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Internal Energy of a Material

Internal energy (U) is the total energy contained within a substance due to the motion and interactions of its molecules. It consists of two components:

• Kinetic energy – the energy associated with the translational, rotational, and vibrational motion of molecules.
• Potential energy – the energy stored in intermolecular forces that arise from the relative positions of the molecules.

The symbol U is used to denote internal energy, and its change is represented by ΔU. Both temperature and volume influence U. Raising the temperature increases kinetic energy, while changing the volume alters intermolecular distances, affecting potential energy.

First Law of Thermodynamics

The first law states that the change in internal energy of a system equals the heat added to the system plus the work done on the system:

ΔU = Q + A

In this expression:

• Q is the heat transferred to the system.
• A is the work done on the system (positive when work is done on the system, negative when the system does work on the surroundings).

Heat Engines

A heat engine converts thermal energy into mechanical work. It consists of three main components:

1. Hot source (reservoir) – supplies heat at a high temperature T₁.
2. Working part – expands, does work, and transfers energy.
3. Cold source (reservoir) – receives waste heat at a lower temperature T₂ (where T₂ < T₁).

Molecular Arrangement in Different Phases

The arrangement of molecules varies markedly among solids, liquids, and gases:

• Solid: Molecules are very close together and ordered in a regular lattice, held by strong intermolecular forces.
• Liquid: Molecules remain close but lack long‑range order, allowing them to slide past one another.
• Gas: Molecules are far apart and move independently, with weak intermolecular forces.

When temperature rises, molecular motion becomes faster, increasing kinetic energy.

Phase Changes

Phase transitions involve the absorption or release of latent heat without a change in temperature until the transition is complete.

Key points about specific phase changes:

• During melting, temperature remains constant until all solid has become liquid.
• Boiling occurs throughout the liquid volume, not only at the surface.
• Sublimation bypasses the liquid phase entirely.

Specific Heat Capacity

The specific heat capacity (c) of a substance is the amount of heat required to raise the temperature of 1 kg of the material by 1 °C (or 1 K). Its unit is J · kg⁻¹ · K⁻¹.

The heat transferred to a mass m undergoing a temperature change ΔT is given by:

Q = m·c·ΔT

Latent Heats

Latent heat refers to the heat absorbed or released during a phase change at constant temperature:

• Latent heat of fusion (λ) – heat needed to melt 1 kg of a solid. Formula: Q = m·λ.
• Latent heat of vaporization (L) – heat needed to vaporize 1 kg of a liquid. Formula: Q = m·L. For water at 100 °C, L ≈ 2.26·10⁶ J/kg.

Temperature Scales

The Kelvin and Celsius scales have identical degree sizes; a change of 1 °C equals a change of 1 K. Absolute zero, the point where molecular motion would cease, is defined as 0 K.

Conversion formulas:

• Celsius to Kelvin: T = t + 273.15 (where T is Kelvin and t is Celsius).
• Celsius to Fahrenheit: T(°F) = 1.8·t + 32.

Reference points differ:

• Celsius: 0 °C (ice) and 100 °C (boiling).
• Fahrenheit: 32 °F (ice) and 212 °F (boiling).

Crystalline vs. Amorphous Solids

Crystalline solids possess an ordered lattice and a well‑defined melting point. Amorphous solids lack long‑range order, resulting in a gradual softening rather than a sharp melting point.

Summary of Key Formulas

Understanding these concepts provides a solid foundation for analyzing thermal processes, designing heat engines, and solving problems involving heat transfer and phase changes.