Chapter 3: The Metric System
(Lecture Notes)
The metric system offers simplicity and basic units.
Physical Quantity
Length
Mass
Volume
Time
Basic Metric unit
Meter
Gram
Liter
Second
Symbol
m
g
L
S
METRIC PREFIXES
The Metric system is a decimal system that 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
giga
mega
kilo
deci
centi
milli
Micro
nano
SYMBOL
G
M
k
d
c
m
u
n
MULTIPLE/FRACTION
1,000,000,000=1x10 9
1,000,000= 1x10 6
1,000 = 1x 103
0.1=1x10 -1
0.01=1x10 -2
0.001=1x10-3
0.000001=1x10-6
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
length
Mass
Time
Temperature
Electric current
Light intensity
Amount of substance
SI basic unit
Meter
Kilogram
Second
Kelvin
Ampere
Candela
mole
Symbol
m
kg
s
K
A
cd
mol
METRIC-ENGLISH CONVERSIONS
The metric system is used in most parts of the world. However, some countries like the
United States still use the English system. The following can be used as Metric-English
conversion factors:
Physical Quantity
Length
Mass
Volume
Time
English Unit
1 inch(in)
1 pound(lb0
1 quart(qt)
1 second(sec)
Metric Unit
1in=2.54cm
1lb=454g
1qt=946mL
1sec=1.00s
VOLUME BY CALCULATION
The volume of a box shaped solid is equal to length times width times height (or
thickness). Volumes of regularly shaped solids can be calculated. Students should
however take note of the unit of the parameters given and the unit of the answer, they
need to be in the same units.
Example:
A sheet of tin measures 35.0cm by 25.0cm, and the volume is 1.36cm 3. What is the
thickness of the foil in centimeters?
V=L x W x H
Height = __V__
WxL
=1.36cm3
25.0cm x 35.0cm
=0.00155cm
=1.55x10-3cm
CUBIC VOLUME AND LIQUID VOLUME
In the metric system, the basic unit of liquid volume is the liter. A Liter is equivalent to
the volume occupied by a cube of exactly 10cm per 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 solids
on the other hand can be calculated from its measured dimensions. Volume of irregular
solids can be measured indirectly by the amount of water they displace. The volume of
water is measured before and after emersion of the solid:
V (final) – V (initial) = V (displaced) = V (solid object)
DENSITY
The term density expresses the concentration of mass. Density is the amount of mass
per unit of volume.
Density (D) = ___Mass (g)______
Volume (cm3 or mL)
The units of density for solids and liquids are g/cm3 or g/mL.
The units of density for gases are g/L
Density of liquids and solids varies slightly with temperature (but we will ignore this
small effect for now). Density of gases however, varies greatly with temperature and
pressure.
The metric standards 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 equivalent to
1g/ml or 1.00g/mL
When you have three non-miscible liquids with different densities in the same container,
you will observe three layers of liquids. The one with the highest density sinks to the
bottom of the container, while the one with the lowest density floats on top. The liquid
with the intermediate density will be in the middle.
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 factors will be: 13.6g and 1mL
1ml
13.6g
Example
A 1.00-in cube of copper measures 2.54cm on a side. What is the mass of the copper
cube? (Given: density of copper = 8.96g/cm3)
8.96g = 1cm3 --------- unit equation
1cm3 and 8.96g -------unit factors
8.96g
1cm3
Finding the volume of the cube: V = L x W x T
=2.54cm x 2.54cm x2.54cm
=16.4cm3
Finding the mass of the cube: since D=M/V, then M=DxV
16.4cm3 x 8.96g =147g
1cm3
SPECIFIC GRAVITY
This is the ratio of the density of a liquid to the density of water at 4 0C
Specific gravity (sp gr) is unitless 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 used two
readings for his scale. The first was from an ice bath, which he assigned as 0, and the
temperature of his underarm, which he assigned as 96. And so he calibrated the
thermometer from 0 to 96, each division is called a Fahrenheit degree (0F).
The scale was elevated to freezing and boiling point of water as the standard reference
points. The freezing point of water was assigned 320F while the boiling was assigned
2120F. The Fahrenheit scale later became the basic unit for the 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 on the lowest possible
temperature. The unit temperature was Kelvin unit (K), a basic unit in the S.I. On the
Kelvin scale, the coldest temperature is assigned 0K, and each division is equal to 1K.
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
0C = (0F – 32) / 1.8
0F
= (oC x 1.8) +32
0C
+ 273 = K
HEAT AND SPECIFIC HEAT
Heat is the flow of energy from an 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 the temperature of 1g of water
by 1 degree on the Celsius scale. A kilocalorie (kcal) is the amount of heat necessary to
raise the temperature of 1000g of water by 1 degree on the Celsius scale.
A food calorie (Cal) is spelled with a capital letter to distinguish it from the 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 kilocalories, 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)
We can rearrange this equation to:
Heat transferred (cal) = Mass (g) x Specific heat (cal/g0C) x temperature change (0C)