Unit 5: Solids, Liquids and Gases: Chapter 18: Density and Pressure

Density and Pressure

Density

  • Density is a way of characterizing materials.

  • Matter exists in three basic forms: solid, liquid, and gas.

  • Solids often have high density, liquids are often less dense than solids, and gases have very low densities.

  • Definition: Density ($\rho$) of a material is calculated using the mass (m) of a certain volume (V) of the material.

  • Equation: \rho = \frac{m}{V}

  • Units for density: kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).

Example 1

  • A piece of iron has a mass of 390 kg and a volume of 0.05 m³. What is its density?

  • Density = mass / volume

  • Density = \frac{390 \text{ kg}}{0.05 \text{ m}^3} = 7800 \text{ kg/m}^3

Example 2

  • The mass of 50 cm³ of a liquid and a measuring cylinder is 146 g. The mass of the empty measuring cylinder is 100 g. What is the density of the liquid in kg/m³?

  • Mass of 50 cm³ of liquid = 146 g - 100 g = 46 g = 0.046 kg

  • 50 cm³ = 0.00005 m³

  • \rho = \frac{0.046 \text{ kg}}{0.00005 \text{ m}^3} = 920 \text{ kg/m}^3

  • Alternatively, \rho = \frac{46 \text{ g}}{50 \text{ cm}^3} = 0.92 \text{ g/cm}^3 = 920 \text{ kg/m}^3

Practical Investigation: Density of Solids

  • Measure the mass and volume of a sample to determine the density.

  • Use a half-meter rule to measure the length, width, and height of a regular solid.

  • For irregular solids, use a displacement can and measuring cylinder to determine the volume.

  • Ensure the measuring cylinder is on a level surface and read the scale straight on to avoid parallax error.

  • Use weighing scales to measure the mass of the solid.

Pressure

  • Definition: Pressure is the force per unit area.

  • Units: Pascals (Pa), where 1 Pa = 1 N/m²

  • Equation: p = \frac{F}{A}, where p is pressure, F is force (in newtons), and A is area (in square meters).

Example 3

  • An elephant has a weight of 40000 N, and her feet cover a total area of 0.1 m². A woman weighs 600 N and the total area of her shoes in contact with the ground is 0.0015 m². Who exerts the greatest pressure on the ground?

  • Elephant: p = \frac{40000 \text{ N}}{0.1 \text{ m}^2} = 400000 \text{ Pa}

  • Woman: p = \frac{600 \text{ N}}{0.0015 \text{ m}^2} = 400000 \text{ Pa}

  • They both exert equal pressure.

Pressure in Liquids and Gases

  • Pressure in liquids acts equally in all directions when the liquid is at rest.

  • Air pressure exerted by the atmosphere on our bodies is about 100,000 Pa.

Magdeburg Hemispheres Experiment

  • Demonstrates the effects of air pressure.

  • Two large metal bowls are put together, and the air is pumped out.

  • The bowls cannot be pulled apart due to the external air pressure.

Example 4

  • A laboratory set of Magdeburg hemispheres has a surface area of 0.045 m². What is the total force on the outside of the hemispheres?

  • F = p \times A = 100000 \text{ Pa} \times 0.045 \text{ m}^2 = 4500 \text{ N}

Pressure and Depth

  • Pressure in a liquid increases with depth.

  • Pressure difference equation: p = h \times \rho \times g, where h is height (m), $\rho$ is density (kg/m³), and g is gravitational field strength (N/kg).

Derivation of Pressure Difference Equation

  • Force at the bottom of a water column: F = (A \times h \times \rho) \times g

  • Pressure: p = \frac{F}{A} = \frac{A \times h \times \rho \times g}{A} = h \times \rho \times g

Example 5

  • A simple barometer uses a column of mercury to measure air pressure. If the column of mercury is 0.74 m high, what is the air pressure? The density of mercury is 13600 kg/m³, and g = 10 N/kg.

  • p = h \times \rho \times g = 0.74 \text{ m} \times 13600 \text{ kg/m}^3 \times 10 \text{ N/kg} = 100640 \text{ Pa}

Weather and Pressure

  • Variations in atmospheric pressure influence weather systems.

  • Meteorologists use maps showing atmospheric pressure variations to predict weather.

  • Low-pressure regions create winds as air flows from high-pressure areas.

  • Atmospheric pressure decreases with height.

Formulae:

Here are the formulas from the provided text:

  • Density(: \rho = \frac{m}{V} (kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³))

  • Pressure: p = \frac{F}{A} (Pascals (Pa), where 1 Pa = 1 N/m²)

  • Pressure difference: p = h \times \rho \times g (h is height (m), \rho is density (kg/m³), and g is gravitational field strength (N/kg))