Conversion between units

1 calorie (cal) of energy will heat 1 gram of water from 14.5° to 15.5°C. 

1 000 joules will raise the temperature of a cup of water by about 1°C. 

Although SI is the internationally accepted system of measurement in science, other units are encountered. Conversion factors are found in Table 1-4. For example, common non-SI units for energy are the calorie (cal) and the Calorie (with a capital C, which represents 1 000 calories, or 1 kcal). Table 1-4 states that 1 cal is exactly 4.184 J (joules). 

You require approximately 46 Calories per hour (h) per 100 pounds (lb) of body mass to carry out basic functions required for life, such as breathing, pumping blood, and maintaining body temperature. This minimum energy requirement for a conscious person at rest is called the basal metabolism, A person walking at 2 miles per 

Express the rate of energy use by a walking woman (46 -I- 45 = 91 Calories per hour per 100 pounds of body mass) in kilojoules per hour per kilogram of body mass. 

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TABLE 2.5 Conversion between Units of Concentration in ppm, pphm, ppb, ppt, and Molecules cm 3, Assuming 1 atm Pressure and 25°C ... 

Chemical engineers and scientists will know that the data they use are expressed in a great variety of different units. The length of a rod may be variously described as 12 in, 1 ft, 0.3048 m, 304.8 mm, etc. These lengths are all equivalent. Inch, foot, metre and millimetre define the size of the unit and 12, 1, 0.3048 and 304.8 define the number of the units in each system. There are many useful references in the literature that discuss conversion between units and tabulate conversion factors.1,4,5... 

The following table gives the conversion between units used in this book for expressing structural parameters and corresponding units of the International System of Units (SI). ... 

With standardisation on SI units in Europe and non-standardisation in other areas of the world, knowledge of conversion between units of measurements is essential, e.g. 

Stoichiometry is the calculation of quantitative relationships between reactants and products in chemical reactions. Scientists use stoichiometry to balance chemical equations, make conversions between units of measurement (e.g. grams to moles), and determine the correct amount of reactants to use in chemical reactions. 

In order to avoid conversion between units in the process of operation, several dimensionless numbers are used. 

A few examples are utilized to show various calculations for the conversions between units, as previously indicated. 

For conversions between units, we are usually given a quantity in some unit and asked to find the quantity in a different unit. These calculations often take the following form ... 

The important final step in solving any problem is to be sure the answer makes sense. Let s use Example 3.5 to establish a method of checking conversions between units. Notice that a week is a larger unit than a day. Notice also that 5 is a smaller number than 35. The two equal quantities, 5 weeks and 35 days, are made up of a smaller number of larger units and a larger number of smaller units. This is the same... 

As an aside, note the homogeneous and heterogeneous ET rate constants have different units. It is, in fact, not straightforward to compare these rate constants obtained through different methods and conversions between units can be approximate. Different theories can model the ET transfer as an electron diffusion coefficient (Dg, cm s ), a first-order reaction (knop. s ) or a second-order (kgx, M s ) process. This produces the diversity of units found in the literature for electron transport in MPCs. Their equivalences are ... 

The rate constants for second-order reactions can be expressed in dm mol sec, or, if the rate is measured from the change of gas pressure at constant volume, as described in eq. (2.12), in (pressure) V(time)". The conversion between units of pressure and those of concentration for gas phase reactions which are not first order, can be obtained from the perfect gas equation, from which, for the general case of a reaction of order n, the variation in the total gas pressure can be related to the change in the total gas concentration hy p = cRT... 

Conversions between English and metric units can be made using Table 1.3. 

Conversions between concentration units are relatively straightforward provided you first decide on a fixed amount of solution. The amount chosen depends on the unit in which concentration is originally expressed. Some suggested starting quantities are listed below. 

The logarithm base in Eq. (4-5) determines the units of self information. The two most common units are bits (base 2) and nats (base e) the conversion between them is given by... 

There is a fixed relation between the measure of a quantity of work and that of the quantity of heat obtained from it by complete conversion. If these- two measures are expressed in terms of the erg and the calorie respectively as units, there will also be a relation between the erg and the calorie. Heat, considered as a form of energy, may be measured in ergs, i.e., in work units, and to convert the measure of a quantity of heat expressed in calories into the measure. of the same quantity expressed in ergs, we must find the number of times the erg is contained in the calorie, and multiply this by the measure of the given quantity of heat in calories. It is a relation between units which is involved. 

Pressure units are summarized in Table 4.1. It is important to be familiar with them and to be able to make conversions between them. In Example 4.2, for instance, the pressure in pascals could have been obtained by using a conversion factor derived from Table 4.1 ... 

As explained in Section A, to convert between units, we use a conversion factor of the form... 

Integers and exact numbers In multiplication or division by an integer or an exact number, the uncertainty of the result is determined by the measured value. Some unit conversion factors are defined exactly, even though they are not whole numbers. For example, 1 in. is defined as exactly 2.54 cm and the 273.15 in the conversion between Celsius and Kelvin temperatures is exact so 100.000°C converts into 373.150 K. 

Liaw et al. reported that conversions between the neutral sparteine [Fe(NO)2] complex 133 and the anionic Fe(NO)2 [Fe(NO)2(S2C3Hg)] 137 proceed via the cationic sparteine Fe(NO)2 -complex 135 through oxidation by NO" " and transfer of the [Fe(NO)2] -unit to the chelating ligand S-(CH2)3-S 136 (Scheme 35). The resulting anionic complex 137 is stable in contrast to the cationic complex 135. The cationic complex 135 also acts as a [Fe(NO)2] donor in the presence of the DNIC [(PhS)2Fe(NO)2] 138 to yield Roussin s red ester 139. The bidentate thiol ligand S-(CH2)3-S 136 promotes the stability of the anionic DNIC Fe(NO)2 ... 

No deaths or evidence of toxicity were attributable to diisopropyl methylphosphonate administered for 26 weeks in the drinking water of rats at concentrations of 0.6 ppb, 6.0 ppb, 10 ppm, and 1,000 ppm (6.6x 10"7, 6.6x 10"5, 0.011, and 1.1 mg/kg/day, respectively) (Army 1978). It should be noted that there is some confusion concerning the concentration units used in this study (EPA 1989). EPA (1989) states that conversions between ppm and mg/L were incorrectly calculated using the air conversion factor. 

For the rest of the control loop, Gc is obviously the controller transfer function. The measuring device (or transducer) function is Gm. While it is not shown in the block diagram, the steady state gain of Gm is Km. The key is that the summing point can only compare quantities with the same units. Hence we need to introduce Km on the reference signal, which should have the same units as C. The use of Km, in a way, performs unit conversion between what we dial in and what the controller actually uses in comparative tests. 2... 

Note that any signal may be conveniently measured in terms of electrons or of energy per unit surface (J cm-2). To carry the conversion between the two modes, one has to use the wavelength dependence of the QE of the chip and the surface of the pixel. 

Experimental plug flow reactors may be small diameter tubes or packed beds with a larger ratio of diameter to length. The argument in favor of their employment is that they may simulate commercial units more closely. Rate data from pilot plant or commercial units also may need to be analyzed. A short packed bed may be operated with a high recycle ratio and will thus achieve substantially isothermal behavior and may have appreciable change in conversion between the net input and output streams. 

Unfortunately, many of the standard equations encountered in electrochemistry require the concentration unit of mol cm (moles per cubic centimetre). The conversion between mol cm and the familiar mol dm is as follows ... 

The composition of a mixture need not be given in terms of the mole fractions of its components. Other scales of concentration are frequently used, in particular, when one of the components, say. A, can be designated as the solvent and the other (or others), B, (C,...) as the solute (or solutes). When the solute is an electrolyte capable of dissociation into ions (but not only for such cases), the molal scale is often employed. Here, the composition is stated in terms of the number of moles of the solute, m, per unit mass (1 kg) of the solvent. The symbol m is used to represent the molal scale (e.g., 5 m = 5 mol solute/1 kg solvent). The conversion between the molal and the rational scale (i.e., the mole fraction scale, which is related to ratios of numbers of moles [see Eq. (2.2)] proceeds according to Eqs. (2.32a) or (2.32b) (cf. Fig. 2.4) ... 

The osmolahty of a contrast agent solution is proportional to the number of independent particles in the solution and is strongly influenced by both the concentration of the contrast agent (or any other constituents) and the temperature of the solution. The osmotic pressure of a contrast agent preparation is given in milliosmol kg water (mosm kg ), in Megapascal (MPa) or in atmospheres (at). Conversion between the different units follows the equation 1 osm kg = 1000 mosm kg = 2.58 MPa = 25.5 at. In a multi-component system, the osmolality is defined as... 

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