LECTURE NOTE 3
The metric system offers simplicity and basic unit. Although the English system
was common, a committee was for over ten and a new system was agreed on called
Metric system.
Physical Quantity
Length
Mass
Volume
Time
Basic Metric unit
Meter
Gram
Liter
Second
Symbol
m
g
L
S
METRIC PREFIXES
Metric system is a decimal system but uses a prefix to express a multiple or a
fraction of a basic unit. A metric prefix increases or decreases a basic unit by a factor of
10.
PREFIX
SYMBOL
MULTIPLE/FRACTION
giga
G
1,000,000,000=1x10 9
mega
M
1,000,000= 1x10 6
kilo
K
1,000 = 1x 103
deci
d
0.1=1x10 -1
centi
c
0.01=1x10 -2
milli
m
0.001=1x10-3
Micro
µ
0.000001=1x10-6
nano
n
0.000000001=1x10-9
The metric system is sometimes referred to as International system of
measurement (SI), but SI is an extension of metric system. The SI system is more
comprehensive and sophisticated. The international system of units has the following as
base units.
Physical Quantity
SI basic unit
Symbol
length
Meter
m
Mass
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
Electric current
Ampere
A
Light intensity
Candela
cd
Amount of substance
mole
mol
METRIC-ENGLISH CONVERSIONS
Most part of the world, the metric system is used, however, some parts of
America still uses the English system. The following can be used as Metric-English
conversion table:
Physical Quantity
English Unit
Metric Unit
Length
1 inch(in)
1in=2.54cm
Mass
1 pound(lb)
1lb=454g
1
Volume
Time
1 quart(qt)
1 second(sec)
1qt=946mL
1sec=1.00s
VOLUME BY CALCULATION
The volume of a rectangular solid is equal to length multiplied by width
multiplied by thickness. Volumes of a regular solid can be calculated. Students must
however take note of the unit of the parameters given and the unit of the answer, they
must all be in the same units.
Example:
A sheet of tin measures 35.0cm by 25.0cm, and the volume is 1.36cm3. What is the
thickness of the foil in centimeters?
V=L x W x thickness
Thickness= V
WxL
=1.36cm3
25.0cm x 35.0cm
=0.00155cm
=1.55x10-3cm
CUBIC VOLUME AND LIQUID VOLUME
In metric system, the basic unit of liquid volume is liter. A Liter is equivalent to
the volume occupied by a cube exactly 10cm on a side. A cube is a solid,
V= length x Width x thickness
V= 10cm x 10cm x10cm
V= 1000cm3
Recall 1L= 1000mL, combining,
1000cm3 = 1L = 1000mL
Therefore, 1cm3 = 1 mL
VOLUME BY DISPLACEMENT
Volume of liquids can be measured with calibrated glassware. Volume of regular
solid on the other hand can be measured by calculations; the volumes of irregular solids
cannot be measured using volume measured or by calculations Volume of irregular solids
or gases can be measured indirectly by the amount of water it displaces. The volume of
water is taken before emersion of the solid or in the case of gases, before the experiment
is started.
V (final) – V (initial) = V (displaced)
DENSITY
The term density expresses the concentration of mass. Density is the amount of
mass per volume.
Density (d) = mass (g)
Volume (cm3)
The units for solids and liquids: g/cm3 or g/mL.
The unit of gases: g/L
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Density varies slightly with temperature (but we will ignore this small effect for
now). Density of gases however, varies greatly with temperature and pressure.
Metric standard for mass and volume were based on water; a mass of 1kg was set
equal to 1L volume of water. Therefore density of water is 1kg/L which is equal to 1g/ml
or 1.00g/mL
When you have three liquids with different densities in the same container, you
will observe three layers of liquids. The one with the highest density stays in the bottom
of the container, while the one with the next lower density floats on top of the one at the
bottom, the one with the least density floats on top of the second one.
APPLYING DENSITY AS A UNIT FACTOR
Since density relates mass and volume, it can be used as a unit factor. For
example, the density of mercury is 13.6g/mL,
The unit equation will be: 13.6g = 1mL
The unit factor will be: 13.6g = 1mL
1ml
13.6g
Example
A 1.00-in cube of copper measures 2.54cm on a side. What is the mass of copper cube?
(Given: d of copper = 8.96g/cm3)
8.96g = 1cm3 --------- unit equation
1cm3 = 8.96g
8.96g 1cm3
Finding the volume of the cube: V = L x W x T
=2.54cm x 2.54cm x2.54cm
=16.4cm3
16.4cm3 x 8.96g
1cm3
=147g
SPECIFIC GRAVITY
This is the ratio of the density of a liquid to the density of water at 40C
Specific gravity (sp gr) is unit less because the density units cancel out. The density of
water is 1.00g/cm3 while specific gravity of water is 1.00.
TEMPERATURE
Hotness or coldness of the atmosphere is determined by how fast the tiny air
molecules are moving. If the temperature is warmer, molecules move faster and have
more energy while they move slower with less energy when cooler.
Temperature is a measure of the average kinetic energy of an individual particle.
The instrument used to measure temperature is thermometer.
Gabriel Fahrenheit, a German scientist invented the mercury thermometer. He got
two ranges of readings from a bath of ice, which he gave 0, and the temperature from his
underarm, which he gave 96. And so he calibrated the thermometer from 0 to 96, each
division is called Fahrenheit degree (0F).
The scale was elevated to freezing and boiling point of water as the standard
reference point. The freezing point of water was assigned 320F while the boiling was
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assigned 2120F. The Fahrenheit scale later became the basic unit for English system of
measurement.
Anders Celsius, proposed a similar scale, but on his scale, the freezing point of
water was assigned 00C while the boiling point was assigned 1000C. The scale was
divided into 100 parts, each division called 10C.The Celsius degree is also referred to as a
centigrade degree and is a basic unit in the metric system.
William Thomson (Lord Kelvin), proposed a scale based the lowest possible
temperature. The unit temperature was Kelvin unit (K), a basic unit in the S.I. unit. On
Kelvin scale, the coldest temperature is assigned 0K, each division is equal to 10C. The
lowest temperature is called ABSOLUTE ZERO = -273.150C
0K is equivalent to -2730C
Freezing point of water is 273K
Boiling point of water is 373K
Converting from one Scale to Another
00C = (0F – 320F) 1000C
1800F
0
F = (C x 1800F) +320F
1000C
0oC + 273 = K
HEAT AND SPECIFIC HEAT
Heat is the flow of energy from object at higher temperature to an object at lower
temperature. Heat and temperature are both a measure of kinetic energy. Heat measures
total energy while temperature measures average energy. Heat is expressed in unit of
calories or kilocalories.
A calorie (cal) is the amount of heat necessary to raise 1g of water 1degree on the
Celsius scale. A kilocalorie (kcal) is the amount of heat necessary to raise 1000g of water
1 degree on the Celsius scale.
A food calorie (Cal) is spelled with a capital letter to distinguish it from metric
calorie.
1 Cal (food calorie) = 1 kcal (1000 cal)
The S.I. unit for energy is Joule (J)
1 cal = 4.184 J
The heat produced by chemical reactions is often expressed in kilocalorie, and
kilojoules (kJ). 1kcal = 4.184kJ
SPECIFIC HEAT
Specific heat is the heat required to bring about a given change in temperature.
The surface of the earth is covered with water, and fortunately its high specific heat helps
to regulate climate and maintain moderate temperature.
Specific heat (sp ) is the heat required to raise the temperature of 1g of a substance
by 1oC. The unit of specific heat is calories per gram per 0C.
Specific heat (cal/g0C) = heat (cal)
Mass (g) x temperature change (0C)
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