Isometric line

We could have obtained a series of curves from the variables p and 0, or v and 0, according as we assume v or p to be constant. If v be constant, the resulting curves are called isometric lines, or isochores if p be constant the curves are isopiestic lines, or isobars. 

Figure 4.3. State diagram of a ferromcignetic in a zero field (/) and the isometric line (2) as an analogue of the state diagram of polymer solution (de Gennes, 1979) [Reprinted from P.J. de Gennes Scaling Concepts in Polymer Physics. Copyright 1979 by Coriifll University Press. Used by permission of Cornell University Press]...

In this concentration range the isometric line Mo and A7o(0) S almost coincide (see Figure d.3) so that x becomes constant (xq) and... 

In the graphic representation of temperature, pressure, and volume, an isometric line shows how the temperature and pressure of a gas relate to each other at constant volume. 

We now proceed to the other end (4> > 4> ). All thermocfynamic properties tend to become independent of in this limit. Thus, we may set = or 4>p = 0 in calculating them. looking back at eq. (X.58) wh p = 1/2 MH, we see that this will again be obtained by taking H- Q. Thus, the isometric line becomes very close to the coexistence curve. This limit corresponds to the region marked S in the figure. 

The data, most of whichwere presented as pressure—volume values along isotherms, were first reduced to pressure—temperature values along isometrics (lines of constant volume). The isometric lines plotted on pressure—temperature coordinates were found to be straight lines for all but limited areas, i.e., for all except at pressures over 160 to 180 atm., and near the critical point (see Fig. 1). For these linear areas then. 

The slopes and intercepts of the linear parts of the isometric lines, for the entire range from 26 to 70 cm /mole were correlated as a function of the molar volume. This correlation is presented in Fig. 2. 

As was discussed above, the available data indicate a definite curvature of the isometric lines plotted on P-T coordinates at the higher pressures. These data are not extensive enough at high pressures to establish any definite trend for this curvature. It is therefore apparent that an extrapolation of these data to pressures over 200 atm is not justified or prudent. A need for additional data, particularly at pressures above 200 atm and at volumes less than 26 cm /mole would be a useful and important addition to the data presently available. A program is presently in progress at CEL-NBS for obtaining additional measurements of P-V-T data and it is hoped this will not only extend the range of available values but will also serve to resolve some of the uncertainty in the present data, as indicated above. 

Iracture line cuts across the isometric lines. It may also be seen that whitening or crazing occur at lower strains when the stress is low. 

If this sample contains also folded-chain crystals (reasons for their appearance during orientational crystallization were stated before), under isometric conditions they undergo melting at a higher temperature (at point 1 with respect to the oriented melt with transition to line A2) than under the conditions of free heating (point 1 with transition in the isotropic melt to line At). 

Fig. 11 —Isometric views and associated contour line plots of film shape for k=2.9 and rolling speed of 0.021 and 0.042 ms" (Ref. [56]).

Figure 5. An isometric view of the new injection system, showing the dipole magnets B1 and B2, the electrostatic deflectors D1-D4, and the aperture plate A A. The positions of the electrostatic quadrupoles Q1 and Q2 are indicated also. The principal rays for beams of two different isotopes in the deflected up position are indicated by the solid lines, with the undeflected rays shown as...

In response to M. Kac s classical paper Can one hear the shape of a drum (M. Kac, 1966), much research effort was invested in two complementary problems - to identify classes of systems for which Kac s question is answered in the affirmative, or to find examples which are isospectral but not isometric. In the present paper we shall focus our attention to quantum graphs and in the following lines will review the subject of isospectrality from this intentionally narrowed point of view. The interested reader is referred to (T. Sunada, 1985 C. Gordon et.al., 1992 S. Chapman, 1995 P. Buser et.al., 1994 Y. Okada et.al., 2001 S. Zelditch, 2004) for a broader view of the field where spectral inversion and its uniqueness are discussed. 

Output displays will be required to bring the abstract aspects of voluminous output data into some form that appeals to the experience of the user. Isopleth maps are useful, as are three-dimensional isometric plots like SYMVu, produced by Harvard University. Printer plots of concentration maps will undoubtedly enjoy an even greater application, because of the common availability of line printers or teletypewriters as output devices. Examples of these techniques are symap and grid, both produced by Harvard University. 

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 ... 

The vapor pressures of most hydrocarbons will plot as straight lines on this chart. The Cox Charts for normal paraffin and isometric paraffin hydrocarbons are given in Figures 2-7 and 2-8,1 Tire dot on each vapor-pressure line indicates the critical point. The vapor-pressure line should... 

Since every detail of a plant design must be recorded on paper, many other kinds of drawings also are required for example, electrical flow, piping isometrics, instrument lines, plans and elevations, and individual equipment drawings in all detail. Models and three-dimensional representations by computers also are now standard practice in many design offices. 

In 1853 Ossian Bonnet discovered the isometric transformation between minimal surfaces that bears his name. He wrote "Chacfue surface minima a line conjuguee qui est developpable sur elle" every minima surface has a "conjugate" minimal surface into which it can be developed). 

A piping isometric (Figure 3-8) shows a 6-inch (Schedule 40) line with six 90°LR elbows and two flow-through tees. The actual length of... 

Calculate the overall pressure drop between points 1 and 2 for a 6-inch (Schedule 40, ID=6.065 inch) line for kerosene. Liquid conditions are flow rate - 900 gpm, density at 60°F, p = 51 lb/ft and temperature, t = 321°F. Figure 3-8 shows an isometric layout of the pipeline with fittings. 

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