Dimensional analysis : The seven basic quantities lead to the number of derived quantities for example pressure, volume, force, speed, density, etc. The units for such quantities can be attained by defining the derived quantity in terms of base quantities using the base units. For instance, speed (velocity) is expressed in distance/time. So the unit is m/s or ms-1. The unit of force mass*acceleration can be given as Kg ms-2 and the unit for acceleration can be given as ms-2.
Table 1.1 Seven basic S.I. units
Length
|
Mass
|
Time
|
Temperature
|
Electric Current
|
Luminous Intensity
|
Amount of substance
|
|
metre (m)
|
Kilogram (kg)
|
Second (s)
|
Kelvin (K)
|
Ampere (A)
|
Candela (Cd)
|
Mole (mol)
|
Table 1.2 Derived Units
|
Physical quantity
|
Unit
|
Symbol
|
|
Area
|
square metre
|
m2
|
|
Volume
|
cubic metre
|
m3
|
|
Velocity
|
metre per second
|
ms-1
|
|
Acceleration
|
metre per second square
|
ms-2
|
|
Density
|
kilogram per cubic metre
|
kg m-3
|
|
Molar mass
|
kilogram per mole
|
kg mol-1
|
|
Molar volume
|
cubic metre per mole
|
m3 mol-1
|
|
Molar concentration
|
mole per cubic metre
|
mol m-3
|
|
Force
|
newton (N)
|
kg m s-2
|
|
Pressure
|
pascal (Pa)
|
N m-2
|
|
Energy work
|
joule (J)
|
kg m2 s-2, Nm
|
Table 1.3 Standard prefixes use to reduce the basic units
|
Multiple
|
Prefix
|
Symbol
|
Submultiple
|
Prefix
|
Symbol
|
|
1024
|
yotta
|
Y
|
10-1
|
deci
|
d
|
|
1021
|
zetta
|
Z
|
10-2
|
centi
|
c
|
|
1018
|
exa
|
E
|
10-3
|
milli
|
m
|
|
1015
|
peta
|
P
|
10-6
|
micro
|
m
|
|
1012
|
tera
|
T
|
10-9
|
nano
|
n
|
|
109
|
giga
|
G
|
10-12
|
pico
|
p
|
|
106
|
mega
|
M
|
10-15
|
femto
|
f
|
|
103
|
kilo
|
k
|
10-18
|
atto
|
a
|
|
102
|
hecto
|
h
|
10-21
|
zeto
|
z
|
|
101
|
deca
|
da
|
10-24
|
yocto
|
y
|
Table 1.4 Conversion factors
1 m = 39.37 inch
|
1 cal = 4.184 J
|
1 e.s.u. = 3.3356 ´ 10-10 C
|
1 mole of a gas = 22.4 L at STP
|
1 inch = 2.54 cm
|
1 eV = 1.602 ´ 10-19J
|
1 dyne = 10-5 N
|
1 mole a substance = N0molecules
|
1 litre = 1000 mL
|
1 eV/atom =96.5 kJ mol-1
|
1 atm = 101325 Pa
|
1 g atom = N0 atoms
|
1 gallon (US) = 3.79 L
|
1 amu = 931.5016 MeV
|
1 bar = 1 ´ 105 N m-2
|
t (oF) = 9/5 t (oC) + 32
|
1 lb = 453.59237 g
|
1 kilo watt hour = 3600 kJ
|
1 litre atm = 101.3 J
|
1 g cm-3 = 1000 kg m-3
|
1 newton =1 kg m s-2
|
1 horse power = 746 watt
|
1 year = 3.1536 ´ 107 s
|
1Å = 10-10 m
|
1 J = 1 Nm =1 kg m2s-2
|
1 joule = 107 erg
|
1 debye (D) = 1 ´ 10 -18esu cm
|
1nm = 10-9 m
|
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