Variables, dependent intensive

Before describing these thermodynamic variables, we must talk about their properties. The variables are classified as intensive or extensive. Extensive variables depend upon the amount while intensive variables do not. Density is an example of an intensive variable. The density of an ice crystal in an iceberg is the same as the density of the entire iceberg. Volume, on the other hand, is an extensive variable. The volume of the ocean is very different from the volume of a drop of sea water. When we talk about an extensive thermodynamic variable Z we must be careful to specify the amount. This is usually done in terms of the molar property Zm, defined as... 

The original intensity of the radiation is defined as t. A part of the intensity is absorbed, another part is transmitted, still another part is scattered, and a part of the total intensity is refiected. The components, S and T, are processes which are independent of the wavelength (firequency) of the incident photons, whereeis R and A are primarily wavelength dependent. It is here that the factor of "color" arises. The exact amount of energy extracted from lo by each process is a complex set of variables depending upon the type and arrangement of atoms composing the solid. 

In four samples, all from Bamana sculptures, the signal of haem has been detected. The intensity is different for the diverse samples, which means that the state of conservation of haem is variable depending on each sample. Nevertheless, the two-dimensional mapping... 

Depending on the source of the graphite, one obtains distinctly different IR/PA spectra (frequently caused by adsorbed species) and the response of the DTGS detector of an IR spectrometer turns out to be a more accurate measure of variable source intensity (12). A normalization technique (13) requiring measurement of the spectrum at two different mirror velocities and corrected by black body spectra taken at the same two velocities appears to be the best normalization method reported thus far. 

Figure 12.4—Fluorescence intensity. Depending on the point from which fluorescence is emitted in solution, a variable light intensity will reach the detector. By specific positioning of the excitation and emission windows, it is possible to estimate the re-absorption of fluorescence radiation (by comparison between sectors a and c in the figure) and the absorption of the incident radiation (by comparison between sectors a and b). In practice, fluorescence emitted from the central region of the cell is collected.

B) We have pointed out that experimental studies are usually arranged so that the system is univariant. The experimental measurements then involve the determination of the values of the dependent intensive variables for chosen values of the one independent variable. Actually, the values of only one dependent variable need be determined, because of the condition that the Gibbs-Duhem equations, applicable to the system at equilibrium, must be... 

Partial molar quantities are ratios of two extensive variables and are, therefore, intensive variables. As intensive variables they are independent of the size of the system and dependent only on other intensive variables. We can take our partial derivatives to be dependent on P, T, and c — 1 concentrations and write Eq. (7) as... 

Path lengths are not applicable to x- and gamma rays since their intensities decrease exponentially path lengths in solid tissne are variable, depending on particle energy, electron density of material, and other factors. 

Amtec spectrophotometers are designed to measure angular dependent intensity and correlation function either separately or concurrently. The photon correlation option enables sizing to be carried out from 5 nm to 3 pm. Rotation is continuously variable between 10° and 160° with angular resolution of 1/60° in the manual model and 1/100° in the step motor version. 

Porphyrins are ideal for investigations of light-induced charge separation and oxygen transport in vesicular solutions. Their intense Soret band at 400 nm allows measurement at concentrations down to 10 M their fluorescence spectra being detectable even at 10 M. Photo- and redox chemistries are extremely variable depending on the central metal ion and substituents. ... 

Derivatives of the extensive variable, E, with respect to three independent, extensive, variables (S,V,N), yield three corresponding dependent, intensive, thermodynamic variables T, p, p, temperature, pressure and chemical potential. It would, therefore, be nice to have a formalism that allows thermodynamic functions to be defined in which the independent variables S or V or N... 

In equilibriim thermodynamics the energy of a system may be considered to be a homogeneous bilinear function of pairs of intensive and extensive variables, either of which can be considered as the independent variable. For example, either pressure or volume may be considered as an independent variable depending upon the environment. The difference between the heat capacity at constant volume and at constant pressure is well known in equilibrium thermodynamics. Thus, in a single component equilibrium system where temperature. 

Another important variable featuring the propagation of a wave is the irradiance, often called radiation intensity, introduced in Chapter 7 when the Lambert-Beer-Bouguer law was invoked in support of the theory of influence. In Section 9.7.6 it will be shown that in a three-dimensional space the irradiance is given by the product of the euergy couceutration times the wave velocity o, which make this variable dependent on the wave frequency or wavelength ... 

What has just been said, to the effect that two intensive properties of a phase usually determine the values of the rest, applies to mixtures as well as to pure substances. Thus a given mixture of alcohol and water has definite properties at a chosen pressure and density. On the other hand, in order to specify which particular mixture is under discussion it is necessary to choose an extra set of variables, namely, those describing the chemical composition of the system. These variables depend on the notion of the pure substance namely, a substance which cannot be separated into fractions of different properties by means of the same processes as those to which we intend to apply our... 

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