CHAPTER 17 Density The use of an equation

Introduction Which is heavier iron or wood? Many people say iron and yet an iron nail is lighter than a wooden tree! What people mean is that iron and wood have different densities.

Equation To measure density, we need to measure the mass of a definite volume of the substance. In fact: If the mass is measured in kg (kilograms) and the volume in m3 (cubic metres), the density is measured in kg/m3 (kilogram per cubic metre) Sometimes the mass is measured in g (grams) and the volume in cm3 (cubic centimetres) so the density is measured in g/cm3 (gram per cubic centimetre)

Table Here are the densities of several substances: Substance Density Solid Liquid Gas Kg/m3 g/cm3 Gold 19 000 19 Mercury 14 000 14 Lead 11 000 11 Iron 8 000 8 Water 1 000 1 Ice 920 0.92 Petrol 800 0.80 Air 1.3 0.0013

Example An engineer needs to know the mass of a steel beam (girder) which is 20m long, 0.1m wide and 0.1m high. (Density of steel = 8000kg/m3) Answer Calculating the volume first we have Volume of girder = length × width × height = 20m × 0.1m × 0.1m = 0.2m3 Formula: Therefore mass = 8000 × 0.2 = 1600kg

Experiment to measure density Find the density of a solid in three stages: Find the mass of the solid by using a balance metre and the volume by using a measuring cylinder. Remember to put your eye at the right level, and to read the bottom of the meniscus. Use the formula: What is the density of the stone shown here?

Applications Geologists need to measure the density of rocks. It helps them to identify the kind of rock, and where it comes from. Milk inspectors and beer inspectors measure the density of the liquid to see if it has been watered down.

Summary 1. Changing round the formula: 2. 3. Mass = volume × density Density of water = 1000kg/m3 = 1g/cm3

Exercise 1 An object has a mass of 100 grams and a volume of 20 cubic centimetres. What is its density? Ans. 5g/cm3 A water tank measures 2m × 4m × 5m. What mass of water will it contain? Ans. 40 000kg