7.1 Density

Have you ever noticed that a small piece of iron feels much heavier than a large piece of wood of the same size? Or that oil floats on water, but a stone sinks? These observations are explained by a property called density. Density is a fundamental characteristic of matter that describes how much mass is packed into a given volume. It helps us understand why some objects float and others sink, and it is essential for identifying materials and understanding their behavior.

Definition

Density is defined as the mass per unit volume of a substance. It tells us how much matter is packed into a given space.

Mathematically: Density = MassVolume or ρ = mV where: - ρ (rho) is the density. - m is the mass. - V is the volume.

The SI unit of density is kilogram per cubic metre (kg/m³). A smaller, more convenient unit is gram per cubic centimetre (g/cm³). 1 g/cm³ = 1000 kg/m³

Main Idea

The main idea is that density is a property of a material that depends on how closely packed its particles are. Solids, where particles are tightly packed, generally have higher densities than liquids, and liquids have higher densities than gases. Density is a characteristic property of a substance, meaning it can be used to identify materials. It also determines whether an object will float or sink in a fluid.

Core Concept

Definition and Formula The text states: "Density of a material tells us how much matter a substance has in its unit volume. The substance, which has more closely packed atoms, has more matter in a fix volume. Therefore, it is denser substance."

The formula is: ρ = mV

• SI unit: kg/m³
• Common unit: g/cm³
• For liquids: g/mL (grams per millilitre)
• Conversion: 1 g/cm³ = 1000 kg/m³

Density of Different States of Matter The text states: "Solids like metals; rocks etc. are denser materials because they have closely packed atoms in the given volume. Substances in which atoms are far from each other, they have small amount of matter in a fix volume, so they are less dense. It is the reason why liquids and gases have less density than solids. Density of solids is greater than liquids and density of liquids is greater than gases."

• Solids: Highest density (particles closely packed).
• Liquids: Intermediate density (particles less closely packed).
• Gases: Lowest density (particles far apart).

Density is a Characteristic Property The text states: "Density of small amount of a substance is the same as the density of its bulk because density is calculated by the amount of matter in its unit volume."

This means that density does not depend on the size or shape of the object. A small piece of iron has the same density as a large iron block. This makes density a useful property for identifying materials.

Density and Temperature The text states: "Density of a material changes with the temperature."

When a substance is heated, its particles move faster and spread out, causing the substance to expand. This increases the volume while the mass remains constant, so the density decreases. Conversely, cooling a substance causes it to contract, increasing its density.

The Densest Material The text states: "Osmium metal is the most dense material at room temperature and pressure. Its density is 22.59 g/cm³. It is harder than diamond."

Detailed Explanation

Density is a fundamental concept in physics and engineering. It explains why objects float or sink, how materials can be identified, and how substances behave under different conditions.

• Example: Wood (density ≈ 0.5 g/cm³) floats on water (density 1.0 g/cm³).
• Example: Iron (density ≈ 7.9 g/cm³) sinks in water.

This principle is known as buoyancy and is governed by Archimedes' principle.

• Mass of the particles: Heavier atoms/molecules result in higher density.
• Spacing between particles: Closer packing results in higher density.

Solids have tightly packed particles, so they are generally denser than liquids and gases. Gases have widely spaced particles, so they have low density.

• Iron: 7900 kg/m³
• Gold: 19300 kg/m³
• Ice: 920 kg/m³
• Polythene: 900 kg/m³
• Petrol: 800 kg/m³
• Pure water: 1000 kg/m³
• Mercury: 13600 kg/m³
• Air: 1.3 kg/m³
• Carbon dioxide: 2.0 kg/m³

Example from Text The text provides an example (Example 7.1): "You find a material in the shape of cube of side length 5 centimetre. Mass of this cube is 500 grams. Find the density of this material?" - Given: Mass m = 500 g, Side length s = 5 cm - Volume: V = s³ = 5³ = 125 cm³ - Density: ρ = 500125 = 4 g/cm³

Intermediate Level

In physics, density is a characteristic property of a material, defined as mass per unit volume (ρ = m/V). It is an intensive property, meaning it does not depend on the amount of substance. The SI unit is kg/m³, but g/cm³ is also commonly used.

Density is determined by the arrangement of particles. Solids have closely packed particles and high density. Liquids have less closely packed particles and lower density. Gases have widely spaced particles and very low density. Density can change with temperature (thermal expansion) and pressure (for gases).

Density is important for determining whether an object will float or sink. An object floats if its density is less than the fluid's density and sinks if it is greater. This principle is used in ship design (ships are less dense than water overall because they contain air) and in measuring the density of unknown substances.

The density of a substance can be measured by determining its mass (using a balance) and its volume (using geometric formulas for regular objects or displacement methods for irregular objects).

Important Points

• - Density: Mass per unit volume.
• - Formula: ρ = m/V.
• - SI unit: kg/m³.
• - Common unit: g/cm³.
• - Conversion: 1 g/cm³ = 1000 kg/m³.
• - States of matter: Solids > Liquids > Gases (in general).
• - Characteristic property: Density is the same for a given material, regardless of size.
• - Temperature effect: Density decreases with increasing temperature (usually).
• - Float or sink: Object floats if its density is less than the fluid's density.

Remember

• - Density = Mass / Volume.
• - Formula: ρ = m/V.
• - SI unit: kg/m³.
• - 1 g/cm³ = 1000 kg/m³.
• - Solid > Liquid > Gas (typical densities).
• - Density is constant for a given material.
• - Float: Density less than fluid. Sink: Density greater than fluid.

Common Mistakes

• - Thinking density depends on the size of the object: Density is a characteristic property and is the same for a small piece and a large block of the same material.
• - Forgetting to use consistent units: When calculating density, make sure mass and volume are in compatible units (e.g., grams and cm³, or kg and m³).
• - Confusing density with weight: Density is mass per unit volume. Weight is the force of gravity on an object. They are different quantities.

Quick Revision

Density is the mass per unit volume of a substance, given by ρ = m/V. It is measured in kg/m³ (SI) or g/cm³. Density is a characteristic property of a material, meaning it does not depend on the object's size. Solids generally have higher densities than liquids, and liquids have higher densities than gases, because their particles are more closely packed. Density determines whether an object will float or sink in a fluid.

60-Second Revision

• Formula: ρ = m/V.
• SI unit: kg/m³.
• 1 g/cm³ = 1000 kg/m³.
• Solid > Liquid > Gas.
• Characteristic property.
• Float: Density < fluid. Sink: Density > fluid.

Frequently Asked Questions (FAQs)

• Q1. What is density?
• Answer: Density is the mass per unit volume of a substance. It tells us how much matter is packed into a given space.

• Q2. What is the formula for density?
• Answer: The formula is:
• ρ = mV
• where m is mass and V is volume.

• Q3. What is the SI unit of density?
• Answer: The SI unit of density is kilogram per cubic metre (kg/m³). Another common unit is gram per cubic centimetre (g/cm³).

Q4. Why do solids generally have higher densities than liquids and gases? Answer: Solids have closely packed particles, so they have more mass in a given volume. Liquids have less closely packed particles, and gases have widely spaced particles, resulting in lower densities.

• Q5. Does density depend on the size of the object?
• Answer: No. Density is a characteristic property of a material. A small piece of iron has the same density as a large iron block.

Q6. How does temperature affect density? Answer: In general, when a substance is heated, it expands (volume increases) while its mass remains constant, so its density decreases. Cooling has the opposite effect.

• Q7. How does density determine whether an object floats or sinks?
• Answer: An object floats in a fluid if its density is less than the fluid's density. It sinks if its density is greater than the fluid's density.

• Q8. What is the densest material?
• Answer: Osmium is the densest naturally occurring element at room temperature and pressure, with a density of 22.59 g/cm³.

Multiple Choice Questions (MCQs)

• Q1. Density is defined as:
• A. Mass × volume
• B. Mass / volume
• C. Volume / mass
• D. Mass + volume

• Correct Answer: B
• Explanation: The text defines density as mass per unit volume, ρ = m/V.

• Q2. The SI unit of density is:
• A. kg/m³
• B. g/cm³
• C. N/m²
• D. J/kg

• Correct Answer: A
• Explanation: The text states that the SI unit of density is kilogram per cubic metre (kg/m³).

• Q3. Which state of matter generally has the highest density?
• A. Solid
• B. Liquid
• C. Gas
• D. Plasma

• Correct Answer: A
• Explanation: The text states that solids are denser than liquids and gases because their atoms are closely packed.

• Q4. If the mass of an object is 500 g and its volume is 125 cm³, its density is:
• A. 2 g/cm³
• B. 4 g/cm³
• C. 5 g/cm³
• D. 10 g/cm³

• Correct Answer: B
• Explanation: ρ = 500125 = 4 g/cm³, as calculated in the text.

• Q5. Density is a:
• A. Vector quantity
• B. Scalar quantity
• C. Base quantity
• D. Derived quantity

• Correct Answer: B
• Explanation: Density is a scalar quantity (it has magnitude but no direction).

• Q6. Which of the following materials is the densest?
• A. Water
• B. Iron
• C. Air
• D. Wood

• Correct Answer: B
• Explanation: Iron (7900 kg/m³) is much denser than water (1000 kg/m³), air (1.3 kg/m³), and wood (varies, but typically less than water).

• Q7. An object will float in water if its density is:
• A. Greater than water
• B. Less than water
• C. Equal to water
• D. Zero

• Correct Answer: B
• Explanation: An object floats if its density is less than the fluid's density.

• Q8. When a substance is heated, its density generally:
• A. Increases
• B. Decreases
• C. Remains the same
• D. Becomes zero

• Correct Answer: B
• Explanation: Heating causes expansion (volume increases), so density decreases (mass remains constant).

• Q9. The density of a small piece of iron compared to a large iron block is:
• A. Greater
• B. Less
• C. The same
• D. Depends on the shape

• Correct Answer: C
• Explanation: Density is a characteristic property and does not depend on the size of the object.

• Q10. 1 g/cm³ is equal to:
• A. 1 kg/m³
• B. 100 kg/m³
• C. 1000 kg/m³
• D. 0.001 kg/m³

• Correct Answer: C
• Explanation: 1 g/cm³ = 1000 kg/m³.

Frequently Asked Questions (FAQs)

Q1. What is the difference between density and specific gravity? Answer: Density is mass per unit volume (e.g., kg/m³). Specific gravity is the ratio of a substance's density to the density of water. It is a dimensionless quantity.

Q2. Why does ice float on water? Answer: Ice is less dense than liquid water (ice has a density of about 920 kg/m³, while water is 1000 kg/m³). This is because the hydrogen bonds in ice create an open, hexagonal structure that takes up more volume. So, ice floats.

Q3. How is the density of an irregular solid measured? Answer: The mass is measured using a balance. The volume is measured using the displacement method (submerging the object in a measuring cylinder and measuring the volume of water displaced). Density is then calculated as mass/volume.

Q4. Why does the density of a gas change with pressure? Answer: Gases are compressible. Increasing the pressure on a gas decreases its volume (while mass remains constant), so its density increases. Decreasing the pressure increases the volume, decreasing the density.

• Q5. What is the density of water?
• Answer: The density of pure water is approximately 1000 kg/m³ (or 1 g/cm³) at 4°C.

• Q6. What is the density of air?
• Answer: The density of air at sea level and room temperature is approximately 1.2 to 1.3 kg/m³.

Q7. How does the density of a material relate to its buoyancy? Answer: An object will float in a fluid if its average density is less than the fluid's density. It will sink if its average density is greater. This is the principle of buoyancy, described by Archimedes' principle.

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