Ideal measured value

Accuracy of a measurement is the degree of conformity of an indicated value to an accepted standard or ideal value [4]. Repeatability is the closeness of agreement among a number of consecutive measurements of the output for the same value of the input. Each individual measurement x deviates from the correct or ideal measured value /< [2, 8]. This difference is called the measuring error or deviation di[Eq. (1)]. 

Values for the thermodynamic functions as a function of temperature for condensed phases are usually obtained from Third Law measurements. Values for ideal gases are usually calculated from the molecular parameters using the statistical mechanics procedures to be described in Chapter 10. In either... 

Thus, one can be far from the ideal world often assumed by statisticians tidy models, theoretical distribution functions, and independent, essentially uncorrupted measured values with just a bit of measurement noise superimposed. Furthermore, because of the costs associated with obtaining and analyzing samples, small sample numbers are the rule. On the other hand, linear ranges upwards of 1 100 and relative standard deviations of usually 2% and less compensate for the lack of data points. 

Ideally, the design team is responsible for making concurrent analyses of the actual test data as the data become available The team s understanding of the anticipated relations can be established by requiring the team scientists to make real time predictions of two kinds during the course of the experiment One kind occurs within a test condition In this case the data obtained to date from a particular test condition are used to predict the measurement values to be expected at a specified future date, say a week or month later for the same test condition A second kind of prediction involves across test conditions In this case the data obtained at one test condition are used to predict the measurement values for a different test condition at future specified dates ... 

The performance curve presents graphically the relationship between the probability of obtaining positive results PPRy i.e. x > xLSp on the one hand and the content x within a region around the limit of discrimination xDIS on the other. For its construction there must be carried out a larger number of tests (n > 30) with samples of well-known content (as a rule realized by doped blank samples). As a result, curves such as shown in Fig. 4.10 will be obtained, where Fig. 4.10a shows the ideal shape that can only be imagined theoretically if infinitely exact decisions, corresponding to measured values characterized by an infinitely small confidence interval, exist. 

Larger production capacities result in greater C102 emissions. The initial emission value is reached around 15 min after the peak value has occurred. The measured values displayed in Fig. 25.4 are plotted with a Poisson fit meaning that a pulse disturbance can be simulated by production tanks in series. For the highest emission peak it is found that the best fit is obtained with ideally three stirred tank reactors the lower peak is smoother and five tanks in series give the best fit. 

The technique is the same as for drawing the graph above. Demonstrate that the readings can be made accurate by the process of zeroing - altering each measured value by a set amount in order to bring the line back to its ideal position. The term drift implies that accuracy is lost over time whereas an inaccurate implies that the error is fixed. 

Solution From Observation IL-4, the student recalls that the ideal gas equation becomes increasingly exact in the limit P —> 0. Accordingly, she plots her measured values of Mapp versus P and extrapolates toward the limit as P —> 0, as shown in the graph. Her new estimate, 50.44, is now within about 0.1% of the true molecular weight (50.49) of the unknown (CH3C1), and could be further improved, if needed, by additional measurement(s) at lower P. 

TABLE 11.2 Measured Thermodynamic Properties (in SI Units) of Some Common Fluids at 20° C, 1 atm Molar Heat Capacity CP, Isothermal Compressibility jS7, Coefficient of Thermal Expansion otp, and Molar Volume V, with Monatomic Ideal Gas Values (cf. Sidebar 11.3) Shown for Comparison... 

In many chemical situations we deduce a value for a property of interest by placing experimentally measured values in the right-hand side of an appropriate formula. For example, if we use the ideal gas equation ... 

F. PVT Measurement of Gases. One of the primary advantages of the vacuum line manipulation of gases is the ease with which quantitative measurements are made. If the problem simply requires dispensing measured amounts of gas, a procedure such as the following may be employed. The ideal gas law is sufficiently accurate for most chemical work if the compounds are well removed from their condensation temperatures and pressures. For example, the van der Waals equation of state for CO2 indicates that 1 mmol of this gas in 25 mL will exert 749.7 torr pressure versus the ideal gas value of 748.4 torr. This disparity in pressures amounts to a 0.2% error, which is less that the other errors involved in routine PVT measurements, and is perfectly adequate for most chemical problems. 

As originally conceived, this handbook was to include worked examples of estimation methods for a group of benchmark chemicals for which reliable properties exist. The advantage of this approach is that the reader is likely to find it easier to apply the estimation methods if there are examples to follow. This proved to be more difficult than was expected and not all these benchmark chemicals are fully treated. Ideally, the estimated values should correspond closely with measured values. In some cases there are significant discrepancies, and this serves to reinforce the message that there remains a need to improve these methods in both accuracy and scope. The subject of estimating chemical properties from molecular structure and from related properties is thus a fruitful topic of research, and will remain so for many years into the future. 

The traceability of the value carried by a reference material (RM) should be demonstrated by the RM producer [13]. The producer shall provide the traceability of results of its measurements to the national or international measurement standards. Where this is not possible, the correlation of results with the values of national or international certified reference materials (CRMs) is required. Ideally, the values of the CRMs should themselves be traceable [2]. 

For the standard state of gaseous substances, we want to calculate thermodynamic properties in the 1.0-bar ideal gas state from measured values of properties at the measurement pressure, P. The calculation consists of the following three steps ... 

Naphthalene. Since Z = 2, the molecule occupies a site of symmetry I in other words, there is an inversion center in the middle of the C4a-C8a bond. With reference to the atom numbering system shown below, the asymmetric unit can be taken as one of the right (1 1,4a), left (5-8,8a), upper (1,2,7,8,8a) or lower (3,4,4a, 5,6) half of the molecule. Note that the idealized molecular symmetry P>2h of naphthalene is not fully utilized in the solid state, and some of the chemically identical bond distances and bond angles have different measured values. 

Out of the parameters appearing in the Young equation, Eq. (1), only the surface tension of the liquid can be simply and accurately measured. However, the measured value of a/ can be used in the Young equation only under a certain condition, as discussed in the following. Gibbs was the first to note that the Young equation may need to be modified, even for an ideal solid surface. This is so because the three interfacial tensions may be influenced by each other at the three-phase contact line, due to the effect that one phase may... 

Cv>f R Polyatomic ideal gas (value must be measured experimentally)... 

Cardona-Martinez and Dumesic [30] have analyzed the problem of surface mobility of the adsorbates for the particular case of adsorption of basic probe molecules on acid sites of oxides. Without equilibration of adsorbate with surface sites, the measured differential heat would only be an average value of the sites that the molecules adsorb on, and differences among sites would not be detected. Thus, ideally, measurements should be made at as a high a temperature as feasible without desorbing or decomposing the adsorbate. 

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