TOPIC TWO - MEASUREMENT I

In order to measure we need to know or define the quantity to be measured and the units

for measuring it. In 1971 a system known as the International System of Units (Systeme’ Internationale) and seven basic units were agreed upon as follows. Other quantities can be obtained from these basic quantities and are referred to as derived quantities.

Basic quantity	SI units	Symbols
Length	Metre	m
Mass	Kilogram	kg
Time	Second	s
Electric current	Ampere	A
Thermodynamic  temperature	Kelvin	K
Luminous intensity	Candela	Cd
Amount of substance	Mole	mol

Length

This is the measure of distance between two points in space. The SI unit for length is the

metre (m).Therefore 1 km = 1000 m

1 Hm = 100 m

1 Dm= 10 m

1 mm = 0.001 m

Length is measured using a metre rule (100 cm), tape measure (100 m, 300 m, 500 m)

Area

This is the measure of the extent of a surface. It is a derived quantity of length. Its SI units are square metres (m2). Other units are cm2, km2, etc. Formulas are used to determine areas of regular bodies while for irregular bodies an approximation of area is used.

Volume

This is the amount of space occupied by matter. The SI units for volume is cubic metre (m3).

Other sub-multiples are cm3, mm3 and l. Hence 1 m3 = 1,000,000 cm3 and 1l= 1,000 cm3.

Volume can be measured using a measuring cylinder, eureka can, pipette, burette, volumetric flask, beaker, etc.

Mass

This is the quantity of matter contained in a substance . Matter is anything that occupies space and has weight. The SI unit for mass is the Kilogram (kg). Other sub-multiples used are grams (g), milligrams (mg) and tonnes (t). 1 kg = 1,000 g = 1,000,000 mg=100 tonnes. A beam balance is used to measure mass.

Density

This is mass per unit volume of a substance. It is symbolized by rho (ρ) and its SI units are

kg/m3. Density = mass / volume.

Examples

1.   A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high.

Calculate the density of the glass in kgm -3. Solution

Density = mass / volume = (187.5 /1000) /(2.0 × 7.5 × 5.0 /1,000,000) = 2,500 kgm-3.

2.   The density of concentrated sulphuric acid is 1.8 g/cm 3. Calculate the volume of 3.1 kg of the acid.

Solution

Volume = mass / density = 3,100 / 1.8 = 1,722 cm3 or 0.001722 m3.

The following is a list of dens ities of some common substances

Substance	Density (g/cm3)	Density (kg/m3)
Platinum	21.4	21,400
Gold	19.3	19,300
Lead	11.3	11,300
Silver	10.5	10,500
Copper	8.93	8,930
Iron	7.86	7,860
Aluminium	2.7	2,700
Glass	2.5	2,500
Ice	0.92	920
Mercury	13.6	13,600
Sea water	1.03	1,030
Water	1.0	1,000
Kerosene	0.80	800
Alcohol	0.79	790
Carbon (iv) oxide	0.00197	1.97
Air	0.00131	1.31
Hydrogen	0.000089	0.089

Example

The mass of an empty density bottle is 20 g. Its mass when filled with water is 40.0 g an d

50.0 g when filled with liquid X. Calculate the density of liquid X if the density of water is

1,000 kgm-3.

Solution

Mass of water = 40 – 20 = 20 g = 0.02 kg.

Volume of water = 0.02 / 1,000 = 0.00002 m3. Volume of liquid = volume of bottle

Mass of liquid = 50 – 20 = 30 g = 0.03 kg

Therefore density of liquid = 0.03 / 0.00002 = 1,500 kgm-3

Relative density

This is the density of a substance compared to the density of water.

It is symbolized by (d) and has no units since it’s a ratio. Relative density (d) = density of substance / density of water. It is measured using a relative density bottle

Example

The relative density of some type of wood is 0.8. Find the density of the wood in kg/m 3.

Solution

Density of substance = d × density of water

Density of subs tance = 0.8 × 1,000 = 800 kgm-3

Densities of mixtures

We use the following formula to calculate densities of mixtures

Density of the mixture = mass of the mixture / volume of the mixture

Example

100 cm3 of fresh water of density 1,000 kgm-3 is mixed with 100 cm3 of sea water of density

1030 kgm-3. Calculate the density of the mixture. Solution

Mass = density × volume

Mass of fresh water = 1,000 × 0.0001 = 0.1 kg

Mass of sea water = 1030 × 0.0001 = 0.103 kg

Mass of mixture = 0.1 + 0.103 = 0.203 kg

Volume of mixture = 100 + 100 = 200 cm3 = 0.0002 m3

Therefore density = mass / volume = 0.203 / 0.0002 =1,015 kg/m3.

Time

This is a measure of duration of an event . The SI unit for time is the second (s). Sub- multiples of the second are milliseconds, microseconds, minute, hour, day, week and year. It is measured using clocks, stop watches, wrist watches, and digital watches.

Accuracy and errors

Accuracy is the closeness of a measurement to the correct value of the quantity being measured. It is expressed as an error. An error is therefore the deviation of measurement to the correct value being measured. The smaller the error the accurate the measurement.

% error = (sensitivity / size measured) × 100.