# Measurement

Basic Measurement

Length – the measured distance between two positions

Area – the amount of surface

Volume – amount of space occupied by an object

Mass – the amount of matter in an object

Density – the mass per unit volume.

Time – the measured duration between two events.

Temperature – the degree of hotness of a substance.

Length l Metre m

Area A square metre m2

Volume V cubic metre m3

Mass m kilogram kg

Density p kilogram per cubic metre kg m-3

Time t second s

Temperature T Kelvin or Degrees Celsius K or °C

In most school laboratory experiments, the metre and kilogram are not convenient units for measurement. The centimetre, millimetre and gram are the most commonly used units.

Alternative Units

Length cm or mm

Area cm2 or mm2

Volume cm3 or mm3

Mass g

Density g/cm3 or g cm-3

Measuring Instruments

Ruler: the length of short straight lines.

Opisometer: the length of short curved lines.

Trundle Wheel: the length of long curved lines.

Callipers: the internal and external diameters to an accuracy of 1 mm.

Vernier Callipers: internal and external diameters to an accuracy of 0.1 mm.

Measuring Cylinder: volume of liquids and small irregular objects.

Overflow Can: volume of large irregular objects.

Pan-top Balance: the mass of objects.

Pipette: to deliver a definite volume of a liquid; the volume is indicated on the reservoir bulb.

Burette: to deliver any volume of a liquid from 0.1 cm3 up to 50 cm3.

Watch or clock: to measure time.

Thermometer: to measure temperature.

Derived Data

Area: the amount of surface of the object – the area of regular objects can be calculated using mathematics and the formulae for these are in the Mathematics Tables.

Volume: the amount of space taken up by an object - the volume of regular objects can be calculated using mathematics and the formulae for these are in the Mathematics Tables.

Density is how concentrated is matter in the object – it is the mass per unit volume calculated by dividing the mass of the object by its volume.

The density of water at 4°C: 1 g/cm3 or 1 g cm-3 or 1 kg/l (one kilogram per litre).

Mandatory Practical Activity 21

Measure the mass and volume of a variety of solids and liquids and hence determine their densities.

(i) Measure the Mass and Volume of a Variety of Solids

The mass of solids is easily measured by using a top pan balance.

Zero the balance first then place the solid on the pan and record the digital reading of its mass.

(a) Measuring the Volume of a Small Irregular Solid – use a measuring cylinder.

Pour some water into a measuring cylinder and record the level e.g. 40 cm3 .

Gently lower the solid into the water by a thread until it is completely submerged – if the solid is less dense than water then push it under with a long thin needle.

Record the new higher level of water e.g. 65 cm3 .

Subtract the readings to find the volume of the solid: 65 cm3 - 40 cm3 = 25 cm3

Make sure the measuring cylinder was perfectly vertical while taking the readings.

Remember to read from the bottom of the meniscus curve.

(b) Measuring the Volume of a Large Irregular Solid – use an overflow can.

Place an overflow can at the side of a sink with the spout overhanging the sink.

Overfill the overflow can and allow the excess water to flow out – wait till the dripping stops – the water surface is level with the bottom of the opening in the can.

Place a clean dry measuring cylinder under the spout.

Gently lower the solid into the water by a thread until it is completely submerged – if the solid is less dense than water then push it under with a long thin needle.

The displaced water flows out of the can from the spout into the measuring cylinder.

Wait for the dripping to stop.

The volume water in the measuring cylinder is the volume of the solid.

The densities of each of the solids are calculated by dividing their mass by their volume.

(ii) Measure the Mass and Volume of a Variety of Liquids

The volume of liquids can be determined by using a measuring cylinder and exact volumes of liquid can be delivered by using a pipette or burette.

A two step process is needed to find the mass of a liquid.

First measure and record the mass of a clean dry beaker using a top pan balance e.g. 30 g.

Pour the liquid into the beaker and measure the mass of the beaker plus the liquid e.g. 70 g.

By subtraction the mass of the liquid is calculated: 70 g – 30 g = 40 g.

If the volume of the liquid is known then its density can be calculated by dividing the mass of the liquid by the volume of the liquid.