suga and Sagawa [1972] originally approximated the two curves, PVRes and PVRd, with two straight lines that intersected in a common point on the volume axis (Vj, the unstressed, or dead, volume). This was a reasonable approximation, since, in their original experiments, the nonlinear portions of the P-V curves were not encountered. Based on this approach, the elastance as a function of time becomes... 

The performances of PLEDs with different kinds of HTL layers were measured in terms of 7-V L-V(Fig. 7.3D), luminous efficiency-voltage (E-V) and power efficiency-voltage (P-V) curves. For PLEDs with PEDOTiPSS as HTL, the maximum luminance was 33,800 cdm (at 12.6 V) and the maximum luminous efficiency was 8.7 cdA" (at 9.6 V). For PLEDs with rGO as HTL, the maximum luminance was 8300 cdm" (at 13.0 V) and the maximum luminous efficiency was 5.0 cdA (at 8.6 V), which were both much lower than those with... 

A typical isotherm of a van der Waals equation is drawn in Fig. 2.99 at low temperature Tj. At the high temperature T the p-V curve is still similar to the ideal gas curve. The effect of the interaction is small (because of the large kinetic energy of the molecules) and nb is small relative to the large V. At T2, one finds a pressure region where three different volumes exist as solution to the van der Waals equation, a first indication that there may be more than just the gaseous state. 

If one draws at T2 a horizontal so that the dotted areas above and below the p-V curve are equal, as illustrated in Fig. 2.99, one can show that the two marked states at the ends of the horizontal are equally stable. They are in equilibrium. One can give proof of the stability by using the free enthalpy, discussed in Sect. 2.2. For the moment it is sufficient to know that the two end points are in thermodynamic equilibrium and all intermediate states along the p-V curve are metastable or unstable (they have a higher free enthalpy). The van der Waals equation leads, thus, at certain temperatures and pressures, to the description of two phases in equilibrium, a small-volume, condensed phase (the liquid), and a large-volume, dilute gas phase (the... 

The overall mechanical properties of the isolated lung are demonstrated by its pressure-volume (P-V) curve. 

The ATF chanistry required to achieve a positive p-v curve to prevent shudder and maintain a sufficiently high friction level to provide adequate torque capacity will depend on the chemistry of the friction materials and the type of materials used to construct the transmission clutches [20]. A typical transmission clutch uses a cellulosic friction material in combination with steel plates. Other friction materials like carbon fiber are also used. Instead of steel plates, aluminum, copper, bronze, tin, and other metallic materials can also be used. In addition to these materials, plastic, nylon, and a variety of elastomeric sealant materials are used to construct other components of the automatic transmission. More recently, ATFs are required to be compatible with electronic circuitry and sensors [21]. Thus, changes in transmission design and materials have a direct effect on the... 

A measurement of the surface tension (ir) as a function of the surface area per molecules (A) at a constant temperature yields the ir-A isotherm for the two-dimensional system. Analogous to the P-V curve for a three-dimensional system, the ir-A curve for such a two-dimensional system may also undergo the gas-liquid and liquid-solid transitions. It has been... 

Figure 7.8 (a) The P-V curve for the expansion of the gas in Figure 7.7(a) from an initial volume Vi to a final volume Vf by the successive removal of the five weights, (b) The P-V curve for the expansion of the gas in Figure 7.7(a), except that the five weights are replaced with twenty smaller weights of equal total mass, (c) The P-V curve for the reversible expansion of the gas in Figure 7.7(a) to a final volume Vf. For comparison, the curve in (c) is reproduced as a dashed line in (a) and (b). 

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