Units conversion CBSE UGC JRF/NET

UNITS &CONVERSION
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UNITS
• Physical quantities are always expressed in terms of number
associated with unit.
– Fundamental Units – Units of mass, length and time cannot be derived
from any other units.
– Basic Units – Seven units of measurement namely mass, length, time,
temperature, electric current, luminous intensity and the amount of
substance.
– Derived Units – Units which can be derived from basic units as –area,
volume, force, work, velocity, energy, density etc.,
• Units of Measurements: -
– In any Environmental Management Program measurement, accounting and
Balancing of materials, pollutants are required.
– Commonly used and accepted system of measurements is necessary to follow.
ENVIRONMENTAL SCIENCES: CBSE UGC-JRF/NET and ARS-NET
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TYPES OF SYSTEMS OF UNITSTYPES OF SYSTEMS OF UNITS
• British System of Units:- in this system Length, Mass and Time are measured in
Foot, Pound and Second (FPS) respectively.
• CGS System: – in this system Length, Mass and Time are measured in
Centimeter, Gram and Second respectively.
• MKS System or International System of Units (SI):-
– Advised by a study committee of French Academy of Science in 1791
Commonly know as Metric System.
– In this system Length, Mass and Time are measured in Meter, Kilogram and
Second respectively.
– In comparison to decimal system of CGS this system is convenient for
handling of units as these are multiple of ten.
– Revised in 1960 by an International Body, General Conference of Weights and
measures was adopted by National Bureau of Standards.
– This Revised set of units known as International System of Units (SI).

SOME BASIC UNITS ANDSOME BASIC UNITS AND
CONVERSION FACTORSCONVERSION FACTORS
_______________________________________________________________________________
Quality Sl units Sl Symbol Multiply by To obtain
fps units
________________________________________________________________________________________
Length meter m 3.2808 ftq
Mass kilogram kg 2.2046 lb
Temperature celsius. ºC 1.8 +32 ºF
Area square meter m2
10.7639 ft2
Volume cubic meter m3
35.314 ft3
Energy kilojoule kJ 0.9478 Btu
Power watt W 3.4121 Btu/h
Velocity meter/second m/s 2.2369 mi/h
Flow rate meter3
/second m3
/s 35.3147 ft3
/s
Density kilogram/meter3
kg/m3
0.06243 lb/ft3
_________________________________________________________________________________________

SYSTEM OF PREFIXESSYSTEM OF PREFIXES
• To express extremely large quantities and extremely small quantities.
________________________________________________
Prefix Symbol Meaning
________________________________________________
micro µ 10-6
milli m 10-3
centi c 10-2
deci d 10-1
deca da 10
hecta h 102
kilo k 103
mega M 106
_______________________________________________________

COMMONLY USED UNITS OF LENGTH, AREA,COMMONLY USED UNITS OF LENGTH, AREA,
VOLUME AND MASSVOLUME AND MASS

1 kilometer (km) = 1000 m
1 m = 100 centimeter (cm)
1 cm = 10 millimeter (mm)
1 hectare = 10,000 m2
1 liter (L) = 1000 mL=1000 cm3
1 m3
= 1000 L=1kL
1 kg = 1000 gram (g)
1 g = 1000 milligram (mg)
1 mg = 1000 micro gram (µg)


SPECIAL FEATURES OF SI UNITSSPECIAL FEATURES OF SI UNITS
• Symbols of units do not have a plural ending. For example, one should write
20cm and not 20cms.
• The symbols of units, which bear the names of the scientists are normally
written in capital letters. For example the unit of ‘Joule’ adopted after the
name of James P. Joule is denoted by ‘J’
• Units combinations should be indicated by means of either a dot or leaving
space in between. For example-kilogram meter may be written as Kg.m or
Kg m.
• Words and symbols should not be used in mixed forms For example-it is not
proper to use J per mole but should be written as either Joule per mole or J
mol-1
. In order to show mathematical operations, only symbols should be
used i.e. J mol-1
and not Joules Mol-1
.
• Units written with a prefix and a power is always a power for complete unit.
For example– cm3
means (centimeter)3
and not centi (meter)3
.
• Exponents also operate on prefixes For example 1mm3
= (10-3
m)3
= 10-9
m3
. It
is therefore, not equal to 10-3
m3
.

CONVERSION OF UNITSCONVERSION OF UNITS
First Step:- Determination of Conversion Factor.
1 Kg = 1000g
               1Kg               1000g
or 1=      ------     or     ---------- = 1
             1000g                           1Kg
Called unit conversion factor
Second Step:- The physical quantity is multiplied by unit
conversion factor while retaining the units of both the physical
quantity as well as the conversion factor so that after
simplification, only the required units are left behind.
Third Step: -In case the conversion involves a number of steps,
each conversion factor is used in such a manner that units of the
preceding cancel out.

UNITS OF CONCENTRATIONUNITS OF CONCENTRATION
• Concentration of pollutants in water or air are expressed as a ratio: mass or
volume of Pollutants in a given mass or volumes of water or air.
• Substance is water are usually expressed in terms of mass of substance per
unit volume of the mixture such as mg/L or µg/L.
• Concentration of substances in liquids are also expressed as ratio of mass
of the substance to a specified mass of mixtures, usually as parts per million
(ppm by weight).
• (Since most of concentration of pollutants is in water are small, one litre of
mixture weighs essentially 1000g,)
      1mg             1              1g 1mg
      -------  x    --------  x   ---------    =    ------- = 1ppm
          L         1000g        1000mg        106
mg
• mg/L and ppm may be used interchangeably as long as the liquid density
can be assumed to be 1000g/L  concentration in liquids are also expressed
in percentage (mass/mass)

EXAMPLE 1EXAMPLE 1
4 kg of common salt is thrown in a pond containing 800m3
water.
What is the resulting concentration of the salt in the water in mg/L,
µg/L?
Solution
4kg                106
mg            1m3
--------   x      ------------  x    --------      =   5 mg/L
800m3
1 kg           103
L
5mg       1000 µg
--------   x      ------------   = 5,000 µg/L
L                      1mg


EXAMPLE 2EXAMPLE 2
For the data of Example 1, calculate the concentration in percentage.
Assume the density of solution as 1000 kg/m3
(or 1000 g/L)
Solution
4kg 1m3
-------- x ------------ x 100 = 0.0005%
800m3
1000 kg
Note: ppm can be changed to percent by dividing by 104
.

CONCENTRATION OF AIR POLLUTANTSCONCENTRATION OF AIR POLLUTANTS
• Concentration of air pollutants are express both in terms of mass of
pollutants (µg or mg) per unit volume (m3
) of the mixture and as percent
or ppm by volume .
• The volume of a gas changes significantly with temperature and
pressure, to calculate volume at different temperature and pressure help
is taken of the relationship.
P1
V1
P2
V2
--------- = -------
T1
T2
Where,
P = Pressure
V = Volume
T = Temperature in degree kilometer

EXAMPLE 3
14 g sulphur is burnt in a room having 5000m3
air maintained at 15ºC Calculate
resulting sulphur dioxide concentration in the air in the room in µg/m3
, ppm and
percent by volume.
Solution: -
Calculate the volume of 5000 m3
air at one atm. pressure at 25ºC and 0ºC,
using V1=V2. T1/T2
5000 (273 +25)
V25 = ---------------------- = 5173.6 m3
(273 + 15)
5000 (273 + 0)
V0 = ------------------- = 4739.6 m3
(273 + 15)
Calculate the mass and volume of SO2 produced at 0 ºC from stochiometric
equation.
S + O2 = SO2
64g SO2
Mass of S02 produced = 14 g S x ------------------ = 28 g
32 g SENVIRONMENTAL SCIENCES: CBSE UGC-JRF/NET and ARS-NET

CONT. EXAMPLE 3
Since 1g mole of a gas occupies 22.4 L at STP
28 g SO2 22.4 L SO2
Volume of SO2 produced at 0ºC= -------------------- x ------------------------- = 9.8 L
64 g SO2/mole 1 mole
28 g SO2 106
µg
--------------------- x ------------------ = 5412 µg/m3
at 25º C
5173.6 m3
air 1 g
and 9.8 L 1 m3
--------------- x ------------ x 106
= 2.06 ppm (or 2.06 x 103
= 2060ppb)
4739.6 m3
103
L
and 2.06
----- = 0.0002 %
104
ppm x mol wt
Note: mg/m3
= ------------------- (at 25 ºC and 1 atm)
24.45

UNIT CONVERSION
Multiply 104
( 106
/ 100)
Percentage PPM
Divide by 104
Multiply 103
PPM PPB
Divide by 103

UNIT CONVERSION
ppm x mol wt
mg/m3
= ------------------- (at 25 ºC and 1 atm)
24.45
mg/m3
x 24.45
ppm = ------------------- (at 25 ºC and 1 atm)
mol wt

UNIT CONVERSION
mg/m3
= mg x 1000µg / m3
= µg/m3
mg
µg/m3
= µg x mg / m3
= mg/m3
1000µg

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Units conversion CBSE UGC JRF/NET

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