Work units, conversion factors

As another example of the use of a unit conversion factor, calculate the number of liters of gasoline required to fill a 12-gallon fuel tank, given that there are 4 gallons in a quart and that a volume of 1 liter is equal to that of 1.057 quarts. This problem can be worked by first converting gallons to quarts, then quarts to liters. The two unit conversion factors required are the following... 

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

The chapter on Radioactive chemicals (Chapter 11) has been updated. Considerations of safety in design (Chapter 12) are presented separately from systems of work requirements, i.e. Operating procedures (Chapter 13). Tlie considerations for Marketing and transportation of hazardous chemicals are now addressed in two separate chapters (Chapters 14 and 15). Chemicals and the Environment are now also covered in two chapters (Chapters 16 and 17) to reflect the requirement that the impact of chemicals on the environment should be properly assessed, monitored and controlled. Although a substantial contribution to atmospheric pollution is made by emissions from road vehicles and other means of transport, and this is now strictly legislated for, this topic is outside the scope of this text. Chapter 18 provides useful conversion factors to help with the myriad of units used internationally. 

It is usually the best practice to work through design calculations in the units in which the result is to be presented but, if working in SI units is preferred, data can be converted to SI units, the calculation made, and the result converted to whatever units are required. Conversion factors to the SI system from most of the scientific and engineering units used in chemical engineering design are given in Appendix D. 

Beginning students often regard the metric system as difficult because it is new to them and because they think they must learn all the English-metric conversion factors (Table 2-3). Engineers do have to work in both systems in the United States, but scientists generally do not work in the English system at all. Once you familiarize yourself with the metric system, it is much easier to work with than the English system is. 

This works out because the ampere (the standard unit of current, abbreviated A) is defined as 1 coulomb per second. Because this equation gives you the amount of charge that has passed through the circuit during its operating time, all that remains is to calculate the number of moles of electrons that make up that amount of charge. For this, you use the conversion factor 1 mol e = 96,500 C. 

For each of the following pairs of units, work out a conversion factor F that will convert a measurement given in one unit to a measurement given in the other, and show the simple steps used in your work. 

Note Although this problem is given to us and worked in mg/mL, any volumetric concentration units could have been used in this problem, so long as the same units are used throughout because the conversion factors cancel. 

When using conversion factors, there are two key points to remember. First, this method works only if you are meticulous in including units with all numerical data. Secondly, if your final answer has the correct units, the answer is probably correct. If your final answer has the wrong units, the answer is almost certainly incorrect. 

In the British system, the unit of work is called the foot-pound (ft-lb), because the pound is a unit of force and the foot is a unit of displacement. These units of work are all related by simple conversion factors. 

The conversion factor approach is quite useful with metric problems. (If you have not yet worked your way through the conversion factor presentation in Unit 4, you might want to do so now.) The metric conversion factors are ones that you can make yourself using the prefixes in Table 15.1. Examples include... 

Some conversion factors for the various units of work and energy are... 

For those of us forced by convention or national origin to work with the so-called English units, there are some other handy conversion factors you should know ... 

A conversion factor (see below) is used when working with English engineering units no factor is necessary for SI metric units. For a given impeller geometry, the power number is a constant for conditions of turbulent agitation. Values of turbulent power numbers for some agitator impellers are shown in Fig. 12.1. 

The previous calculation is an example of the use of the factor label method, also called dimensional analysis, in which a quantity is multiplied by a factor equal or equivalent to 1. The units inclnded in the factor are the labels. In the previous example, 9 is equivalent to 1 hour (h), and the calculation changes the number of hours worked to the equivalent number of dollars. To use the factor label method, first put down the given quantity, then multiply by a conversion factor (a rate or ratio) that will change the units given to the units desired for the answer. The factor may be a known constant or a value given in the problem. 

Quantity Per Units of Measure Conversion Factors Work Centers Conversion Yield Factors Approval... 

The conversion factor between L atm and J can be obtained from the values of R Note that the negative sign for w makes sense, since the gas is expanding and thus doing work on the surroundings. To calculate AE, we must add q and w. However, since q is given in units... 

Occasionally SI units are not convenient, or we are working in an area which has traditionally used a different set of units. Then we need to be able to convert between different sets of units. To do this we simply use the appropriate conversion factors and apply the standard rules of mathematics. Some of these units are given in Appendix 3. 

SI units and equations wBll be used throughout Most of the original work, however, was done in the c.g.s.-e.s.u. system. Table 1 lists the SI units for the electromagnetic properties referred to in this artide, as well as the conversion factors from the SI to the probably more-familiar e.s.u. stem. To convert all equations to their c.g.s.-e.s.u. equivalents replace Co> the permittivity of free space (8.8S x 10 C m by (47t)-. ... 

Normally, heat, work, and kinetic and potential energy terms are determined in different units. To evaluate AH, we will convert each term to kW (kJ/s) using conversion factors given on the inside front cover, first noting that m = (500 kg/h/3600 s/h) = 0.139 kg/s. 

An engineer who is working on the heat transfer analysis of a house in English units needs Ihe convection heat transfer coefficient on the outer surface of the house. But the only value he can find from his handbooks is 14 W/m - °C, which is in SI units. The engineer does not have a direct conversion factor between the two unit systems for the convection heat transfer coefficient. Using the conversion factors between W and Btu/h, m and ft, and C and "F, express the given convection heat transfer coefficient in Btu/h - °F. 

Note that this relation is stated in terms of still another unit, the A unit, which was introduced because of the still remaining uncertainty in the conversion factor. The difference between A and A is only some five parts per million, and the distinction between the two units is negligible except in work of the very highest accuracy. 

This section is designed to fill the gap between the familiar formulas presented above and the assumptions and definitions of terms and physical constants needed to apply them. Values for all physical constants and needed conversion factors are provided, and dimensional analyses are included to show how the final results and their units are obtained. This close focus on the details and units of the equations themselves is followed by worked examples from the chemical literature. The goal is to provide nearly everything the interested reader may need to evaluate his or her own data, with reasonable confidence that he or she is doing so correctly. 

An alternative technique allows us to work Example 13.6 and problems like it using a single unit analysis setup. This technique, illustrated in Example 13.7, uses the universal gas constant, R, as a conversion factor. 

According to Equation (6.11), the units for work done by or on a gas are liters atmospheres. To express the work done in the more familiar unit of joules, we use the conversion factor... 

Since it is frequently necessary to work with extremely large or small numbers, a set of standard prefixes has been introduced to simplify matters (Table 1.13). Symbols and names for all units used in the handbook are given in Table 1.14. Conversion factors for commonly... 

How can we get out of this difficulty One way is to always work exclusively in SI. In that case kg will always mean kgm, and kgf will never appear. Instead the unit of force will always be the N = (1/9.8) kgf. However, then we will be unable to deal with the public, who speak (unintentionally) in kgf and Ibf, or to understand those parts of the enginepring literature that use kgf and Ibf. The other way is to decide we must live w ith the kgf and Ibf, and so we will have to regularly use the force-mass conversion factor whenever units of force and of mass occur in the same equation This conversion factor has the values shown i... 

In summary, if you can do all your work in SI, you need never be concerned about force-mass conversions (N = kg m/s ) or energy conversions (J = N-m=W s). If you are confronted with problems (or literature, or current U.S. legal definitions) involving the kgf, Ibf, cal, kcal, or Btu, you must follow the rules outlined above Always write down the dimensions, treat the dimensions as algebraic quantities, and multiply by 1 as often as needed to get the quantities into the desired set of units, using the appropriate values of the force-mass conversion factor and the thermal-mechanical energy conversion factor. Even in SI, if you stray from the basic units (m, kg, s, A, K, mol, and cd), you will need conversion factors such as... 

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