Time. SI units

Frequency (Section 13 1) Number of waves per unit time Although often expressed in hertz (Hz) or cycles per sec ond the SI unit for frequency is s ... 

The factor 47reQ arises from the choice of SI units. Since ap has units time , the acceleration is divided by c to convert the units of the denominator to length, as required by the definition of the field. 

Power, P, defiaed as the rate at which work is performed, is expressed ia terms of energy divided by time and is most commonly given in units of horsepower, as for the power suppHed by mechanical devices such as diesel engines, or in the SI units of watts, especially when measuring electrical power. One horsepower is equivalent to the amount of power needed to lift 33,000 pounds (14,982 kg) one foot (30.5 cm) in one minute. One watt is equivalent to the power required to perform one joule of work per second. In a simple direct-current circuit where potential is represented by E ... 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

The viscosity ratio or relative viscosity, Tj p is the ratio of the viscosity of the polymer solution to the viscosity of the pure solvent. In capillary viscometer measurements, the relative viscosity (dimensionless) is the ratio of the flow time for the solution t to the flow time for the solvent /q (Table 2). The specific (sp) viscosity (dimensionless) is also defined in Table 2, as is the viscosity number or reduced (red) viscosity, which has the units of cubic meters per kilogram (m /kg) or deciUters per gram (dL/g). The logarithmic viscosity number or inherent (inh) viscosity likewise has the units m /kg or dL/g. For Tj g and Tj p, the concentration of polymer, is expressed in convenient units, traditionally g/100 cm but kg/m in SI units. The viscosity number and logarithmic viscosity number vary with concentration, but each can be extrapolated (Fig. 9) to zero concentration to give the limiting viscosity number (intrinsic viscosity) (Table 2). 

Time. Although the SI unit of time is the second, the minute, hour, day, and other calendar units may be necessary where time relates to calendar cycles. Automobile velocity is, for example, expressed in kilometers per hour. 

Moment of Force (Torque or Bending Moment). Moment of force is force times moment arm (lever arm). Its SI unit is N-m. 

Angular Momentum (Moment of Momentum). Angular momentum is linear momentum (kg-m/s) times moment arm (m). Its SI unit is kg-m /s. For a rotating body the total angular momentum is equal to the moment of inertia I (kg-m ) times the angular velocity CO (rad/s or 1/s). 

Rotational Work. Rotational work is equal to torque (N-m) times angle of rotation (rad). Its SI unit is J. 

Centripetal Acceleration. Centripetal acceleration, /r or CO r, where is the tangential linear velocity (m/s), rthe radius (m), and CO the angular velocity (rad/s), is, like any other linear acceleration, measured in SI units m/s. Centripetal force, equal to mass times centripetal acceleration, is, like any force in SI, measured in newtons. 

Viscosity. Although traditionally of Httle importance in the evaluation of vegetable and insect waxes, viscosity is an important test for mineral and synthetic waxes. One of the most frequently used tests, ASTM D88, is used to measure the time in seconds required for a specified quantity of wax at a specified temperature to flow by gravity through an orifice of specified dimensions. This viscosity is expressed in Saybolt Universal Seconds (SUS) at the temperature of the test. The SI unit for kinematic viscosity is mm /s (=cSt). 

When arriving at the performance of a pump, it is customary to calculate its power output, which is the product of (1) the total dynamic head and (2) the mass of liquid pumped in a given time. In SI units power is expressed in kilowatts horsepower is the conventional unit used in the United States. 

It is usual these days to express all physical quantities in the system of units referred to as the Systeme International, SI for short. The International Unions of Pure and Applied Physics, and of Pure and Applied Chemistry both recommend SI units. The units are based on the metre, kilogram, second and the ampere as the fundamental units of length, mass, time and electric current. (There are three other fundamental units in SI, the kelvin, mole and candela which are the units of thermodynamic temperature, amount of substance and luminous intensity, respectively.)... 

In this book, we will express our thermodynamic quantities in SI units as much as possible. Thus, length will be expressed in meters (m), mass in kilograms (kg), time in seconds (s), temperature in Kelvins (K), electric current in amperes (A), amount in moles (mol), and luminous intensity in candella (cd). Related units are cubic meters (m3) for volume, Pascals (Pa) for pressure. Joules (J) for energy, and Newtons (N) for force. The gas constant R in SI units has the value of 8.314510 J K l - mol-1, and this is the value we will use almost exclusively in our calculations. 

Here, / is the electric field, k is the electrical conductivity or electrolytic conductivity in the Systeme International (SI) unit, X the thermal conductivity, and D the diffusion coefficient. is the electric current per unit area, J, is the heat flow per unit area per unit time, and Ji is the flow of component i in units of mass, or mole, per unit area per unit time. 

The SI unit of activity is the becquerel (Bq) 1 Bq = that quantity of radioactive material in which there is 1 transformation/second. Since activity is proportional to the number of atoms of the radioactive material, the quantity of any radioactive material is usually expressed in curies, regardless of its purity or concentration. The transformation of radioactive nuclei is a random process, and the number of transformations is directly proportional to the number of radioactive atoms present. For any pure radioactive substance, the rate of decay is usually described by its radiological half-life, TR, i.e., the time it... 

D.3.1.2 Absorbed Dose and Absorbed Dose Rate. The absorbed dose is defined as the energy imparted by the incident radiation to a unit mass of the tissue or organ. The unit of absorbed dose is the rad 1 rad = 100 erg/gram = 0.01 J/kg in any medium. An exposure of 1 R results in a dose to soft tissue of approximately 0.01 J/kg. The SI unit is the gray which is equivalent to 100 rad or 1 J/kg. Internal and external exposures from radiation sources are not usually instantaneous but are distributed over extended periods of time. The resulting rate of change of the absorbed dose to a small volume of mass is referred to as the absorbed dose rate in units of rad/unit time. 

Column inlet pressures in hplc can be as much as 200 times atmospheric pressure, and hplc columns are packed using much larger pressures (up to 700 times atmospheric). The SI unit of pressure is the Pascal (1 Pa = 1 Nm-2) normal atmospheric pressure is about 105 Pa. Because it is convenient to express pressure using reasonably small numbers, experimental workers and instrument manufacturers report pressures in bar, or pounds per square inch (psi), or sometimes in kg cm-2. The bar is defined by 1 bar = 105 Pa, so that 1 bar corresponds roughly to normal atmospheric pressure. You will need to be able to convert between these units. 

It is important that a measurement made in one laboratory by a particular analyst can be repeated by other analysts in the same laboratory or in another laboratory, even where the other laboratory may be in a different country. We aim to ensure that measurements made in different laboratories are comparable. We are all confident that if we measure the length of a piece of wire, mass of a chemical or the time in any laboratory, we will get, very nearly, the same answer, no matter where we are. The reason for this is that there are international standards of length, mass and time. In order to obtain comparable results, the measuring devices need to be calibrated. For instance, balances are calibrated by using a standard mass, which can be traced to the primary mass standard (see also Chapter 5). The primary standard in chemistry is the amount of substance, i.e. the mole. It is not usually possible to trace all of our measurements back to the mole. We generally trace measurements to other SI units, e.g. mass as in 40 mg kg-1 or trace back to reference materials which are themselves traceable to SI units. 

Time 2. Supplementary SI units Plane angle second radian s rad Duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of file ground state of the cesium-133 atom. The plane angle between two radii of a circle which cut off on file circumference an arc equal in length to the radius. 

While feet and yards are still used in Britain and other countries, the usual length is now the metre. At the time of the French Revolution in the 18th century and soon after, the French Academy of Sciences sought to systemize the measurement of all scientific quantities. This work led eventually to the concept of the Systeme Internationale, or SI for short. Within this system, all units and definitions are self-consistent. The SI unit of length is the metre. 

The SI unit of time t is the second. The second was originally defined as 1/86 400th part of a mean solar day. This definition is... 

There are seven base SI units length, time, mass, temperature, current, luminous intensity and amount of material. 

The problem with the SI base unit being a kilogram is the kilo part. The philosophical idea behind the SI system says any parameter (physical, chemical, mechanical, etc.) can be derived from a suitable combination of the others. For example, the SI unit of velocity is metres per second (m s-1), which is made up of the two SI fundamental units of length (the metre) and time (the second). A few of these combinations are cited in Table 1.3. 

Equation (8.24) is the integrated first-order rate equation. Being a logarithm, the left-hand side of Equation (8.24) is dimensionless, so the right-hand side must also be dimensionless. Accordingly, the rate constant k will have the units of s-1 when the time is expressed in terms of the SI unit of time, the second. 

---