Lambda curve

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Lambda (A), however, is not restricted to integer values. Since A represents the mean value of the data, and in fact is equal to both the mean and the variance of the distribution, there is no reason this mean value has to be restricted to integer values, even though the data itself is. We have already used this property of the Poisson distribution in plotting the curves in Figure 49-20b. 

An ultraviolet-visible light spectrophotometer (Lambda 10, Perkin Elmer, Norwalk, CT) was used to measure the characteristic absorbance of the samples taken from the receptor half-cell. Using a calibration curve derived from known concentrations of the model dmgs, the concentration of each sample taken from the receptor half-cell could be determined. 

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

Very few examples of heat capacity or compressibility behavior of the type shown in the second column have been observed experimentally, however. Instead, these two properties most often are observed to diverge to some very large number at Tt as shown in the third column of Figure 13.1.1 The shapes of these curves bear some resemblance to the Greek letter, A, and transitions that exhibit such behavior have historically been referred to as lambda transitions. 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

Spectroscopy. UV-VIS reflectance spectra of the pulps were recorded directly after irradiation in the wavelength range 250-750 nm on a Perkin-Elmer Lambda 15 spectrophotometer equipped with an integrating sphere. The reflectance values (RM, strictly speaking the reflectivity of an infinitely thick specimen) at 457 and 557 nm were taken from the reflectance curves. Difference spectra were calculated by subtracting the spectrum of the irradiated pulp from the spectrum of the unirradiated one. 

That s correct. Incidentally, by computing the area under the curve, you can estimate the total amount of energy the Sun radiates. Now I have a formula for you. We can calculate the wavelength lambda-max at which any star emits the greatest amount of radiation. Brunhilde, display radiation formula. On the flexscreen appears ... 

Figure 9.15 Lambda as function of the foam density line, master curve points, measured values with particle foam on basis of Sconapor1 (trade name of EPS by BSL/Dow Chemical)...

The results of endotoxin tests for in-process solutions, bulk materials, and finished parenteral products should be reported in the same units as those assigned to the product. Two factors determine the sensitivity of a BET. For infusion solutions and device extracts, the gel-clot sensitivity or the lowest point on the standard curve (lambda for kinetic LAL) and the amount of dilution determine test sensitivity.For products that have an endotoxin limit in EU/mg, the choice of lambda and the concentration of the test material determine sensitivity. The formula for product-specific sensitivity (PSS) is a convenient way to calculate the sensitivity of a BET for this type of product, where ... 

The heat capacity is based on the drop calorimetry of May (6) (400-1500 K), The pre-melt S-shaped enthalpy curve is reinterpreted as incorporating a lambda transition in view of the enthalpy measurements on K2S by Dworkin and Bredig (7 ) and the occurrence of lambda transitions in other materials having the fluorite or anti-flourite type of structure ( ). The adopted heat capacity shows the maximum of the lambda transition at 50.65 cal... 

Box plots were generated for each scenario comparing the performance of the two imputation methods. Area under the curve extrapolated to infinity (AUCo-inf), % area extrapolated, and terminal half-life (Lambda Z HL) were plotted and compared across different methods. Also the bias and precision associated with the estimation of each of these parameters were compared for the two methods. 

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