Properties of Matter Revision Notes BTER Polytechnic Classes

 

Properties of Matter

The study of the properties of matter involves understanding the behavior of different materials under various conditions such as force, temperature, and pressure. In this chapter, we will cover the basic concepts of elasticity, pressure, and surface tension, which are critical for explaining how materials respond to forces and other environmental factors.

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4.1 Elasticity

Elasticity is the property of a material to return to its original shape and size after the force causing deformation is removed. It explains how objects stretch, compress, or bend and then return to their original form.

4.1.1 Definition of Stress and Strain

1. Stress:

   • Definition: Stress is the force applied per unit area of the material. It represents the internal resistance to deformation within the material.

   • Formula:

     $$\text{Stress} = \frac{F}{A}$$

     Where:

     • $F$ is the applied force (in newtons, N),
     • $A$ is the cross-sectional area (in square meters, m²).

   • Units: The SI unit of stress is Newton per meter squared (N/m²) or Pascals (Pa).

2. Strain:

   • Definition: Strain is the relative deformation produced by stress. It is a dimensionless quantity, representing the change in shape or size of an object relative to its original dimensions.

   • Formula:

     $$\text{Strain} = \frac{\Delta L}{L_0}$$

     Where:

     • $\Delta L$ is the change in length (in meters),
     • $L_0$ is the original length (in meters).

   • Units: Strain is dimensionless (no units).

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4.1.2 Hooke’s Law

• Statement of Hooke’s Law: Hooke’s law states that, within the elastic limit, the stress applied to a material is directly proportional to the strain produced.

  $$\text{Stress} \propto \text{Strain}$$

  Or,

  $$F = k \cdot x$$

  Where:

  • $F$ is the force applied,
  • $k$ is the spring constant (a measure of the stiffness of the material),
  • $x$ is the displacement or extension of the material.

• Elastic Limit: Beyond a certain limit (the elastic limit), the material does not return to its original shape and size, and permanent deformation occurs.

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4.2 Modulus of Elasticity, Significance of Stress-Strain Curve

1. Modulus of Elasticity:

   • It is a measure of the stiffness of a material and defines how much strain occurs when a certain amount of stress is applied.
   • Formula for Young’s Modulus (for tensile stress and strain): $$E = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L_0}$$ Where:
     • $E$ is Young’s modulus (Pa),
     • $F$ is the force applied (N),
     • $A$ is the cross-sectional area (m²),
     • $\Delta L$ is the change in length (m),
     • $L_0$ is the original length (m).

2. Significance of Stress-Strain Curve:

   • A stress-strain curve provides valuable information about the mechanical properties of materials, such as the elastic limit, yield strength, and ultimate tensile strength.
   • Key Points on the Curve:
     • Elastic Region: The linear part of the curve where stress is proportional to strain, following Hooke’s Law.
     • Yield Point: The point at which the material begins to deform plastically and cannot return to its original shape.
     • Ultimate Strength: The maximum stress the material can withstand before failure.
     • Fracture Point: The point where the material breaks or fractures.

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4.3 Pressure

Pressure is defined as the force exerted per unit area on the surface of an object. It can be exerted by solids, liquids, and gases, and is an important concept in fluid mechanics.

4.3.1 Definition, Units

• Definition: Pressure is the force applied perpendicular to the surface of an object per unit area over which the force is distributed.

• Formula:

  $$P = \frac{F}{A}$$

  Where:

  • $P$ is the pressure (in Pascals, Pa),
  • $F$ is the force (in newtons, N),
  • $A$ is the area (in square meters, m²).

• Units: The SI unit of pressure is Pascal (Pa), where $1 \, \text{Pa} = 1 \, \text{N/m}^2$.

4.3.2 Atmospheric Pressure, Gauge Pressure, Absolute Pressure

1. Atmospheric Pressure: The pressure exerted by the weight of the Earth's atmosphere. At sea level, atmospheric pressure is approximately $1 \, \text{atm} = 1.013 \times 10^5 \, \text{Pa}$.

2. Gauge Pressure: The pressure relative to atmospheric pressure. It can be positive (above atmospheric pressure) or negative (below atmospheric pressure).

   • Formula: $$P_{\text{gauge}} = P_{\text{absolute}} - P_{\text{atmospheric}}$$

3. Absolute Pressure: The total pressure exerted on a system, including atmospheric pressure.

   • Formula: $$P_{\text{absolute}} = P_{\text{gauge}} + P_{\text{atmospheric}}$$

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4.4 Surface Tension

Surface tension is the force that acts on the surface of a liquid, causing it to behave like a stretched elastic membrane. It is responsible for phenomena such as the formation of droplets and the ability of some insects to walk on water.

4.4.1 Cohesive and Adhesive Forces

1. Cohesive Force: The force that attracts molecules of the same substance to each other. In the case of liquids, this leads to the formation of a surface film.

2. Adhesive Force: The force that attracts molecules of a liquid to the molecules of a different substance (e.g., liquid to glass). This is responsible for phenomena like water climbing up a thin tube (capillary action).

4.4.2 Angle of Contact

• Angle of Contact (or contact angle) is the angle formed between the tangent to the liquid surface and the solid surface. It provides insight into the wettability of a surface by a liquid.
  • If the angle is less than 90°, the liquid wets the surface (adhesion is greater than cohesion).
  • If the angle is greater than 90°, the liquid does not wet the surface (cohesion is greater than adhesion).

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4.5 Applications of Surface Tension

1. Formation of Droplets: Surface tension causes liquid to form droplets. For example, water droplets are spherical because surface tension minimizes the surface area.
2. Capillary Action: This phenomenon occurs when liquid rises in narrow tubes due to surface tension and adhesive forces between the liquid and the tube walls. It is seen in plants and in the movement of liquid in thin capillaries.
3. Detergents and Soap: Detergents reduce surface tension, allowing water to spread and clean surfaces more effectively.

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4.6 Effect of Temperature and Impurity on Surface Tension

1. Effect of Temperature:

   • As temperature increases, surface tension decreases. This is because the molecules in the liquid gain more kinetic energy and are less tightly held together.
   • Example: The surface tension of water decreases as the temperature increases.

2. Effect of Impurity:

   • The presence of impurities can either increase or decrease the surface tension, depending on the nature of the impurity. Surfactants (like soap) lower surface tension, while some other substances can increase it.

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Summary of Key Concepts:

1. Elasticity: The ability of a material to return to its original shape after deformation.
2. Stress and Strain: Stress is the force per unit area, and strain is the relative deformation caused by stress.
3. Hooke's Law: Stress is proportional to strain within the elastic limit.
4. Modulus of Elasticity: Measures the stiffness of a material.
5. Pressure: Force per unit area, with different types (atmospheric, gauge, absolute).
6. Surface Tension: The force that acts on the surface of a liquid, leading to behaviors like droplet formation and capillary action.
7. Effect of Temperature and Impurities: Temperature decreases surface tension, while impurities can either increase or decrease it.

These properties are fundamental in various engineering applications such as material selection, fluid dynamics, and surface science.