Typical Calculations

For Solid or Liquid. For either of these final states, it is necessary to have heat capacity data for the solid down to ternperamres approaching absolute zero. 

The integration indicated by Equation (11.21) then is carried out in two steps. From approximately 20 K up, graphical or numerical methods can be used (see Appendix A). However, below 20 K, few data are available. Therefore, it is customary to rely on the Debye equation in this region. 

Use of Debye Equation at Very Low Temperatures. Generally, it is assumed that the Debye equation expresses the behavior of the heat capacity adequately below about 20 K [9]. This relationship [Equation (4.68)], 

For a Gas. The procedure for the calculation of the entropy of a gas in its standard state is substantially the same as the that for a solid or liquid except for two factors. If the heat capacity data have been obtained at a pressure of 1 atm (101.325 kPa), the resultant value of Sjj, is appropriate for that pressure and must be corrected to the standard state pressure of 1 bar (0.1 MPa). This correction is given by 

In addition to the correction for the new standard state, it is necessary to correct for the transformation from the real gas at standard pressure to the ideal gas at standard pressure, which is defined as the standard state.  

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The analysis for I using the Volhard method requires a back titration. A typical calculation is shown in the following example. 

The contact energy E of a given conformation is typically calculated by summing the values of energies over all nonbonded contacts in the lattice. 

The preliminary assessment of noncarcinogcnic risk associated with a hazardous waste site as recommended by the USEPA is typically calculated in four major steps (6). 

A slope factor is generated in the second part of the evaluation. Based on the evaluation that the chemical is a known or probable human carcinogen, a toxicity value that defines quantitatively the relationship between dose and response (i.e., the slope factor) is calculated. Slope factors are typically calculated for potential carcinogens in classes A, Bl, and B2. Quantitative estimation of slope factors for the chemicals in class C proceeds on a case-bycase basis. 

Typical calculations starting at bottom and working up the column. 

Note This example is included because it represents typical calculations however, refrigerant R-12 is in process of being phased-out of availability, and the number values of the example showing R-12 cannot be used/substituted (except in concept) for any other newer replacement refrigerant. 

Testing of Drilling Fluids 652. Composition and Applications 664. Oil-Based Mud Systems 675. Environmental Aspects 682. Typical Calculations in Mud Engineering 687. Solids Control 691. Mud-Related Hole Problems 695. Completion and Workover Fluids 701. 

The mud rheological properties t, n and K are typically calculated based upon tbe data from two (or more)-spee(l rotational viscometer experiments. For these experiments, the following equations are applicable ... 

There is experimental consensus on the most important parameters of singlelayer polymer photovoltaic devices, the short circuit current / , the open circuit voltage V c, and the filling factor FF. From these parameters the efficiencies of PPV based devices were typically calculated to be around 0.1% under monochromatic low light intensities. Efforts to extend the classical semiconductor picture of... 

In the second method a solution of the approximate strength required is prepared, and this is standardised against some standard alkaline substance, such as sodium tetraborate or anhydrous sodium carbonate standard potassium iodate or pure silver may also be used (see Section 10.84). If a solution of an exact strength is required, a solution of an approximate strength somewhat greater than that desired is first prepared this is suitably diluted with water after standardisation (for a typical calculation, see Appendix 17). 

The actual 2/ system [34] lists 13 correction rules and 169 fragment values, including 14 new heterocyclic fragments as well as doubly and triply halogenated methyls. A typical calculation is depicted in Fig. 14.1 for quinidine. The 2/system is the only fragment method allowing manual log P calculation. Computerized... 

DbJDst ratios to within 3 s.d. We consider that these lattice strain parameters can be used to derive Z)Ra from Dsa, or even Dsr, although that correction would be inaccurately large. Typical calculated DbJDbo. ratios are 0.01-0.07. 

Methods for the calculation of pressure drop through pipes and fittings are given in Section 5.4.2 and Volume 1, Chapter 3. It is important that a proper analysis is made of the system and the use of a calculation form (work sheet) to standardize pump-head calculations is recommended. A standard calculation form ensures that a systematic method of calculation is used, and provides a check list to ensure that all the usual factors have been considered. It is also a permanent record of the calculation. Example 5.8 has been set out to illustrate the use of a typical calculation form. The calculation should include a check on the net positive suction head (NPSH) available see section 5.4.3. 

In an equilibrium flash process a feed stream is separated into liquid and vapour streams at equilibrium. The composition of the streams will depend on the quantity of the feed vaporised (flashed). The equations used for equilibrium flash calculations are developed below and a typical calculation is shown in Example 11.1. 

The elimination constant for a chemical in plasma. Typically calculated using the formula Kel = — ln[10] x b where b is the slope of the linear regression line of the log of the mean plasma concentrations vs. time from the tmsx to 24 hours. 

At this point, the reader may wonder whether our prediction of the greater variation of AEpq is somewhat arbitrary. However, it must be realized that the decrease in AEpq is the result of two combined effects, i.e. a lowering of the vacant sigma MO and the simultaneous raising of the lone pair AO as A1 is replaced by A2. Typical calculated AEpq values are shown in Table 29. It can be seen that the variation is large. 

Thus, the composition of the vapour is conveniently found from that of the liquid by use of the relative volatilities of the components. Examples 11.14-11.17 which follow illustrate typical calculations using multicomponent systems. Such solutions are now computerised, as discussed further in Volume 6. 

Deviations from ideality in real solutions have been discussed in some detail to provide an experimental and theoretical basis for precise calculations of changes in the Gibbs function for transformations involving solutions. We shall continue our discussions of the principles of chemical thermodynamics with a consideration of some typical calculations of changes in Gibbs function in real solutions. 

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