CHAPTER 1THE SCOPE OF PHYSICS

CONTAIN:1. INTRODUCTION 2. SYSTEM OF UNITS (MEASUREMENT). 3. DIMENSION. 4. UNIT AND DIMENTION5. SIGNIFICANT FIGURE

DESCRIPTIVE PART 1: What is PHYSICS? The word 'Physics' comes from the Greek word 'phusis' meaning 'nature', introduced by the ancient scientist 'Aristotle'. Man has always been fascinated by nature. The branch of science which is devoted to the study of nature and natural phenomena is called Physics. It is expected that all the events in nature take place according to some basic laws. Thus Physics (the knowledge of nature) is the science concerned with the discovery and understanding of the most basic fundamental laws of the universe that control the way everything in the world around us behaves. Discoveries in basic physics have important ramifications for all of science. Physics is the scientific study of matter and energy and how they interact with each other. Physics deals with matter on scales ranging from sub-atomic particles (i.e. the particles that make up the atom and the particles that make up those particles) to stars and even entire galaxies. Physics is the truly universal science. There are many fields of physics, for example: mechanics, electricity, heat, sound, light, condensed matter, atomic physics, nuclear physics, and elementary particle physics. Physics is the foundation of all the physical sciences, such as chemistry, material science, and geology and is important for many other fields: biology, medicine, computing, ice hockey, and television, list goes on.The physics was divided in main two branches:

i. Classical mechanics ii. Quantum mechanics.

The Mechanics or classical physics is an important field of physics. Developed by Sir Isaac Newton in the 17th century, the laws of mechanics and the law of gravity successfully explained the orbits of the moon around the earth and the planets around the sun. Newton’s laws are used to design cars, clocks, airplanes, earth satellites, bridges, buildings, just about everything, it seems, except electronics.

Electricity is another example of physics, one that you may experience as a spark when you touch a doorknob on a dry winter day. The electrical attraction of protons and electrons is the basis for chemistry. Magnetism is another force of nature, familiar to us from refrigerator magnets and compasses. In the 19th century, James Clerk Maxwell combined electricity and magnetism. He showed that light is an electromagnetic wave that travels through empty space. The Quantum mechanics deals Einstein’s theory of relativity and other modern concepts of twentieth century are discussed. The modern physics divided in to: Atomic physics, Elementary physics, Nuclear physics, Molecular physics, Plasma physics, Medical physics, Solid state physics, Astronomical physics, and many others.

2: Physical Quantities:Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time.Extensive and Intensive Quantities:Extensive: when its magnitude is additive for subsystems (volume, mass, etc.)Intensive when the magnitude is independent of the extent of the system (temperature, pressure, etc.)

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Some physical quantities are prefixed in order to further qualify their meaning:Molar is added to refer to a quantity which is expressed per unit mass (such as specific heat capacity)Specific is added to refer to a quantity which is expressed per unit amount of substance (such as molar volume).

There are also physical quantities that can be classified as neither extensive nor intensive, for example angular momentum, area, force, length, and timeCoordinates are sets of numbers that describe position along a line, on a surface or in space. Latitude and longitude, or declination and right ascension, each is a system of coordinates on the surface of a sphere on the globe of the Earth or the globe of the heavens.

3: Unit: Unit is the universally accepted definite amount of a physical quantity taken as a standard for the measurement of the same physical quantity of any amount. E.g. Kilogram (kg), meter (m), second (s), and etc some physical quantities have no units, since each is expressed by a ratio of similar physical quantities. For example, mechanical advantage, velocity ratio, refractive index, atomic weight, and etc. It means, a unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.

4: Fundamental Quantities: The first standard units of measurement were established by the French Academy of Sciences in the 1790. The measurement of any quantity is made relative to particular standard or unit and this unit must be specified along with the numerical value of the quantity. Fixing the unit of only three physical quantities forms a system of units, which contains the unit of every physical quantity. These quantities are called “fundamental quantities”, and their units are called “fundamental units”. A physical quantity is a physical property that can be quantified. This means it can be measured or calculated and expressed in numbers. For example, "mass" is a physical quantity that can be expressed by stating a number of some basic measurement units. A quantity of mass might be represented by the symbol m, and could be expressed in the unit’s kilograms.

Basic SI quantities:The International System of Units SI is the modern form of the metric system. The SI was developed in 1960 from the old meter-kilogram-second (MKS) system, rather than the centimeter-gram-second (CGS) system. The system is nearly universally employed. In all there are seven SI base units: the meter for distance, the kilogram for mass, the second for time, the ampere for electric current, the Kelvin for temperature, the mole for amount of substance, and the candela for intensity of light.

5: Derived Quantities:The quantities other than fundamental quantities are, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. Thus, Derived physical quantities are those, each of which associates one or more fundamental physical quantities. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units.

6: System of Units:Measurements have an important role not only in physics but also in every branch of science and everywhere in our day-to-day life. To solve problems and to understand the basics of the Physics it is very important to know what is a physical quantity, types of physical quantities, what is a unit, what are the units of different physical quantities, types of units, symbols of units.

1. S.I. System of units:In 1960, an international committee established a set of standards for length, mass, and other basic quantities. The system established is an adaptation of the metric system, and it is called the SI system of units. In this system, the units of length, mass, and time are the meter, kilogram, and second, respectively. Other SI standards established by the committee are those for temperature (the Kelvin), electric current (the ampere), luminous intensity (the candela), and the amount of substance (the mole). The laws of physics are expressed in terms of basic quantities that require a clear definition. In mechanics, the three basic quantities are length (L), mass (M), and time (T). All other quantities in mechanics can be expressed in terms of these three.

Set of fundamental and derived units for the accurate measurement of physical quantities is called “system of units”.

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There are seven base units of the SI:i. The Meter:

The unit of length as the meter was defined as the distance between two fixed points on a platinum–iridium bar stored under controlled conditions kept at the International Bureau of Weights and Measures at Sevres, France.

In the 1960s and 1970s. Meter the unit of length is defined as 1650763.73 times the wave length of orange light emitted by

krypton -86 atoms. In October 1983, the meter (m) was again redefined as the distance traveled by light in vacuum during a

time of second.1m = 100 cm1 cm =10 mm

ii. The Kilogram: One kilogram defined as the mass of a platinum-iridium cylinder3.9cm in diameter and 3.9cm in height

kept at the International Bureau of Weight and Measurement at Sevres, France, established in 18871 kilogram = 1000 gm1gm = 1000 mg

One a.m.u or u is used as the unit of mass in atomic physics. Mass of a C12 atom is 12 atomic mass units. One u is defined as 1/12th of the mass of one C12 atom.

iii. The Second Before 1960, the standard of time was defined in terms of the mean solar day for the year 1900. The one

second was originally defined as of a mean solar day. In 1967, the atomic clock was adopted, choosing caesium-133 atom, which emits electromagnetic

radiation of a precise and unvarying frequency, corresponding to the transition between two hyperfine levels of the ground state.

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom

1day = 24 hours1hour = 60 min. 1min = 60 sec.

iv. The Ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite

length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 Newton per meter of length

v. The Kelvin:

The Kelvin, unit of thermodynamic temperature, is the fraction of the thermodynamic temperature of the triple point of water. Is 273.16 K.

vi. The Mole: The mole is the amount of substance of a system which contains as many elementary entities as there are

atoms in 0.012 kilogram of carbon-12.

vii. The Candela: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic

radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

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It can be defined as the unit of luminous intensity “the luminous intensity in the perpendicular direction

of surface square meter of a perfect black body at the temperature of freezing platinum under the pressure of 1.013255x105 N/m2 of that surface”.

Supplementary unit:1. RADIAN: This is the SI unit of (supplementary) plane angle. One radian is the plane angle between two

radii of a circle which cut off on the circumference of an arc equal to the length of the radian.2. STERADIAN: This is the SI unit of solid angle. One steradian is the solid angle which, with its vertex at

the centre of the sphere, cuts off an area of the surface of the sphere, equal to that of a square having sides of length equal to the radian of the sphere.

3. CURIE: This is the SI unit of radioactivity. One curie is the quantity of any radioactive substance which undergoes 3.7 x 1010 disintegrations per second.

2. British engineering system:In addition to SI system of units, another system of units is the British engineering system (sometimes called the conventional system), is still used in the United States despite acceptance of SI by the rest of the world. In this system, the units of length, force, and time are the foot (ft), pound, and second, respectively. In this system mass is derived quantity of unit “slug”. After fixing the units of fundamental quantities, the units of any other quantities are easily derived. For example, Force, F = m aF= 1kg. 1m / sec²1Newton = 1kg.m sec-²

Similarly, for other derived units are derived for derived quantities from their formulae.The constant value of acceleration due to gravity is 9.8 m / sec² in MKS system, 980 cm / sec² in CGS system and 32 ft / sec² in FPS system of units. F = m a One pound = 1 slug 1ft. sec- 2

1 slug = one pound / 1ft. sec- 2

1 slug = 4.45 N / 0.3048 m sec- 2

1 slug = 14.60 kg.

The conversion of mass in CGS and MKS system of units:

10 milligram = 1 centigram1 gram = 1x10-3 kilogram 10 centigram = 1decigram 10 decigram = 1 gram 10 gram = 1decagram10 decagram = 1 hectogram10 hectogram = 1 kilogram10 kilogram = 1 miriagram10 miriagram = 100 kilogram = 1 quintal 10 quintal = 1 metric tone1kg= 2.21 lb = 2.06x1026 a.m.u = 0.0685 slug1slug= 32.2lb = 14.6 kg.1amu= 1.66x10-27kg

Other units of length in MKS and CGS systems:10 millimeter = 1centimeter 10 centimeter = 1 decimeter 10 decimeter = 1 meter 10 meter = 1 decameter 10 decameter = 1hectometer 10 hectometer = 1 kilometer 1 hectometer = 100 meters10 kilometer = 1 miria meter1 m = 39.4 in = 3.23 ft

1 mile = 1.61km = 5280 ft1 km = 0.621 miles1 angstrom =10-10m1 light year = 9.46x1012 km= 9.46x1015 m1 parsec = 3.26 light year 1 parsec= 3.084x1013 km1 fathom= 6 ft 1 Fermi= 1 femto meter = 1015 m

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Units of length in FPS system:12 inches = 1 foot3 foot = 1 yard220 yard = 1 furlong

1760 yard = 1mile = 8 furlong =63, 360 inches

Relation between units of length in different systems:1 inch = 2.54 cm1 foot = 30.48 cm1 mile = 160934 cm

1 cm = 0.3937 inch1 meter = 39.37inch = 1.094 yard1 kilometer = 0.621 mile

Force:1 lb= 4.45 N 1 N= 105 dyne = 0.225 lb Energy and power:1joule= 107erg =2.78x10-7 kWh1 electron volt =1.6x10-19 joule=1.6x10-12 erg

1 horse power = 746 watts = 550Ft.Pound /sec

7: Dimension: The word dimension has a special meaning in physics. It usually denotes the physical nature of a quantity. Whether a distance is measured in the length unit feet or the length unit meters, it is still a distance. We say the dimension—the physical nature—of distance is length.For example, the symbol we use for speed is v, and in our notation the dimensions of speed are written, as [LT-1] another example, the dimensions of area, for which we use the symbol A, are The dimensions of area, volume, speed, and acceleration are listed in below, as well as other quantities:

Quantity Definition Formula Units Dimensions

MECHANICAL

Length or Distance fundamental D m (meter) [ L ]Time fundamental T s (second) [ T ]Mass fundamental M kg (kilogram) [ M ]Area distance2 A = d2 m2 [ L2 ]Volume distance3 V = d3 m3 [ L3 ]Density mass / volume d = m/V kg/m3 [ M L-3 ]Velocity distance / time v = d/t m/s [ L T-1 ]Acceleration Velocity / time a = v/t m/s2 [ L T-2 ]Momentum mass × velocity p = mv kg·m/s { M L T-1 ]Force or  Weight Mass×

accelerationMass× (acceleration. of gravity)

F = maW = mg

N (Newton) = kg·m/s2

[ M L T-2 ]

Pressure or Stress force / area p = F/A Pa (Pascal)=N/m2 = kg/(m·s2)

[ M L-1 T-2 ]

Energy or WorkKinetic EnergyPotential Energy

Force × distancemass × velocity2/ 2mass× (Acc: gravity)× height

E = FdK.E=1/2mv2

PE = mgh

J (joule)=N·m=g·m2/s2

[ M L2 T-2 ]

Power energy / time P = E/t W (watt)=J/s = kg·m2/s3

[M L2 T-3 ]

Impulse force × time I = Ft N·s = kg·m/s [M L T-1 ]Action energy × time

momentum × distanceA = EtA = pd

J·s = kg·m2/s [M L2 T-1 ]

ANGUL

Angle FundamentalΘ

°(degrees) or rad (radians) 360° = 2π rad

Dimension less

Cycles fundamental N cyc (cycles) Dimension lessFrequency cycles / time f = n/t Hz (hertz) = cyc/s = [ T-1 ]

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AR

1/ sAngular Velocity angle / time ω = θ/t rad/s = 1/ s [ T-1 ]Angular acceleration

angular velocity/ time α = ω/t rad/s2 = 1/ s2 [ T-2 ]

Moment of Inertia mass × radius2 I = m r2 kg·m2 [ M L2 ]Angular Momentum Radius × momentum

mom. Of inert.× (angular velocity)

L = r pL = I ω

kg·m2/s [ M L2T-1 ]

Torque Radius × force mom. of inert.×(angular acceleration)

T = r FT = I α

N·m = kg·m2/s2 [ M L2 T-2 ]

THERMAL

Temperature fundamental T °C (Celsius) or K (Kelvin)

[ K ]

Heat heat energy Q J (joule) = kg·m2/s2 [ M L2 T-2 ]Entropy heat / temperature S = Q/T J/K [ M L2 T-2 K-1 ]

ELECTRO

MAGNETIC

Electric Charge(+/-) Current× time Q C (coulomb) [ C ]Current charge / time i = q/t A (amp) = C/s [ C T-1]Voltage or Potential energy / charge V = E/q V (volt) = J/C [ M L2 C-1 T-2 ]Resistance voltage / current R = V/i Ω (ohm) = V/A [ M L2 C-2 T-1 ]Capacitance charge / voltage C = q/V F (farad) = C/V [ C2 T2 M-1 L-2 ]Inductance voltage/(current/ time) L =

V/(i/t)H (Henry) = V·s/A [ M L2 T-2 ]

Electric Field voltage / distance force / charge

E = V/dE = F/q

V/m = N/C [ M L C-1 T-2 ]

Electric Flux electric field ×area φE = EA V·m = N·m2/C [ M L3 C-1 T-2 ]Magnetic Field force / (charge ×

velocity)B = F/qv T (tesla)= Wb/m2 =

N·s/(C·m)[ M C-1 T-1]

Magnetic Flux magnetic field × area φM = BA Wb (Weber)=V·s= J·s/C

[ M L2 C-1 T- 1]

8: Significant Figures:When physical quantities are measured, the measured values are known only to within the limits of the experimental uncertainty. The value of this uncertainty can depend on various factors, such as the quality of the apparatus, the skill of the experimenter, and the number of measurements performed. The concept of significant figures is often used in connection with rounding.When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the least accurate of the quantities being multiplied, where “least accurate” means “having the lowest number of significant figures.” The same rule applies to division.

When numbers are added or subtracted, the number of decimal places in the result should equal the smallest number of decimal places of any term in these.The rules for identifying significant digits when writing or interpreting numbers are as follows:

1. All non-zero digits are considered significant. Ex: 1, 20, and 300 all have one significant figure. Their significant figures are 1, 2, and 3 respectively. 123.45 have five significant figures: 1, 2, 3, 4 and 5.

2. Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 have five significant figures: 1, 0, 1, 1 and 2.

3. Leading zeros are not significant. For example, 0.00012 has two significant figures: 1 and 2.Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 have six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 have five significant figures. This convention

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clarifies the precision of such numbers; for example, if a result accurate to four decimal places is given as 12.23 then it might be understood that only two decimal places of accuracy are available. Stating the result as 12.2300 makes clear that it is accurate to four decimal places.

4. The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:

5. A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, 1300has three significant figures (and hence indicates that the number is accurate to the nearest ten).

6. The last significant figure of a number may be underlined; for example, "20000" has two significant figures.

7. A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.

A number with all zero digits (e.g. 0.000) has no significant digits, because the uncertainty is larger than the actual measurement.

Short questions and Answers

Question #1What is an atomic clock?An atomic clock is a clock that keeps time using natural characteristic frequencies of atoms, such as cesium, hydrogen or rubidium. Atomic clocks are extremely stable because the atom's characteristic frequencies are not affected by factors like temperature, pressure or humidity.

Question #2How long is a nanosecond, a picoseconds or a femto second? A nanosecond is one billionth of a second, and picoseconds are one trillionth of a second. Timekeeping technology has not yet reached the stage where we can measure femto seconds. However, just for the record, a femto second is a thousand times smaller than picoseconds!

Question #3What is an atomic Balance? Atomic balances, which are capable of measurement of nano particles mass, are described. The precision of measurements is defined by the geometry of measuring micro console and may be as high as 10-19 g. Atomic balance can also measure lateral stress and surface tension in thin films (also in mono layers). Experimental data on the atomic balance usage as highly sensitive gas and liquid analyzers, chemical and biological sensors are presented

Quantity UNIT Alternatives Definition/NotesA:Acceleration, angular  s-2 rad.s-2 [Angular Velocity] /

[Time]. 

Abbé number  1  Dimensionless  Inverse of refractive index. 

Absorbed radiation dose  m2.s-2 J.kg-1, Gy  [Energy] / [Mass]. 

Absorbed dose rate  m2.s-3 Gy.s-1 [Absorbed dose] / [Time]. 

Acceleration, linear  m.s-2   [Velocity] / [Time] 

Action  kg.m2.s-1 J.s  [Energy] [Time]. 

Activity of radioactive source  s-1 Bq  [Events] / [Time]. 

Angular acceleration  s-2 rad.s-2 [Angular Velocity] / [Time]. 

Angular moment of inertia  kg.m2   [Mass] [Distance2]. 

Angular moment of motion  kg.m2.s-1 J.s  [Moment of motion] [Distance]. Like [action]. 

Angular velocity  s-1 rad.s-1 [Plane angle] / [Time]. 

Area  m2   [Distance] [Distance]. 

B:Baud rate  bit.s-1 Baud  [Information] / [Time]

Also: information flux. 

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Bulk modulus  kg-1.m.s2 Pa-1 [Pressure] / ([Volume] / [Volume]). 

Same as compressibility.C:Capacitance, electric  kg-1.m-2.s4.A2 C.V-1, F  [Charge] / [Potential] 

Circulation  m2.s-1 J.s.kg-1 [Angular moment of motion]/[Mass] 

Characteristic impedance  kg.m2.s-3.A-2 V.A-1, Ω, ohm  √ ([Mag.Permeability] / [El.Permittivity]). 

Charge, electric  s .A C  [Current] [Time] 

Charge, quantum  1  Dimensionless  [Charge] / [Elementary charge quantum] 

Charge, molecular/ionic, 

quantum1  Dimensionless  [Charge of a molecule or

ion] /[Elementary charge quantum]

Charge density  m-3.s.A  C.m-3 [Charge] / [Volume] 

Charge/mass ratio  kg-1.s.A  C.kg-1 [Charge] / [Mass]. Same as specific charge. 

Charge, molar  s.A.mol-1  C.mol-1 [Charge] / [Quantity] 

Chemical potential, molar  kg.m2.s-2.mol-1 J.mol-1 [ΔInternalEnergy] / [Quantity Of Substance]. 

Collision cross section  m2   [Distance] [Distance]. Same as cross section. 

Compressibility  kg-1.m.s2 Pa-1 [Pressure] / ([Volume] / [Volume]). 

Same as bulk modulus.Compression modulus  kg-1.m.s2 Pa-1 [Pressure] / ([Volume] /

[Volume]). 

Same as compressibility.Concentration, molar  m-3.mol   [Quantity] / [Volume].

Same as molar density. 

Concentration, by mass  1  Dimensionless  [Mass of substance] / [Total mass]. 

Same as mass concentrationConcentration, by volume  1  Dimensionless  [Volume of substance] /

[Total volume]. 

Same as volume concentration.

Concentration, by weight  1  Dimensionless  [Mass of substance] / [Total mass]. 

Same as mass concentrationConductance, electric  kg-1.m-2.s3.A2 A.V-1, S  [Current] / [Potential].

Inverse of resistance. 

Conductivity, electric  kg-1.m-3.s3.A2 S.m-1 1 / [Resistivity]. 

Conductivity, molar  kg-1.s3.A2.mol-1 S.m2.mol-1 [El.conductivity] / [Concentration]. 

Conductivity, thermal  kg.m.s-3.K-1 W.m-1.K-1 [Heat flux] / ([Distance] [ΔTemperature]). 

Convergence  m-1 dioptry  in optics, but not only ... 

Count rate  s-1   [Events] / [Time]. 

Cross section  m2   [Distance] [Distance]. 

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Cryoscopic constant  kg.mol-1.K K/(mol/kg)  [ΔTemperature] / [Molality]. 

Current, electric  A  A   

Current density (electric)  m-2.A   [Current] / [Area]. Same as current intensity. 

Current intensity (electric)  m-2.A   [Current] / [Area]. Same as current density. 

Current noise, variance nJ2  s.A2 A2/Hz [Current]2 / Bandwidth]

Curvature radius  m    of a line in plane/space or surface in space 

D:Density of electric charge  m-3.s.A  C.m-3 [Charge] / [Volume] 

Density of electric current  m-2.A   [Current] / [Area]. Same as current intensity. 

Density of energy  kg.m-1.s-2 J.m-3 [Energy] / [Volume]. 

Density of mass  kg.m-3   [Mass] / [Volume]. Same as specific density. 

Density of substance  m-3.mol   [Quantity] / [Volume]. Same as concentration. 

Dielectric constant  1  Dimensionless  [Permittivity] / [Permittivity of vacuum]. 

Same as relative permittivity.

Dielectric strength  kg.m.s-3.A-1 V.m-1 [Potential] / [Distance]. Same as electric strength.

Diffusion coefficient  m2.s-1   [Distance2] / [Time]. 

Diffusivity, thermal  m2.s-1   ([∂Temperatute] / [∂Time]) / [∇2Temperature].

Dipole moment, electric  m.s.A  C.m  [Charge] [Distance] 

Dipole moment, magnetic  m2.A J.T-1 [Current] [Area] 

Dispersive power  1  Dimensionless  Ratio of differences of refractive indices. 

Dispersivity quotient  m-1   [Refractive index] / [ΔWavelength] 

Distance  m    in all Euclidean n-dimensional spaces. 

Dose of absorbed radiation  m2.s-2 J.kg-1, Gy  [Energy] / [Mass]. 

Dose rate  m2.s-3 Gy.s-1 [Absorbed dose] / [Time]. 

Drift speed  m.s-1   Steady-state speed of an object. .

Duration  s  s   

Dynamic viscosity  kg.m-1.s-1 Pa.s  ([Force] [Area]) / [Velocity] 

E:Ebullioscopic constant  kg.mol-1.K K/(mol/kg)  [ΔTemperature] /

[Molality]. 

Electric capacitance  kg-1.m-2.s4.A2 C.V-1, F  [Charge] / [Potential] 

Electric charge  s .A C  [Current] [Time] 

Electric conductance  kg-1.m-2.s3.A2 A.V-1, S  [Current] / [Potential]. Inverse of resistance. 

Electric conductivity  kg-1.m-3.s3.A2 S.m-1 1 / [Resistivity]. 

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Electric conductivity, molar  kg-1.s3.A2.mol-1 S.m2.mol-1 [El.conductivity] / [Concentration]. 

Electric current  A  A   

Electric dipole moment  m.s.A  C.m  [Charge] [Distance] 

Electric field strength  kg.m.s-3.A-1 V.m-1 [Potential] / [Distance]. 

Also called electric intensityElectric field gradient  kg.s-3.A-1 V.m-2 [ΔEl.field strength] /

[Distance]. 

Electric flux density  m-2.s.A C.m-2 [Charge ] / [Area]. 

Also called electric induction

Electric inductance  kg.m2.s-2.A-2 V.s.A-1, H  [Potential] / [current / dt ] 

Electric induction  m-2.s.A C.m-2 [Charge] / [Area]. 

More properly electric flux density

Electric intensity  kg.m.s-3.A-1 V.m-1 [Potential] / [Distance]. 

More properly electric field strength

Electric permittivity  kg-1.m-3.s4.A2 F.m-1 [El.flux density] / [El.field strength]. 

Electric permittivity, relative  1  Dimensionless  [Permittivity] / [Permittivity of vacuum]. 

Same as dielectric constant.Electric polarization  m-2.s.A C.m-2 [Charge] / [Area]. Like

electric flux density 

Electric potential  kg.m2.s-3.A-1 W.A-1, J.C-1, V  [Power] / [Current], [Energy] / [Charge] 

Electric quadrupole moment  m2.s.A  C.m2 [El.dipole] [Distance] 

Electric resistance  kg.m2.s-3.A-2 V.A-1, Ω  [Potential] / [Current] 

Electric resistivity  kg.m3.s-3.A-2 Ω.m  ([Resistance] [Length]) / [Area]. 

Electric strength  kg.m.s-3.A-1 V.m-1 [Potential] / [Distance]. 

Also called dielectric strength.

Electromagnetic vector potential 

kg.m.s-2.A-1 V.s.m-1, T.m [El.field strength] [Time], 

[Mag.flux density] [Distance]

Electromotive force (emf)  kg.m2.s-3.A-1 V  [Potential] 

Electrostriction coefficient  kg-2.m-2.s6.A2 m2.V-2 ([ΔVolume] / [Volume]) / [Electric field strength]2. 

Energy  kg.m2.s-2 N.m, J  [Force] [Distance], [Power] [Time]. 

Energy, molar  kg.m2.s-2.mol-1 J.mol-1 [Energy] / [Quantity]. 

Energy, specific  m2.s-2 J.kg-1 [Energy] / [Mass]. 

Energy density  kg.m-1.s-2 J.m-3 [Energy] / [Volume]. 

Energy flux  kg.m2.s-3 J.s-1, W  [Energy ] / [Time]. Same as power. 

Enthalpy  kg.m2.s-2 J  Like energy and heat. 

Enthalpy, molar  kg.m2.s-2.mol-1 J.mol-1 [Enthalpy] / [Quantity]. Like molar heat. 

Enthalpy, specific  m2.s-2 J.kg-1 [Enthalpy] / [Mass]. Like

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 10

specific heat. 

Entropy  kg.m2.s-2.K-1 J.K-1 [Heat] / [Temperature]. 

Entropy, molar  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Entropy] / [Quantity]. 

Entropy, specific  m2.s-2.K-1 J.K-1.kg-1 [Entropy] / [Mass]. 

Evolution rate on log-scale  s-1   d{ln(Q)} / dt = (dQ / dt) / Q. 

Also relative evolution rate.Expansion coefficient, thermal 

K-1   ([Length] / [Length]) / [Temperature]. 

Exposure  kg-1.s.A C.kg-1 [Charge] / [Mass]. Used for ionizing radiations. 

Extinction coefficient  m-1   In transmission of a radiation through space. 

F:Force  kg.m.s-2 N  [Mass] [Acceleration]. 

Force, thermodynamic  kg.m.s-2.mol-1 N/mol  [Chemical potential] / [Distance]. 

Free energy  kg.m2.s-2 J  Also Helmholtz function. Like energy. 

Free energy, molar  kg.m2.s-2.mol-1 J.mol-1 [Free energy] / [Quantity]. 

Also molar Helmholtz function.

Free energy, specific  m2.s-2 J.kg-1 [Free energy] / [Mass]. 

Also specific Helmholtz function.

Free enthalpy  kg.m2.s-2 J  Also Gibbs function. Like energy. 

Free enthalpy, molar  kg.m2.s-2.mol-1 J.mol-1 [Free enthalpy] / [Quantity]. 

Also molar Gibbs function.Free enthalpy, specific  m2.s-2 J.kg-1 [Free enthalpy] / [Mass]. 

Also specific Gibbs function.

Frequency of waves or events  s-1 Hz   

Frequency drift rate  s-2 Hz.s-1 [Frequency] / [Time]. 

Friction coefficient  1  Dimensionless  [Tangential force] / [Normal force]. 

Fugacity  kg.m-1.s-2 Pa  Effective pressure in real gases. 

G:g-factor of a particle  1  Dimensionless  [Magnetic moment] /

([Spin].[Bohr magneton]) 

Gradient, of electric field  kg.s-3.A-1 V.m-2 [ΔEl.field strength] / [Distance]. 

Gradient, of magnetic field  kg.m-1.s-2.A-1 T.m-1 [ΔMag.flux density] / [Distance]. 

Gradient, thermal  K.m-1   [ΔTemperature] / [Distance]. 

Same as temperature gradient.

Gravitational field intensity  m.s-2   [Force] / [Mass], [Acceleration].Same as

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 11

gravityGravitational field potential  m2.s-2   [Energy] / [Mass].  

Gravity  m.s-2   [Force] / [Mass], [Acceleration]. 

Same as grav. field intensityGyromagnetic ratio  kg-1.s.A Hz.T-1 [Mag.moment] / [Angular

moment of motion]. 

H:Half life  s    typically of a radioactive

substance 

Hamiltonian  kg.m2.s-2 J  [Force] [Distance], [Power] [Time]. Like energy.

Hardness  kg.m-1.s-2 N.m-2 [Force] / [Area] 

Heat  kg.m2.s-2 J  Like energy. 

Heat, molar  kg.m2.s-2.mol-1 J.mol-1 [Heat] / [Quantity]. 

Heat, specific  m2.s-2 J.kg-1 [Heat] / [Mass]. 

Heat capacity  kg.m2.s-2.K-1 J.K-1 [Heat] / [ΔTemperature]. 

Heat capacity, molar  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Heat capacity] / [Quantity]. 

Heat capacity, specific  m2.s-2.K-1 J.K-1.kg-1 [Heat capacity] / [Mass]. 

Heat | Thermal conductivity  kg.m.s-3.K-1 W.m-1.K-1 [Heat flux] / ([Distance] [ΔTemperature]). 

Heat flux  kg.m2.s-3 J.s, W  [Heat] / [Time]. Like power. 

Heat flux density  kg.s-3 W.m-2 [Heat flux] / [Area]. Same as irradiance. 

I:Illuminance  cd.sr.m-2 lm.m-2, lx  [Luminous flux] / [Area]. 

Impedance, characteristic  kg.m2.s-3.A-2 V.A-1, Ω, ohm  √ ([Mag.Permeability] / [El.Permittivity]). 

Impact resistance  kg.s-2 J.m-2 [Energy] / [Area] 

Inductance  kg.m2.s-2.A-2 V.s.A-1, Wb.A-1, H  [Potential] / [dCurrent/dt], [Mag.flux] / [Current] 

Induction, electric  m-2.s.A C.m-2 [Charge] / [Area].Same as electric flux density

Information  bit-1 bit  One bit is the elementary information quantum. 

Information flux  bit.s-1 Baud  [Information] / [Time]. Also called baud rate. 

Intensity of electric current  m-2.A   [Current] / [Area]. Same as current density. 

Internal energy  kg.m2.s-2 J  Like energy and heat. 

Internal energy, molar  kg.m2.s-2.mol-1 J.mol-1 [Internal energy] / [Quantity]. Like molar heat. 

Internal energy, specific  m2.s-2 J.kg-1 [Internal energy] / [Mass]. Like specific heat. 

Ion mobility  kg-1.m-1.s2.A m2.s-1.V-1  [Velocity] / [Electric field strength].

Ionic force (strength)  m-3.mol   Sum ([Concentration] [Ionic quantum charge]2).

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 12

Ionic quantum charge  1  Dimensionless  [Ion charge] / [Elementary charge quantum] 

Ionic strength (force)  m-3.mol   Sum ([Concentration] [Ionic quantum charge]2).

Irradiance  kg.s-3 W.m-2 [Heat flux] / [Area]. Same as heat flux density 

J:Joule-Thomson coefficient  kg-1.m.s2.K K.Pa-1 [Temperature] / [Pressure]. 

K:Katalytic activity  mol.s-1 katal  [Quantity] / [Time]. 

Same as molar production rate.

Kinematic viscosity  m2.s-1   [Dynamic viscosity] / [Density] 

K-space vector  m-1   Same as reciprocal space position. 

L:Lagrangian  kg.m2.s-2 J  [Force] [Distance],

[Power] [Time]. Like energy.

Length  m  m   

Logarithmic ratio logb(A/A')  1  log in any base b  Applicable to any ratio of like quantities. 

Logarithmic ratio ln(A/A')  1  Np  neper. Uses natural logarithm. 

Logarithmic ratio Log(P/P')/10 

1  dB  Decibel. Uses base-10 logarithm. Aplies only to power P.

Logarithmic ratio Log(X/X')/20 

1  dB  Decibel. Aplies to voltages (X = V) and currents (X = I).

Logarithmic scale differential  1  Dimensionless  dQ / Q , d{ln(Q)}, for any quantity Q 

Also relative differential.Luminance  cd.m-2   [Luminosity] / [Area] 

Luminosity  cd  cd  Same as luminous intensity. 

Luminous flux  cd.sr  lm  [Luminosity] [Solid angle] 

Luminous intensity  cd  cd  Same as luminosity. 

M:Magnetic dipole moment  m2.A J.T-1 [Current] [Area]. Like

magnetic moment. 

Magnetic field gradient  kg.m-1.s-2.A-1 T.m-1 [ΔMag.flux density] / [Distance]. 

Magnetic field strength  m-1.A   [Current] / [Distance]. 

Also called magnetic intensity

Magnetic flux  kg.m2.s-2.A-1 V.s, W.s.A-1, Wb  [Potential] [Time], [Power] / [current / dt] 

Magnetic flux density  kg.s-2.A-1 Wb.m-2, T  [Mag.flux] / [Area]. 

Also called magnetic induction.

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 13

Magnetic induction  kg.s-2.A-1 Wb.m-2, T  [Mag.flux] / [Area]. 

More properly magnetic flux density.

Magnetic intensity  m-1.A   [Current] / [Distance]. 

More properly magnetic field strength

Magnetic moment  m2.A J.T-1 [Current] [Area] 

Magnetic permeability  kg.m.s-2.A-2 H.m-1 [Mag.flux density] / [Mag.field strength]. 

Magnetic permeability, relative 

1  Dimensionless  [Permeability] / [Permeability of vacuum]. 

Magnetic quadrupole moment 

m3.A m.J.T-1 [Mag.dipole] [Distance] 

Magnetic susceptibility  1  Dimensionless  [Relative permeability]-1. 

Magnetization  m-1.A   [Mag.moment] / [Volume]. 

Like magnetic field strength.

Magnetogyric ratio  kg.s-1.A-1 T.Hz-1 [Angular moment of motion] / [Mag.moment]. 

Magnetomotive force (mmf)  A    [Current] [Number fo turms] 

Magnitude of a star  1  Dimensionless  M - m'= -100.4 (S/S'), whereS,S' are the luminous fluxes of two stars.

Mass  kg  kg   

Mass density  kg.m-3   [Mass] / [Volume]. Same as specific density. 

Mass concentration  1  Dimensionless  [Mass of substance] / [Total mass]. 

Also concentration by weight.

Mass flow  kg.s-1 kg  [Mass] / [Time]. 

Same as mass production rate.

Mass production rate  kg.s-1   [Mass] / [Time]. Same as mass flow. 

Mass, molar  kg.mol-1   [Mass]/[Quantity] 

Modulus of compression  kg-1.m.s2 Pa-1 [Pressure] / ([ΔVolume] / [Volume]). 

Same as compressibility.Modulus of rigidity  kg.m.s-2 N, N.rad-1 [Force] / [ΔAngle]. Same as

shear modulus. 

Mobility, ionic  kg-1.m-1.s2.A m2.s-1.V-1  [Velocity] / [Electric field strength].

Molality  kg-1.mol mol/kg  [Quantity] / [Mass]. A way to specify concentration of a solution. 

Molar charge  s.A.mol-1  C.mol-1 [Charge] / [Quantity] 

Molar concentration  m-3.mol   [Quantity] / [Volume]. Same as concentration 

Molar conductivity, electric  kg-1.m-3.s3.A2.mol-1 S.m-1.mol-1 [El.conductivity] / [Concentration]. 

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 14

Molar density  m-3.mol   [Quantity] / [Volume]. Same as concentration. 

Molar energy  kg.m2.s-2.mol-1 J.mol-1 [Energy] / [Quantity]. 

Molar enthalpy  kg.m2.s-2.mol-1 J.mol-1 [Enthalpy] / [Quantity]. Like molar heat. 

Molar entropy  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Entropy] / [Quantity]. 

Molar free energy  kg.m2.s-2.mol-1 J.mol-1 [Free energy] / [Quantity] Also molar Helmholtz function.

Molar free enthalpy  kg.m2.s-2.mol-1 J.mol-1 [Free enthalpy] / [Quantity]. Also molar Gibbs function.

Molar heat  kg.m2.s-2.mol-1 J.mol-1 [Heat] / [Quantity]. 

Molar heat capacity  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Heat capacity] / [Quantity]. 

Molar internal energy  kg.m2.s-2.mol-1 J.mol-1 [Internal energy] / [Quantity]. Like molar heat. 

Molar mass  kg.mol-1   [Mass] / [Quantity] 

Molar production rate  mol.s-1 katal  [Quantity] / [Time]. Like katalytic activity. 

Molar refractivity  m3.mol-1   [( r2- 1 ) / (r2 +2 )] / [Concentration], 

where r is the refractive index.

Molar relaxivity  m3.s-1.mol-1   [Relaxation rate] / [Concentration]. 

Molar solubility  m-3.mol   [Quantity] / [Volume]. Same as concentration 

Molar volume  m3.mol-1   [Volume] / [Quantity]. 

Molarity  m-3.mol   [Quantity] / [Volume]. 

Same as concentration or molar density

Molecular quantum charge  1  Dimensionless  [Charge of a molecule] / [ Elementary charge quantum] 

Moment of force  kg.m2.s-2 N.m  [Force] [Distance]. 

Moment of motion  kg.m.s-1   [Mass] [Velocity], [Mass flow] [Distance]. 

Mutual inductance  kg.m2.s-2.A-2 V.s.A-1, Wb.A-1, H  [Potential] / [dCurrent/dt], [Mag.flux] / [Current] 

N:Notch resistance  kg.s-2 J.m-2 [Energy ] / [Area] 

O:Osmotic pressure  kg.m-1.s-2 Pa  

P:Peltier coefficient  kg.m2.s-3.A-1 W.A-1, V [Heat flux] / [Current]. 

Permeability, magnetic  kg.m.s-2.A-2 H.m-1 [Mag.flux density] / [Mag.field strength]. 

Permittivity, electric  kg-1.m-3.s4.A2 F.m-1 [El.flux density] / [El.field strength]. 

Permittivity, relative  1  Dimensionless  [Permittivity] / [Permittivity of vacuum]. Dielectric

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 15

constant. 

Phase angle  1  rad  φ in exp( i(ωt + φ )) 

Phase drift rate  s-1 rad.s-1 [Phase angle] /[Time]. 

Pi coefficient, molar  kg.m-1.s-2.mol-1 J.m-3 [ΔInternalEnergy] / [ΔVolume]. 

Piezzoelectric coefficient  kg.m.s-3.A-1 V.m-1 [Electric field strength] / ([ΔLength] / [Length]). 

Plane angle  1  rad   

Polarization, electric  m-2.s.A C.m-2 [Charge]/ [Area]. Like electric flux density. 

Position vector  m    in all Euclidean n-dimensional spaces. 

Potential, electric  kg.m2.s-3.A-1 W.A-1, J.C-1, V  [Power] / [Current], [Energy] / [Charge] 

Power  kg.m2.s-3 J.s-1, W  [Energy] / [Time]. Equivalent to energy flux. 

Prandtl number  1  Dimensionless  [Kinematic viscosity] / [Thermal diffusivity]. 

Poynting vector  kg.s-3 W.m-2 [El.field strength] / [Mag.field strength]. 

Like irradiance.Pressure  kg.m-1.s-2 N.m-2, Pa [Force] / [Area]. 

Probability of an event  1    Real number lying in the interval [0,1]. 

Probability density on ln-scale 

1  Np-1 [Probability] / [Natural-logarithmic ratio] 

Q:Quadrupole moment, electric  m2.s.A  C.m2 [El.dipole] [Distance] 

Quadrupole moment, magnetic 

m3.A m.J.T-1 [Mag.dipole] [Distance] 

Quantity of substance  mol  mol   

Quantum charge  1  Dimensionless  [Charge] / [Elementary charge quantum] 

Quantum charge,molecular or ionic 

1  Dimensionless  [Molecule/ion charge] / [Charge quantum] 

Quotient of dispersivity  m-1   [Refractive index] / [ΔWavelength] 

R:Radiance  kg.s-3.sr-1 W.m-2.sr-1 ([Power] / [Area]) / [Solid

angle]. 

Radiation dose  m2.s-2 J.kg-1, Gy  [Energy] / [Mass]. 

Radiation dose rate  m2.s-3 Gy.s-1 [Absorbed dose] / [Time]. 

Radioactivity  s-1 Bq  [Events] / [Time]. 

Radius of curvature  m    of a line in plane/space or surface in space 

Ratio of like quantities  1  Dimensionless   

Reciprocal space position  m-1   Same as k-space vector. 

Redox potential  kg.m2.s-3.A-1 V  Same as reduction potential. 

Reduction potential  kg.m2.s-3.A-1 V  Same as redox potential. 

Refractive index  1  Dimensionless  Light speeds ration (in a medium) / (in vacuum). 

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 16

Refractivity, molar  m3.mol-1   [( r2 - 1) / ( r2 + 2 )] / [Concentration] 

Refractivity, specific  m3.kg-1   [( r2 - 1) / ( r2 + 2)] / [Specific density], 

Relative differential  1  Dimensionless  dQ / Q, d{ln(Q)}, for any quantity Q. 

Also log-scale differential.Relative evolution rate  s-1   d{ln(Q)} / dt = (dQ / dt) / Q.

Also evolution rate on log-scale.

Relative permeability, magnetic 

1  Dimensionless  [Permeability] / [Permeability of vacuum]. 

Relative permittivity, electric  1  Dimensionless  [Permittivity] / [Permittivity of vacuum]. Dielectric constant. 

Relative variation  1  Dimensionless  ΔQ/Q, for any quantity Q. 

Relaxation rate  s-1   1/ [Relaxation time]. Used in all branches of Science. 

Relaxation time  s    Used in all branches of Science. 

Relaxivity, molar  m3.s-1.mol-1   [Relaxation rate] / [Concentration]. 

Resistance, electric  kg.m2.s-3.A-2 V.A-1, Ω  [Potential] / [Current] 

Resistance to impact  kg.s-2 J.m-2 [Energy] / [Area]. Same dimension as notch resistance.

Resistivity, electric  kg.m3.s-3.A-2 Ω.m  ([Resistance] [Length]) / [Area]. 

Reynolds number  1  Dimensionless  [Velocity] [length] / [ Kinematic viscosity] 

S:Seeback coefficient  kg.m2.s-3.A-1.K-1 V.K-1 [Potential] / [Temperature. 

Same as thermoelectric power.

Self-diffusion coefficient  m2.s-1   [Distance2] / [Time]. 

Shear modulus  kg.m.s-2 N, N.rad-1 [Force] / [ΔAngle]. 

Same as modulus of rigidity.

Solid angle  1  sr   

Solubility, molar  m-3.mol   [Quantity] / [Volume]. Same as concentration 

Specific charge  kg-1.s.A  C.kg-1 [Charge] / [Mass]. Charge/mass ratio. 

Specific density  kg.m-3   [Mass] / [Volume]. Same as density of mass

Specific energy  m2.s-2 J.kg-1 [Energy] / [Mass]. 

Specific enthalpy  m2.s-2 J.kg-1 [Enthalpy] / [Mass]. Like specific heat. 

Specific entropy  m2.s-2.K-1 J.K-1.kg-1 [Entropy] / [Mass]. 

Specific free energy  m2.s-2 J.kg-1 [Free energy] / [Mass]. 

Also specific Helmholtz

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 17

function.Specific free enthalpy  m2.s-2 J.kg-1 [Free enthalpy] / [Mass]. 

Also specific Gibbs function.

Specific heat  m2.s-2 J.kg-1 [Heat] / [Mass]. 

Specific heat capacity  m2.s-2.K-1 J.K-1.kg-1 [Heat capacity] / [Mass]. 

Specific internal energy  m2.s-2 J.kg-1 [Internal energy] / [Mass]. Like specific heat. 

Specific refractivity  m3.kg-1   [( r2 - 1 ) / ( r2 + 2 )] / [Specific density] 

Specific volume  m3.kg-1   [Volume] / [Mass]. 

Speed  m.s-1   [Distance] / [Time]. Same as velocity. 

Spin  1  Dimensionless  of a quantum particle 

Star magnitude  1  Dimensionless  m - m' = -100.4 ( S / S' ), where 

S,S' are luminous fluxes of two stars.

Surface density of charge  m-2.s.A  C.m-2 [Charge] / [Area] 

Surface element  m2   [Distance] [Distance]. Same as area 

Surface energy  kg.s-2 J/m2 [Energy] / [Area]. Same as surface tension. 

Surface tension  kg.s-2 N/m  [Force] / [Length]. Same as surface energy. 

Susceptibility, magnetic  1  Dimensionless  [Relative permeability]-1. 

Stress  kg.m-1.s-2 Pa, N.m-2 [Force] / [Area]. Same as pressure. 

T:Temperature  K  K   

Temperature gradient  K.m-1   [Temperature] / [Distance]. 

Same as thermal gradient.Tension  kg.m-1.s-2 Pa, N.m-2 [Force] / [Area]. Like

pressure. 

Thermal conductivity  kg.m.s-3.K-1 W.m-1.K-1 [Heat flux] / ([Distance] [Temperature]). 

Same as heat conductivity.Thermal diffusivity  m2.s-1   ([∂Temperatute] / [∂Time]) /

[∇2Temperature].Thermal expansion coefficient 

K-1   ([ΔLength] / [Length]) / [Temperature]. 

Thermal gradient  K.m-1   [ΔTemperature] / [Distance]. 

Same as temperature gradient.

Thermodynamic force  kg.m.s-2.mol-1 N/mol  [Chemical potential] / [Distance]. 

Thermoelectric power | Thermo power 

kg.m2.s-3.A-1.K-1 V.K-1 [Potential] / [ΔTemperature]. 

Same as Seeback coefficient.

Thomson coefficient  kg.m2.s-3.A-1.K-1 W.K-1.A-1 [Heat flux] /

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 18

([ΔTemperature] [Current]). 

Time  s  s   

Torque  kg.m2.s-2 N.m  [Force] [Distance]. 

Same as moment of force.V:van der Waals constant: a  kg.m5.s-2 Pa.m6 a in (p+ a / V2) ( V - b) =

RT.van der Waals constant: b  m3   b in ( p+ a / V2) ( V- b ) =

RT.van der Waals virial constant: A 

kg-1.m5.s-2.mol-2   A in p =( n / V) RT+ ( n / V )2 (RTB – A ).

van der Waals virial constant: B 

kg-1.m3.mol-1   B in p = ( n / V )RT + ( n / V)2 (RTB - A).

Variance of current noise nJ2  s.A2 A2/Hz [Current]2 / [Bandwidth]

Variance of voltage noise nV2  kg2.m4.s-5.A-2 V2/Hz [Voltage]2 / [ Bandwidth]

Vector potential, electromagnetic 

kg.m.s-2.A-1 V.s.m-1, T.m [El.field strength] [ Time], [Mag.flux density] [Distance] 

Velocity  m.s-1   [Distance] / [Time]. Same as speed. 

Verdet constant  kg-1.m-1.s2.A1 rad.m-1.T-1 ([Angle] / [Length]) / [Magnetic flux density] 

Virial coefficient: second  kg.m5.s-2.mol-2 Pa.(mol.m-3)-2 A in p= (n / V) RT + A (n / V)2 + B (n / V )3 +C(n / V)4.

Virial coefficient: third  kg.m8.s-2.mol-3 Pa.(mol.m-3)-3 B in p =( n / V) RT + a (n / V)2 + B (n / V)3 + C( n / V )4.

Virial coefficient: fourth  kg.m11.s-2.mol-4 Pa.(mol.m-3)-4 C in p =( n / V )RT + A( n/V)2+B(n / V)3 + C( n / V)4.

Viscosity, dynamic  kg.m-1.s-1 Pa.s  ([Force] / [Area] ) / [ΔVelocity] 

Viscosity, kinematic  m2.s-1   [Dynamic viscosity] / [Density] 

Voltage noise, variance nV2  kg2.m4.s-5.A-2 V2/Hz [Voltage]2 / [Bandwidth]

Volume  m3   [Area] [Distance] 

Volume concentration  1  Dimensionless  [Volume of substance] / [Total volume] 

W:Wavelength  m    [Wave velocity] /

[Frequency]. 

Wave number  m-1   [Number of waves] / [Distance]. 

Work function  kg.m2.s-2 J, eV  [Energy] needed to remove an electron. 

Y:Young modulus  kg.m-1.s-2 N.m-2, Pa [Stress]/[ΔLength] /

[Length]). 

CONSTANT VALUES

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 19PREFIXES AND SUFFIXES

Speed of sound=331m/sec=1200km/h=1090 ft/sec1 mile per hour (mph) =1.47 ft/sec=0.447 m/sMass of earth = 5.98x1024 kgMean radius of earth = 6.37x106 m = 3960 mil Mean earth–sun distance=1.49x108 km=2.39x 105 milMean earth–moon distance=3.8 x105km=2.39 x105 milSpeed of light=3.00x108 m/sec=1.86 x105 miles /secCharge of electron and proton =1.6x10-19 coulombsMass of proton = 1.67x 10 –27 kgMass of electron = 9.11x 10 –31 kgElectric current: 1 abampere = 10 amperesElectric charge: 1 abcoulomb = 10 coulombsCapacitance: 1 abfarad = 109 farads = 1 gigafaradInductance: 1 abhenry = 10-9 Henry = 1 annoyerResistance: 1 abhor = 10-9 ohm = 1 nanoConductance: 1 abhor = 109 SiemensMagnetic flux density: 1 abets =10-4 tesla =1 gaussPotential: 1 abbot = 10-8 volt = 10 Nan voltsPower: 1 abaft = 10-7 watt = 0.1 microwattErg: 1 erg = 10-7 JDyne: 1 dyn = 10-5 NPoise: 1 P = 1 dyn s/cm2 = 0.1 Pa sStokes: 1 St = 1 cm2/s = 10-4 m2/sGauss: 1 G = 10-4 TOersted: 1 Oe = (1000/(4 )) A/mMaxwell: 1 Mx = 10-8 WbStilb: 1 sb = 1 cd/cm2 = 104 cd/m2

Magnetic flux: 1 baneberry = 10-8 Weber = 1MaxwellAtomic mass constant mu =1.660 538 73(13) ×10-27 kgAvogadro constant L, NA = 6.022141 99(47)×1023 mol-1

Bohr magneton µB = 9.274 008 99(37) × 10-24 J T-1

Boltzmann constant k = 1.380 650 3(24) × 10-23 J K-1 Electron charge e = 1.602 176 462(63) × 10-19 CElectron mass me = 9.109 381 88(72) × 10-31 kgFaraday constant F = 9.648 534 15(39) × 104 C mol-1

Loschmidt's constant NL= 2.686 777 5(47)×1025 m-3

Planck constant h = 6.626 068 76(52) × 10-34 J sProton mass mp =1.672 621 58(13) × 10-27 kgSpeed of light c = 2.997 924 58 × 108 m s-1

Neutron mass mn = 1.674 927 16(13) × 10-27 kg Stefan-Boltzmann constant = 5.670 400(40) × 10-8 W m-2 K-4

Newton's gravitational constant G= 6.673(10) × 10-11 N m2 kg-2

Permeability of vacuum µ0 =4×10-7NA-2=1.256637061×10-6 NA-2

Molar gas constant R= 8.314 472(15) J K-1 mol-1 Permittivity of vacuum 0 =8.854187 817× 10-12 F m-1

Molar volume = (ideal gas, 101.325 kPa) Vm 2.241 399 6(39) × 10-2 m3

mol-1

Prof: Najeeb Mughal, Edited by Tarvesh Kumar Page 20

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