Energy

Energy: Definition and Mathematical Representation

Introduction

Energy is a fundamental physical quantity that describes the capacity to perform work or produce change. It exists in many forms such as kinetic, potential, thermal, chemical, and nuclear energy. Energy is a conserved quantity—meaning it cannot be created or destroyed, only transformed from one form to another.

Definition

In physics, energy is commonly defined through the work-energy principle:

$W=\mathrm{\Delta }E$

Where:

• $W$ is the work done,
• $\mathrm{\Delta }E$ is the change in energy of the system.

Energy can be kinetic, potential, thermal, or other types, depending on the system being considered.

SI Unit

The SI unit of energy is the joule (J), defined as:

$1\mathrm{J}=1\mathrm{k}\mathrm{g}\mathrm{\cdot }{\mathrm{m}}^{\mathrm{2}}/{\mathrm{s}}^{\mathrm{2}}$

This is equivalent to the energy transferred when a force of one newton moves an object one meter.

Forms of Energy

Kinetic Energy

Energy possessed by a moving object:

$E_k=\frac{1}{2}m{v}^2$

Where:

• $m$ is the mass of the object,
• $v$ is its velocity.

Potential Energy

Stored energy due to position or configuration. For gravitational potential energy near Earth's surface:

$E_p=mgh$

Where:

• $m$ is the mass,
• $g$ is acceleration due to gravity,
• $h$ is height above a reference level.

Mechanical Energy

The sum of kinetic and potential energy in a system:

$E_{\text{mechanical}}=E_k+E_p$

Thermal Energy

Energy related to the temperature of a system due to the kinetic energy of its particles.

Chemical and Nuclear Energy

Stored in bonds between atoms and subatomic particles; released through chemical reactions or nuclear fission/fusion.

Law of Conservation of Energy

The total energy in an isolated system remains constant:

$E_{\text{initial}}=E_{\text{final}}$

Or more generally:

$\mathrm{\Delta }{E}_{\text{total}}=0$

This is one of the most important principles in all of physics and engineering.

Applications

Energy is central to:

• Mechanics
• Thermodynamics
• Electrodynamics
• Engineering and technology (power generation, transport, etc.)
• Environmental science and sustainability

See Also

• Work (physics)
• Power
• Kinetic Energy
• Potential Energy
• Conservation Laws
• Thermodynamics