Internal Energy, Heat, and Wave Motion: A Comprehensive Guide

Posted on Nov 9, 2024 in Physics

Internal Energy and Heat

What is Internal Energy?

Internal energy is the total kinetic and potential energy of all the particles within a body. It depends on the amount of matter (more particles mean more internal energy), the type of substance, and the temperature.

Temperature and Heat

Temperature measures the average kinetic energy of a body’s particles. Absolute zero (-273.15°C) is the temperature at which particles have zero kinetic energy. Heat, or thermal energy, is the energy exchanged between two bodies at different temperatures or during a state change. It’s measured in Joules (J). One calorie is the heat needed to raise the temperature of 1g of water by 1°C (1 cal = 4.18 J).

Two bodies in contact at the same temperature are in thermal equilibrium.

Specific Heat

Specific heat (c_e) is the heat required to raise the temperature of 1kg of a substance by 1K. It’s measured in J/(kg*K).

The relationship between heat and temperature change is: Q = mcΔT, where Q is heat, m is mass, c is specific heat and ΔT is change in temperature.

Water Equivalent

The water equivalent of a calorimeter is the mass of water that absorbs the same amount of heat as the calorimeter.

Changes of State

The boiling point is the temperature at which a liquid changes to a gas. The boiling point of water is 100°C at one atmosphere of pressure. The melting point is the temperature at which a solid changes to a liquid. The melting point of water is 0°C at one atmosphere of pressure.

Latent heat (L) is the heat required to change the state of 1kg of a substance at its melting or boiling point. It’s measured in J/kg.

Thermal Expansion of Solids

Linear expansion coefficient (α): Relates the change in length to the change in temperature.
Surface expansion coefficient (β): Relates the change in area to the change in temperature.
Cubic expansion coefficient (γ): Relates the change in volume to the change in temperature.

Mechanical Equivalent of Heat

The mechanical equivalent of heat is the relationship between work and heat: 1 cal = 4.18 J or 1 J = 0.24 cal.

Wave Motion

What are Waves?

Wave motion is the propagation of a vibration through a medium. Waves transmit energy without transporting matter.

Types of Waves

By Dimension of Propagation:

One-dimensional: Waves propagate in one direction (e.g., waves on a string).
Two-dimensional: Waves propagate on a surface (e.g., ripples in water).
Three-dimensional: Waves propagate in three spatial dimensions (e.g., sound, light).

By Medium:

Mechanical waves: Require a material medium (e.g., sound).
Electromagnetic waves: Can propagate in a vacuum (e.g., light).

By Particle Vibration Direction:

Longitudinal waves: Particles vibrate parallel to wave propagation (e.g., sound).
Transverse waves: Particles vibrate perpendicular to wave propagation (e.g., light).

Wave Properties

Focus: The origin of the disturbance.
Crest: The highest point of a wave.
Trough: The lowest point of a wave.
Amplitude (A): Maximum displacement from equilibrium (meters).
Wavelength (λ): Distance between two consecutive points in the same vibration state (meters).
Period (T): Time for one complete vibration (seconds).
Frequency (f): Number of vibrations per second (Hz).
Speed of propagation (v): Distance traveled by the wave per unit time (m/s). v = λ/T = λf

Wave Intensity and Energy

Intensity: Related to amplitude; higher amplitude means higher intensity.
Energy: Related to frequency; higher frequency means higher energy.

Sound

Sound is a form of energy caused by vibrations that propagate as mechanical, longitudinal, three-dimensional waves. Sound requires a source, an elastic medium, and a receiver.

Sound Characteristics

Tone: Distinguishes high-pitched from low-pitched sounds (related to frequency).
Intensity: Perceived as loudness (related to amplitude).
Timbre: Relates to the waveform and allows us to distinguish sounds of the same frequency and amplitude from different sources.

Sound Reflection

Echo: Occurs when the incident and reflected sounds are distinguishable (time delay > 0.1s).
Reverberation: Occurs when the reflected sound overlaps with the incident sound (distance to obstacle < 17m).

Light

Light is a form of energy that allows us to see.

Refractive Index

Refractive index (n) is the ratio of the speed of light in a vacuum (c) to the speed of light in a medium (v): n = c/v. n is always greater than 1.

Laws of Reflection

The incident ray, reflected ray, and normal are coplanar.
The angle of incidence equals the angle of reflection (i = r).

Laws of Refraction (Snell’s Law)

The incident ray, refracted ray, and normal are coplanar.
n₁sin(i) = n₂sin(r), where n₁ and n₂ are the refractive indices of the two media.