Experimental Methods and Instrumentation for Chemical Engineers PDF

Chapter 1 Introduction G.S. Patience Polytechnique Montréal 1.1 OVERVIEW Experimental methods and instrumentation—for the purpose of systematic, quantifiable measurements—have been a driving force for human development and civilization. Anthropologists recognize tool making, together with language...

Chapter 1 Introduction G.S. Patience Polytechnique Montréal 1.1 OVERVIEW Experimental methods and instrumentation—for the purpose of systematic, quantifiable measurements—have been a driving force for human development and civilization. Anthropologists recognize tool making, together with language and complex social organizations, as a prime distinguishing feature of Homo sapiens from primates and other animals. However, the animal kingdom shares many practices characteristic of experimentation, instrumentation and innova- tion. Animals measure distance, height, size, estimate probabilities and adapt objects for tasks: cheetahs, for example, gauge distance between themselves and their prey before giving chase. Several species devise tools: branches are levers for large arboreal primates that travel through the forest from tree to tree; chimpanzees modify sticks as implements to extract grubs from logs; beavers cut down trees and use mud and stones to build dams and lodges; and, Betty the crow bends a wire to make a hook to get food out of a narrow tube. If the act of modifying a twig to extract grubs is considered “tool making” then we need a more specific definition to differentiate humans from other species. Man uses tools to make tools and adopts a methodology to improve an out- come or function. One of the earliest examples of applying methodology is when early hominids manufactured chopping and core tools—axes and fist hatchets—before the Lower Paleolithic period (from 650 000 to 170 000 BC): they produced blades and implements by cleaving rocks with a certain force at a specific angle to produce sharp edges. The raw material—a rock—is modified through the use of an implement—a different rock—to produce an object with an unrelated function (cutting, scraping, digging, piercing, etc.). Striking rocks (flint) together led to sparks and the discovery of how to make fire. Throughout the day, we measure mass, size, time, temperature and use in- struments. The clothes that we wear, the food that we eat, the objects that we manipulate have all been developed and optimized with standardized procedures and advanced instrumentation. Sensors have increased the efficiency and safety of automobiles: gauges in the car assess gasoline/air ratio, rain on the wind- Experimental Methods and Instrumentation for Chemical Engineers http://dx.doi.org/10.1016/B978-0-44-463782-6.00001-X 1 Copyright © 2018 Elsevier B.V. All rights reserved. 2 Experimental Methods and Instrumentation for Chemical Engineers shield, cabin temperature and whether or not the seat belt is engaged. One of the key factors in homes is maintaining the correct temperature either in rooms, re- frigerators, hot water heaters, ovens, or elements on the stove. Advanced scales display body mass, percent fat, and percent water! Technological development recognizes and applies unrelated or non-obvious phenomena to new applications or to improve existing applications. Advancing technology is achieved through systematic experimental design, trial-and-error testing, or by accident. Man interprets our environment with the five+ senses —sight, sound, smell, touch, hearing, time, nociception, equilibrioception, thermoception—and each has had a historical role to innovate and devise tools. The manufacture of primitive stone tools and fire required a qualitative ap- preciation for the most common measures of mass, time, number, and length. The concept of time has been appreciated for thousands of years. In comparative terms it is qualified by longer and shorter, sooner and later, more or less. Quanti- tatively, it has been measured in seconds, hours, days, lunar months, and years. Calendars have existed for well over 6000 years and clocks—instruments to measure time intervals of less than a day—were common as long as 6000 years ago. Chronometers are devices that have higher accuracy and laboratory models have a precision of 0.01 seconds. The Egyptians were among the first to tell time over the entire day: 10 hours during the daylight, 12 hours at night, and 1 hour at dawn and dusk—the shadow hours. They could tell time at night based on the position of the stars in the sky. During the same period, Babylonians, Chinese, Greeks, and Romans had sun dials to tell time. The Egyptians replaced star gazing with a water clock (clepsydra) to tell time at night: Prince Amenemhet filled a graduated vessel with water and pierced a hole in the bottom to let the water drain (Barnett, 1998). Records of the hourglass date back to the early 13th century. Burning candles and incense sticks predated the hourglass. Recording time requires a numbering system and something to detect a change in quantity. In the simplest form of the water clock, Egyptians read time based on the liquid level in a vessel as indicated by a notch on the side. Notches on bones, wood, stone, and ivory to keep records—tally sticks—date before the Upper Paleolithic (30 000 BC). Medieval Europe relied on this system to record trades, exchanges, and even debt, but it was mainly for the illiterate. Courts ac- cepted tally sticks as legal proof of a transaction. Western civilization continues to use tally marks to update intermediate results. This unary numeral system is written as a group of five lines: the first four run vertically and the fifth runs horizontally through the four. The driving forces to maintain records and develop numbering systems in ancient civilizations were for taxes, lending, land surveying, and irriga- tion. The earliest written records of metrology come from Sumerian clay  Introduction Chapter | 1 3 tablets dated 3000 BC. These tablets had multiplication tables, division prob- lems, and geometry. The first abacus—an ancient calculator—appeared around 2700–2300 BC. Later tablets—1800–1600 BC—included algebra, reciprocal pairs, and quadratic equations (Boyer, 1991). The basis for 60 seconds in a minute, 60 minutes in an hour, and 360◦ in a circle comes from the Sumeri- ans sexagesimal numeral system (Mastin, 2010). Like the Greeks, Romans, and Egyptians, they also had a decimal system. The Pythagorean doctrine was that mathematics ruled the universe and their motto was “all is number.” 1.2 METROLOGY Metrology is the science of measurement and is derived from the Greek words metron (measure) and logos (logic, study, calculation, and reason). The Interna- tional Bureau of Weight and Measures defines it as a science that encompasses theoretical and experimental measures at any level of uncertainty in the fields of science and engineering. It comprises not only the instruments applied to quan- tify the magnitude of a physical phenomenon but also standards, procedures, quality control, training, documentation, etc. Analysis and quantification of un- certainty are core elements, as is traceability—which relates to an instrument’s measurements to known standards as well as the documented accreditations to national and international standards. Together with the physical aspects of recording data accurately and repeat- edly, metrology verifies and validates data collected by the test equipment. Enforcing standards is a critical aspect not only for consumer goods—baby car- riages, helmets, and the like—but also for industrial equipment such as vessel design (pressure vessels), materials of construction (quality of steel), and safety procedures. Along with international organizations that maintain standards for the ba- sic measures of distance, weight, etc., countries also maintain their own system of metrology (Table 1.1). For example, the National Institute of Standards and Technology (NIST), formerly the National Bureau of Standards founded in 1918, maintains both scientific and commercial metrology in the United States. Its mission is to promote American innovation and competitiveness and supplies industry, academia, and government with certified standard reference materials, including documentation for procedures, quality control, and materials for cal- ibration. The German Institute for Standards (DIN) was founded in 1917 while in the United Kingdom the BSI was formed in 1901. Further to national standards, many industries have promoted and main- tained their own standards. One of the most well-known and oldest non- governmental standards organizations is the American Society for Testing and Materials (ASTM), which was established in 1898. It collects and maintains 4 Experimental Methods and Instrumentation for Chemical Engineers TABLE 1.1 International Standards Organizations Organization Founded ASTM (American Society for Testing and Materials) 1898 BSI (British Standards Institute) 1901 SAE (Society of Automotive Engineers) 1905 DIN (Deutsches Institut für Normung) 1917 JIS (Japanese Industrial Standards) 1921 ISO (International Organization for Standards) 1926 NF (Norme Française) 1926 CEN (European Committee for Standardization) 1961 over 12 000 standards that are available to the public and include 82 volumes (at a price of $9700 in 2010). The origin of the organization was the desire to improve the quality of the rail system that had been plagued by breaks. Although the International Organization for Standards—ISO—is a non- governmental organization, it has the authority to set standards that become law through treaties or through the national standards organizations that are repre- sented in the organization and have 163 member countries. It follows ten-steps to make a procedure: 1. Preliminary work item. 2. New work item proposal. 3. Approved new work item. 4. Working draft. 5. Committee draft. 6. Final committee draft. 7. International standard draft. 8. Final international standard draft. 9. Proof of a new international standard. 10. International standard. Three common standards are: ISO 5725 (1998–2005): Accuracy of Measurement Methods and Results Package. ISO 9001 (2008): Quality Systems Management—Requirements. ISO 17025 (2005): General Requirements for Calibration Laboratories. The ISO 9001 standard was originally based on BS 5750. A primary ob- jective of this standard is to ensure the commitment of management to quality with respect to the business as well as to customer needs. The Quality Systems Management standard recognizes that employees require measurable objectives.  Introduction Chapter | 1 5 In addition to a detailed record system that shows the origin of raw materials and how the products were processed, it includes auditing (both internal and external, in the form of certification) at defined intervals to check and ensure conformity and effectiveness. The standard for calibration laboratories (ISO 17025) is closely aligned with the ISO 9001 standard but includes the concept of competency. Moreover, con- tinual improvement of the management system itself is explicitly required as well as keeping up to date with technological advances related to the laboratory. 1.3 SCIENTIFIC METHOD The scientific method is a structured sequence of steps to answer questions or evaluate observations. Many disciplines apply a structured approach to solve problems: a 1600 BC papyrus detailed a procedure to treat disease that started with an examination, followed by diagnosis, treatment and prognosis (Wilkins, 1992). The scientific method first asks a question or makes an observation. The second step involves background research including reading the literature. In the third step, we make a hypothesis (Chapter 3) then test the hypothesis with an experiment. Many experiments rely on instrumentation that we assemble, each of which has a degree of uncertainty. All equipment must be carefully calibrated and monitored before, during, and after the experiments to ensure that the data we collect are reproducible (Chapter 2). If they are irreproducible, then we must re-examine the experimental methodology and instrumentation. After we analyze the data, we communicate our findings by addressing the original hypothesis: 1. Ask a question. 2. Review literature. 3. Formulate a hypothesis. 4. Design and conduct experiments. 5. Analyze the data. a. Evaluate reproducibility and uncertainty. b. Improve reproducibility and reduce uncertainty, if needed. 6. Comment on the hypothesis. 7. Communicate the results. 1.4 INDUSTRIAL QUALITY CONTROL Industrial metrology concerns accuracy as much in the laboratory as in the field but it is more constrained in that measurements must often be made in hostile environments including high temperature, dust, vibration, and other fac- tors. Moreover, time and financial cost are other factors. Companies implement 6 Experimental Methods and Instrumentation for Chemical Engineers quality control systems to account for these factors. The ability to measure accu- rately and consistently and then interpret the results correctly to make coherent decisions is the basis of modern manufacturing. In advanced commercial chem- ical installations, workstations collect thousands of independent measurements at frequencies greater than 1 Hz and store them in massive databases. Opera- tors read data in real time through consoles in a central location. They serve to control the plant, troubleshoot, detect deviations from normal operation, ana- lyze tests designed for process optimization, and are also a historical record in the case of accidents. Additionally, the databases may be used for environmen- tal reporting to the authorities. Online analytical devices are less common than pressure and temperature measurements, but increase the level of confidence in operations and allow for mass balance and process performance calculations in real time—this improves product tracking and troubleshooting capabilities. Duplicate and triplicate measurements of pressure and temperature of critical pieces of equipment improve safety. When a variable like pressure or temper- ature exceeds a threshold value, an alarm sounds and a reading appears on console for the operator to take action. Alarms require operators to intervene while interlocks shut the process or equipment down automatically. In addition to redundant pressure and temperature gauges, engineers install spare pumps and control valves in parallel with the main process equipment. This allows operators to bypass and service equipment it without interrupting plant operation, thereby avoiding costly shutdowns. Although redundant gauges, equipment, and fail-safe devices are mandatory, accidents still happen. The 2010 Macondo well disaster in the Gulf of Mex- ico is an example where instrumentation was insufficient to warn operators of an impending blowout. Human error, instrument error, mechanical failure, and combinations of these factors cause accidents. Often a process operates at the design limits and alarms become a nuisance to operators who then ignore them. Shutting down a process to fix instrumentation or equipment outside the normal maintenance cycle is very expensive and can represent millions of dollars of lost production. Engineers and managers may choose unorthodox methods to keep a plant running. In one example, a vessel operating over 600 ◦ C lost the refractory lined bricks that insulated the metal wall from the high temperature. To avoid an unscheduled shutdown, operators sprayed cold water on the wall. This opera- tion is clearly non-standard and introduced a potentially hazardous situation—if the water spray were inadvertently shut off, the wall temperature could increase sufficiently and perforate and result in an explosion. The chemical industry has made tremendous efforts in producing goods and services in such a way as not to impact the health and well-being of society. Before commissioning a new plant or equipment, engineers and technicians write detailed operating proce- dures covering all aspects of the process to ensure it operates safely.  Introduction Chapter | 1 7 Methodologies to assess safety hazards include: What-if, Checklist (Hu- man Factor Checklist or General Hazards Identification Checklist, for example), Hazard and Operability Study (HAZOP), Failure Mode, and Effect Analysis (FMEA) or a Fault Tree Analysis. Together with general safety, other aspects that engineers assess include occupational health, ergonomics, fire safety, pro- cess safety, product stewardship. Instrumentation is a cornerstone to process safety management. 1.5 UNITS OF PHYSICAL QUANTITIES Throughout history, civilizations have developed systems to measure weight, time, and distance. The notion of weight, or mass, emerged during the same period as counting. Local authorities defined the systems and based them on practical measures—the length of an arm, a foot, or a thumb. In the late 18th century the French National Assembly and Louis XVI commissioned the French Academy of Science to conceive a rational system of measures. The National Convention in 1793 adopted the modern standards of mass and length. Originally, the meter was to be defined as the length of a pendulum, L, for which the half-cycle, t, was equal to 1 s: ! L t =π , (1.1) g where g is the gravitational constant. Eventually, the Assemblée Constituante defined the meter as one ten-millionth of the distance between the equator and the North Pole. In 1795, the gram was defined as the mass of melting ice oc- cupying a cube whose sides equal 0.01 m. In 1799, they changed the reference temperature to 4 ◦ C. At the Metre Convention of 1875, the Système interna- tional (SI) was formally established and a new standard for measuring mass was created: an alloy composed of 90 % Pt and 10 % Ir that was machined into a cylinder with a height and diameter equal to 39.17 mm. Iridium was included in the new “International Prototype Kilogram” to increase hardness. The kilogram is the only unit based on a physical artifact and not a property of nature as well as the only base unit with a prefix. The definition of the meter and the techniques to assess it evolved with tech- nology. In 1799, a prototype meter bar was fabricated to represent the standard. (It was later established that this bar was too short by 0.2 mm since the curvature of the Earth had been miscalculated.) In 1889, the standard Pt bar was replaced with a Pt(90 %)–Ir(10 %) bar in the form of an X. One meter was defined as the distance between two lines on the bar measured at 0 ◦ C. In 1960, the standard was changed to represent the number of wavelengths of a line in the electromag- 8 Experimental Methods and Instrumentation for Chemical Engineers netic emission of 86 Kr under vacuum. Finally, in 1983, the standard was defined as the distance that light travels in a vacuum in 1/299 792 458 s. The standard to measure the base unit of time—the second—has evolved as much as the standard to measure distance. During the 17–19th centuries, the second was based on the Earth’s rotation and was set equal to 1/86 400 of a mean solar day. In 1956, recognizing that the rotation of the Earth slows with time as the Moon moves further away (about 4 cm y−1 ), Ephemeris Time became the SI standard: 1/31556925.9747 the length of the tropical year of 1900. In 1967, the second was based on the number of periods of vibration radiation emitted by a specific wavelength of 133 Cs. The International System of Units (Système international d’unités or SI) rec- ognizes seven base properties (Table 1.2)—time, length, mass, thermodynamic temperature, amount of matter, electrical current, and luminous intensity. Other measures include the plane angle, solid angle, sound intensity, and seismic mag- nitude and intensity. The standard changed from the cgs—centimeter, gram, second—system to SI in 1960. In 1875 at the Convention du Mètre, three in- ternational organizations were formed to oversee the maintenance and evolution of the metric standard: General Conference on Weights and Measures (Conférence générale des poids et mesures—CGPM). International Bureau of Weights and Measures (Bureau international des poids et mesures—BIPM). International Committee for Weights and Measures (Comité international des poids et mesures—CIPM). 1.6 WRITING CONVENTIONS Table 1.2 lists not only the seven standard properties recognized by the Inter- national System of Quantities (SIQ) but also the symbols representing each property and its dimension as well as the base unit and its symbol. All other TABLE 1.2 SI Base Units Base quantity Base symbol Measure SI unit SI symbol Time t T second s Length l, x, y, z, r L meter m Mass m M kilogram kg Amount of matter n N mole mol Temperature T θ kelvin K Luminous intensity lv J candela cd Electrical current I, i I ampere A  Introduction Chapter | 1 9 quantities may be derived from these base properties by multiplication and di- vision (Bureau International des Poids et Mesures, 2006). For example, speed equals distance (length) divided by time: L/T. Kinetic, potential, and thermal are different forms of energy and Leibniz defined it as the product of the mass of an object and its velocity squared: ML2 T −2 with the units kg m2 s−2. SI has designated this expression as the joule (J) to honor the contributions of the 19th century English physicist. Pressure is the force exercised on a unit area and has units of ML−1 T −2. The unit for pressure is the pascal (Pa) named after the French physicist who demonstrated that atmospheric pressure changes with elevation. Quantities or properties are either extensive—properties that are additive for subsystems, for example mass and distance—or intensive, for which the value is system independent like temperature and pressure. Prefixes qualify the meaning of properties like specific and molar. Specific heat capacity is the heat, or energy, required to raise the temperature of a given mass by an increment. Its SI unit is J kg−1 K−1 and the unit of molar heat capacity is J mol−1 K−1 (Table 1.3). The volume occupied by 1 mol of a substance is the molar volume. The minute, hour, day and hectare are symbols that fall outside the standard- ized nomenclature but SI recognizes them as part of the system (Table 1.4). A space or half-high dot separates SI base unit symbols and names in de- TABLE 1.3 SI Coherent Derived Units Quantity Unit Symbol SI base units Force newton N kg m s−2 Pressure pascal Pa kg m−1 s−2 Energy joule J kg m2 s−2 Power watt W kg m2 s−3 Moment of force – Nm kg m2 s−2 Surface tension – N m−1 kg s−2 Dynamic viscosity – Pa s kg m−1 s−1 Heat flux density, irradiance – W m−2 kg s−3 Entropy – J K−1 kg m2 s−2 K−1 Specific entropy, heat capacity – J kg−1 K−1 kg m2 s−2 K−1 Specific energy – J kg−1 m2 s−2 K−1 Molar energy – J mol−1 kg m2 s−2 mol−1 Energy density – J m−3 kg m−1 s−2 Molar entropy – J mol−1 K−1 kg m2 s−2 K−1 mol−1 Thermal conductivity – W m−1 K−1 kg m s−3 K−1 10 Experimental Methods and Instrumentation for Chemical Engineers TABLE 1.4 SI Recognized Units Unit Symbol SI minute min 60 s hour h 3600 s day d 86 400 s hectare ha 10 000 m2 liter L (l is discouraged) 0.001 m3 tonne t 1000 kg decibel dB – electronvolt eV 1.602 176 53 × 10−19 J knot kn 1852 m h−1 fathom ftm 1.828 80 m nautical mile M 1852 m rived units: the viscosity of water at 0 ◦ C equals 0.001 Pa s. Negative expo- nents, a solidus, or a horizontal line indicate division. SI accepts only one solidus, thus atmospheric pressure is 101 325 mkgs2 or 101 325 kg m−1 s−2 but not 101 325 kg/m/s2. Derived unit symbols named after a person are capital- ized (N—Newton, Hz—Hertz, W—Watt, F—Faraday) but they are lower case when written out (one pascal, a newton). Symbols are mathematical entities so it is incorrect to add an “s” to indicate plural or a period except at the end of a sentence—“min.” is unacceptable in the middle of a sentence. Express unit symbols in roman upright type regardless of the font. The International Bureau of Weights and Measures (BIPM—Bureau Interna- tional des Poids et Mesures) (Bureau International des Poids et Mesures, 2006) publishes standards to represent quantities including numerical values, spac- ing, symbols, and combinations of symbols. A space follows numerical values before the unit symbol: 9001 kg. In the case of exponential notation, a space follows the numerical value before the multiplication sign: 9.001 × 103 kg. Plane angular symbols—degrees, minutes, and seconds—are exceptions and follow the numerical value without a space. Temperature, expressed in de- grees Celsius, takes a space after the number—25.0 ◦ C. In 2003, the CGPM recognized the comma and the period as decimal markers. English-speaking countries and most Asian countries adopt a period while other nations use a comma. Separate groups of numbers in multiples of a thousands with spaces (c = 299 792 458 m s−1 ). Up to 9999, spaces are unnecessary (1337 and not 1 337). For numbers between −1 to 1, a zero precedes the decimal marker: R = 0.008 314 kJ mol−1 K−1.  Introduction Chapter | 1 11 Roman numerals are never italicized but running numbers that represent nu- merical values are, like in matrices or variable subscripts (Table 1.5). Symbols representing mathematical constants like π and e are in roman but physical constants, like R, are in italics. Well defined mathematical functions—tan, sin, ln—are in roman but generic functions we define, f (x), are in italics as well as physical quantities that are functions P (t) (pressure P and time t). Add prefixes to units to reduce the number of digits. Many scientific fields have developed their own conventions. For instance, the unit MW is common in the power industry. The unit nm is standard in crystallography to characterize the physicochemical properties of solids—pore diameter is an example. All prefixes are multiples of ten (Table 1.6). Symbols are capitalized for multiple factors greater than 103. The symbols for 1021 and 1024 are the same as for 10−21 and 10−24 except that the former take a capital letter and the latter are in lower case. The micro (10−6 ) is the only Greek letter and the only two-letter symbol is da. 1.7 UNIT CONVERSION SI units dominate the scientific literature but we continue to use the cgs (centimeter-gram-second) and fps (foot-pound-second or Imperial system of units) unit systems, the latter particularly in the United States. SI (mks) sup- planted the cgs system. While most conversions between cgs and SI are straight- forward, conversion between fps and SI is more complicated. In cgs, the gram is the standard mass rather than the kilogram (mks). In fps, the standard unit of mass is the avoirdupois (which means “to have weight” in French) with the abbreviation lb (or lbm —pound-mass), which is derived from the Latin word libra (meaning scale or balance). The factor to convert from pounds to kilograms, by definition, is: 1 lb = 0.453 593 27 kg. The length standard is the centimeter for the cgs system and the foot for the fps system, with the abbreviation ft: 1 ft = 0.3048 m = 30.48 cm. Other length measures in the fps system include the inch (12 in. ft−1 ), the yard (3 ft yd−1 ), and the mile (5280 ft mi−1 ). The gallon is a measure of volume with two definitions: the US gallon is 3.79 L while the imperial gallon is 4.54 L. A barrel of oil equals 0.159 m3. The time standard is the same for all three systems. The cgs and SI sys- tems share the standards for temperature and for quantity of matter (mol). The 12 Experimental Methods and Instrumentation for Chemical Engineers TABLE 1.5 NIST Math Writing Conventions (Patience et al., 2016) Typeface Examples Symbol Description Physical Italic R 8.314 J mol−1 Gas constant constants h 6.626×10−19 J s Planck’s constant Variables Italic E = mc2 E, m, c user-defined, physical Functions Italic f (x) f Quantities Italic t, V time, volume CP C heat capacity Parameters Italic f (x) = β0 + β1 x β 0 , β1 coefficients sin ax a trig. coefficient R2 coeff. of determination n " Running nos. Italic xi i, n i=0 Vectors Italic a = (a1 a2 a3 ) a bold Matrices Italic A Mathematical Roman i Imaginary unit constants e 2.718 28 Euler’s number π 3.141 59 Archimedes’ constant Well defined Roman ln x ln natural functions logarithm tan x tan tangent function Jn (x) Jn Bessel function Mathematical Roman df/dt d differential operators Roman $x = x2 − x1 $ difference Numbers Roman x1 1 FeII II Oxidation state Descriptive Roman Ea a activation in yCO2 in superscript Units Roman g=9.81 m s−2 m, s meter, second 1 ◦C ◦C degree Celsius Elements Roman H2 S H, S hydrogen, sulphur CO2− 3 C, O carbon, oxygen  Introduction Chapter | 1 13 TABLE 1.6 SI Prefixes Multiples Fractions Name Symbol Factor Name Symbol Factor deca da 101 deci d 10−1 hecto h 102 centi c 10−2 kilo k 103 milli m 10−3 mega M 106 micro µ 10−6 giga G 109 nano n 10−9 tera T 1012 pico p 10−12 peta P 1015 femto f 10−15 exa E 1018 atto a 10−18 zetta Z 1021 zepto z 10−21 yotta Y 1024 yocto y 10−24 standard for thermodynamic temperature in fps is the Rankine: 1.8 ◦ R = 1 K. The Fahrenheit scale is the equivalent of the Celsius scale and they are re- lated by: TFahrenheit = 32 ◦ F + 1.8 ◦ F ◦ C−1 × TCelsius. At 0 ◦ C, the temperature in the Fahrenheit scale is 32 ◦ F. The boiling point of water is 212 ◦ F and absolute zero (0 K) equals −459.67 ◦ F (which is equal to 0 ◦ R). In many practical applications, the mol is too small and thus chemical engi- neers adopt the kmol. Adding g in front of mol (g-mol) is unacceptable. In the fps system, the lb-mol is the standard: 1 lb-mol = 453.592 37 mol = 0.453 592 37 kmol. Mixed units are often used in chemistry: molar concentration has the units mol m−3 but almost all chemical literature report mol dm−3 or more commonly mol L−1 or kmol m−3 for industrial scale processes. These units are referred to as molar with the designation of M. Prefixes may be added to M for low values. Thus, µM represents µmol L−1 and nM refers to nmol L−1. As with SI units, important derived units have been assigned independent symbols such as force, energy, and power. The unit of force in SI is the newton (N), which is equal to the product of mass and acceleration: 1 N = 1 kg m s−2. 14 Experimental Methods and Instrumentation for Chemical Engineers The dyne is the derived unit for force in the cgs system: 1 dyn = 1 g cm2 s−1 , 1 N = 105 dyn. Researchers report surface tension dyn cm−1 : the surface tension of distilled water is 72 dyn cm−1 (at 25 ◦ C), which equals 72 mN m−1. In the fps system, the pound force (lbf ) is the quantity measured by an avoirdupois pound at the surface of the earth and is equal to 4.448 N. The lbf and lbm are related through the gravitational constant: 1 lbf = 1 lbm · gc = 1 lbm · 32.174 ft2 s−1. Pressure equals the force applied to an area perpendicular to it. The SI de- rived unit is the pascal with the symbol Pa: 1 N m−2 = 1 kg m−1 s−2 = 1 Pa. Atmospheric pressure equals 101 325 Pa at sea level (but can change by 5 % in a day) and bar and atm are derived units for pressure (but are unacceptable in SI): 1 bar = 100 000 Pa, 1 atm = 101 325 Pa. The unit for pressure in the fps system is the lbf in−2 and its symbol is psi. One atmosphere of pressure equals 14.696 psi and one bar is 14.504 psi. The joule (J) represents energy in SI and the erg in cgs: 1 J = 1 kg m2 s−2 = 107 erg = 107 g cm2 s−2. In chemistry and chemical engineering, we express energy in calorie, which is the energy required to raise 1 g of water by 1 K. The factors to convert to erg and joule are: 1 cal = 4.184 × 107 erg = 4.184 J. The unit for energy in the fps system is the British thermal unit (Btu): 1 Btu = 1055.06 J. The derived unit for power is the watt (W), which is the rate of change of energy conversion: 1 W = 1 J s−1 = 1 kg m2 s−3.