One Measure to Another

here s a list of some common equivalences used when working with lengths. I cover the English and metric equivalences later, in Mixing It Up with Measures.  

The measure equivalences are used to convert from one measure to another. You may need to do more than one computation if there isn t a direct equivalence between units — such as changing inches to yards or yards to miles. 

The Problem Cheryl has 48 rolls of satin ribbon, each containing 15 yards of ribbon. She plans to wrap packages to send overseas as gifts, and each package requires 30 inches of ribbon. How many packages can she wrap  

determine how many yards of ribbon are in those 48 rolls. Then change the yards to feet using 1 yard = 3 feet and the feet to inches using 1 foot = 12 inches. After you have the total number of inches, you can divide by 30 to get the number of packages that can be wrapped. 

Multiplying 48 rolls x 15 yards you get 720 yards. Start with the equivalence involving yards and feet. To change 720 yards to feet, you multiply each side of the equation 1 yard = 3 feet by 720. 

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Each concentration measure is convenient for some types of calculations but inconvenient for others. Consequently, a chemist may need to convert a concentration from one measure to another. Example illustrates the conversion from a mass-based concentration, percent by mass, to a mole-based concentration, molality. Mole... 

In the absence of systematic errors, accidental errors (due to hazards) exist that cannot be controlled because they are indeterminate. The direction and amplitude of these errors varies in a non-reproducible fashion from one measurement to another. 

This diversity of measures of salinity is especially a problem in cross-disciplinary work, where alternative measures from other disciplines are often unfamiliar. The equations needed to convert from one measure to another are... 

Now, although the quantity being measured is a property of the particular sample under study, the degree of expected fluctuation from one measurement to another depends most fundamentally on the measurement process itself—that is, how the assay is conducted—rather than on the particular sample. Since, depending on the circumstances, the amount of fluctuation among attempts to measure the same quantity may be trivial or crucially important, we now consider briefly some basic concepts that help the biochemist deal with variability among measurements. 

Gold surfaces must be thoroughly cleaned to avoid contamination of the surface and to enhance reproducibility from one measurement to another. This procedure must be performed immediately prior to performing the measurement. First, submerge consecutively for 2 min the cantilever on 2mL of tricloroethylene, acetone, ethanol, and deionized water, respectively. 

On the left-hand side is the heat flux Cht, liie surface coefficient of heat transfer, is an empirical constant that depends very much on the nature of the heat transport as well as on the surface structure, in case of two solid bodies on the contact pressure, and on the presence and nature of a fluid medium (gas or liquid) between the two bodies. This is of importance in calorimeters in which the tested substance is put into special containers (crucibles) that are then placed inside the calorimeter. If no measures are taken to ensure well-defined, reproducible heat transfer, the temperature difference involved in the heat exchange between the measuring system and the sample (or respectively, the crucible) may differ from one measurement to another, so variations will occur in the temperature as shown by the sensor relative to the actual temperature of the sample. As a consequence, the measured heat quantity may also differ, leading to an uncertainty of the result. 

Figure 7.19 shows a function of this type. Comparison of the latter with the approximation ri=0 (see Figure 7.18) reveals that the ascent (left of the peak) depends essentially on ti and the descent (right of the peak) on T2, the half-width being distinctly larger than r-i. The time constant Ti depends essentially on the heat transfer resistance Rthi and the heat capacity Cs of the sample (see Eq. (7.16)). Because both quantities vary from one measurement to another, thus causing a variation of Ti, Cs and l thi must be kept relatively small, but and the heat capacity of the sample container Cc must be large. It follows from Eq. (7.16) that... 

Precision is the degree of agreement from one measurement to another. According to the condition of comparison, there are three terms related to... 

The sequence of experimental measurements often in-dicates a substantial change from one measurement to another and therefore the presence of the systematic error This lack of reproducibility in itself raises the question of... 

Finally, in the case of solids, there is the difficulty that surface atoms and molecules differ in their properties from one location to another. The discussion in Section VII-4 made clear the variety of surface heterogeneities possible in the case of a solid. Those measurements that depend on the state of surface atoms or molecules will generally be influenced differently by such heterogeneities. Different methods of measuring surface area will thus often not only give different absolute values, but may also give different relative values for a series of solids. 

Figure Bl.24.14. A schematic diagram of x-ray generation by energetic particle excitation, (a) A beam of energetic ions is used to eject inner-shell electrons from atoms in a sample, (b) These vacancies are filled by outer-shell electrons and the electrons make a transition in energy in moving from one level to another this energy is released in the fomi of characteristic x-rays, the energy of which identifies that particular atom. The x-rays that are emitted from the sample are measured witli an energy dispersive detector.

The transference of a liquid from one vessel to another is best carried out by means of a dropping pipette A (Fig. 30). For measuring out a definite volume of liquid it is obviously an advantage to have a calibrated pipette B (Fig. 30) of i or 5 ml. total capacity. Alternatively, semi-micro burettes reading to 0 02 ml. are particularly convenient for class work. 

A liquid may be transferred from one vessel to another with a dropper pipette (Fig. XII, 1, 2, a or b). If the dropper pipette is calibrated, it may be employed for measuring out a definite volume of liquid. 

The nature of the opening between cells determines how readily different gases and Hquids can pass from one cell to another. Because of variation in flow of different Hquids or gases through the cell-wall openings, a single measurement of fraction open cells does not fully characterize this stmctural variable, especially in a dynamic situation. 

Odors are measured by their intensity. The threshold value of one odor to another, however, can vary greatly. Detection threshold is the minimum physical intensity necessary for detection by a subject where the person is not required to identify the stimulus, but just detect the existence of the stimulus. Accordingly, threshold deterrninations are used to evaluate the effectiveness of different treatments and to estabflsh the level of odor control necessary to make a product acceptable (8). Concentration can also produce different odors for the same matenal. For example, indole (qv) in low concentrations has the smell of jasmine and a low threshold of perception. In high concentrations, it has a strong odor of feces and CX-naphthyl amine as well as a considerably higher threshold of perception. 

Temperature—Volume Correetion (ASTMD1250). Tables are provided to allow the conversion of volumes of asphaltic materials from one temperature to another or, as generally used, to adjust volumes to a temperature of 15.6 °C, the standard basis of measurement in the United States. 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

A transformer is not a source of supply (it only transforms one voltage to another) but it is considered so, in terms of fault level calculations. In fact, it provides a means to add to the impedance of a circuit on the lower voltage side, and limits the fault level of the network to which it is connected. One will appreciate that the capacity of the actual source of supply, on the higher voltage side, will be much larger. On the LV side it is controlled by the impedance of the transformer. It is customary to consider this impedance to determine the fault level on the LV side. The fault level is measured as the dead... 

If the total amount of radioactivity transfened from one cylinder to another is measured the solution of the diffusion equation is... 

Charts are available to convert from one type of measurement to another as shown in Figure 19-13. Many of these charts also show approximate vibration limits. The charts demonstrate the independence of velocity measurements relative to frequency, except at very low and very high frequencies where the amplitude limits are constant throughout the operating speed range. These limits are approximate—the type of machinery, casing, foundation, and bearings must be considered to determine final vibration limits. 

Measurements of the characteristic X-ray line spectra of a number of elements were first reported by H. G. J. Moseley in 1913. He found that the square root of the frequency of the various X-ray lines exhibited a linear relationship with the atomic number of the element emitting the lines. This fundamental Moseley law shows that each element has a characteristic X-ray spectrum and that the wavelengths vary in a regular fiishion form one element to another. The wavelengths decrease as the atomic numbers of the elements increase. In addition to the spectra of pure elements, Moseley obtained the spectrum of brass, which showed strong Cu and weak Zn X-ray lines this was the first XRF analysis. The use of XRF for routine spectrochemical analysis of materials was not carried out, however, until the introduction of modern X-ray equipment in the late 1940s. 

The compressibilities of solvents vary significantly from one solvent to another. The compressibility of cyclohexane is about 0.67% per thousand p.s.i. change in pressure [11] and, thus, for a column operated at 6,000 p.s.i. (mean pressure 3,000 p.s.i.), there will be an error in retention volume measurement of about 2%. In a similar manner, n-heptane has a compressibility of about 1.0% per 1,000 p.s.i. change in pressure [11] and, under similar circumstances, would give an error of about 3% in retention volume measurement. Fortunately, as already discussed in Part 1 of this book, there are other retention parameters that can be used for solute... 

Although the consequences of the high-risk accident sequences may vary from one PSA to another, all PSAs attempt to evaluate realistically, the consequences of hypothetical accident sequences. Expending on the scope of the PSA, these evaluations may include an estimation of the number of latent cancers, the number of immediate fatalities, the probability of core damage, or a number of other consequence measures. 

The step change is close to the situation where the sensor is suddenly moved from one place to another having a different state of the measured quantity. The exponential change could, for example, be the temperature change of a heating coil or some other first-order system. Finally, the velocity fluctuations of room air can be approximated with a sine or cosine function. 

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