1 Fundamental concepts

1.1 Definition and meaning

Energy is a scalar physical quantity associated with a system’s capacity to produce change, perform work, or generate heat. It is not a material substance but a property that can be transferred between systems and transformed from one form to another. In scientific usage, the concept provides a unifying framework for describing motion, interactions, and transformations across many branches of physics and chemistry.

1.2 Historical development

Ideas related to energy developed gradually from early studies of motion, machines, and heat. Classical mechanics provided the foundations for kinetic and potential energy, while the rise of thermodynamics in the 18th and 19th centuries clarified the connection between work, heat, and internal energy. Later advances in electromagnetism, relativity, and quantum theory expanded the meaning of energy to include radiation, mass–energy equivalence, and discrete atomic states.

1.3 Energy as a scalar quantity

Energy has magnitude but no direction, so it is treated as a scalar rather than a vector. This property distinguishes it from quantities such as force or velocity. Scalar character simplifies many physical descriptions, since total energy in a system can often be found by adding contributions from several independent forms.

1.4 Units and measurement

Energy is measured by comparing a process or stored state with a defined unit. Because energy appears in many contexts, several units are used in practice, though scientific work generally relies on the International System of Units.

1.4.1 SI unit: joule

The SI unit of energy is the joule, symbol J. One joule is equal to one newton-meter, the energy transferred when a force of one newton acts through a distance of one meter in the direction of the force. The joule is used across physics, engineering, and related sciences.

1.4.2 Common alternative units

Other units remain common in specific fields. The calorie appears in nutrition and some older thermal contexts. The kilowatt-hour is widely used in electricity billing and large-scale energy accounting. In atomic and particle physics, the electronvolt is useful for very small energy scales.

1.4.3 Measurement methods

Energy is measured indirectly through quantities such as force, displacement, temperature change, electrical current, voltage, or radiation frequency. Instruments include calorimeters for heat, electrical meters for power consumption, spectrometers for atomic transitions, and mechanical setups for work calculations. In many cases, the measured quantity is converted into energy using established physical relationships.

2 Classical forms of energy

2.1 Kinetic energy

Kinetic energy is the energy of motion. A moving object possesses kinetic energy because work must be done to bring it to rest. In classical mechanics, it depends on mass and speed, increasing rapidly as velocity rises.

2.1.1 Translational kinetic energy

Translational kinetic energy refers to the energy of an object moving through space as a whole. For a body of mass m moving at speed v, the classical expression is one-half mv squared. This form is central in mechanics, transportation, and collision analysis.

2.1.2 Rotational kinetic energy

Rotational kinetic energy is associated with spinning motion around an axis. It depends on the object’s moment of inertia and angular speed. Wheels, planets, flywheels, and many machine parts store energy in this form.

2.2 Potential energy

Potential energy is stored energy related to position, arrangement, or deformation. It can often be converted into kinetic energy when a system changes state. The amount depends on the chosen reference and the forces involved.

2.2.1 Gravitational potential energy

Gravitational potential energy arises from the position of a body in a gravitational field. Near Earth’s surface, it increases with height above a reference level. This energy is important in falling objects, water reservoirs, and orbital motion.

2.2.2 Elastic potential energy

Elastic potential energy is stored when a material is stretched, compressed, or otherwise deformed. Springs are the classic example, though many solids and polymers exhibit elastic storage over limited ranges. When released, the stored energy can produce motion.

2.3 Thermal energy

Thermal energy is associated with the random microscopic motion of particles within matter. It is closely related to temperature but not identical to it. In everyday contexts, thermal energy is often understood as the internal energy that can be transferred as heat.

2.4 Chemical energy

Chemical energy is stored in the arrangement of atoms and electrons within molecules and compounds. It is released or absorbed during chemical reactions, including combustion, metabolism, and electrochemical processes. This form of energy is fundamental in fuels, food, and batteries.

2.5 Electrical energy

Electrical energy is associated with electric charges and electric fields. It is carried by currents in circuits, stored in capacitors, and transferred in many forms of technology. Because electrical energy is easy to transport and convert, it is a major practical energy form.

2.6 Radiant energy

Radiant energy is carried by electromagnetic waves, including visible light, infrared, ultraviolet, radio waves, and X-rays. It can travel through vacuum and interact with matter through absorption, emission, and scattering. Sunlight is one of the most familiar examples.

2.7 Sound energy

Sound energy is the energy transported by mechanical waves in a material medium such as air, water, or solids. It arises from vibrating sources and propagates through particle interactions. In most settings, it is a relatively small energy form compared with mechanical or electrical energy.

3 Principles and laws

3.1 Conservation of energy

The conservation of energy states that the total energy of an isolated system remains constant. Energy may change form or move from one part of a system to another, but it is not created or destroyed in ordinary physical processes. This principle is one of the most widely applicable laws in science.

3.1.1 Closed and open systems

In a closed system, energy can be exchanged internally but not with the surroundings. In an open system, energy may cross the boundary in the form of heat, work, radiation, or matter carrying energy. Careful system definition is essential for applying conservation correctly.

3.1.2 Energy transfer and conversion

Energy transfer occurs when energy moves from one object or region to another, such as through work, heat, radiation, or electrical flow. Energy conversion happens when one form becomes another, as when chemical energy turns into thermal and mechanical energy in an engine. Real processes usually involve both transfer and conversion.

3.2 Work and energy

Work is the transfer of energy by a force acting through a displacement, while energy represents the capacity associated with a state or process. The two are closely linked in mechanics and thermodynamics. Work provides a practical way to calculate changes in energy.

3.2.1 Work–energy theorem

The work–energy theorem states that the net work done on an object equals its change in kinetic energy. This relationship connects forces with motion and is central to classical dynamics. It allows problems to be solved without tracking every detail of the motion.

3.2.2 Power and rate of energy transfer

Power is the rate at which energy is transferred or transformed. It is measured in watts, where one watt equals one joule per second. Power matters in engines, electrical systems, and biological activity because it describes how quickly energy is used.

3.3 Energy dissipation

Energy dissipation is the process by which organized energy becomes dispersed into less easily recoverable forms, often as heat. Although total energy is conserved, usable energy may decrease in quality or concentration. Dissipation is common in real-world systems and limits efficiency.

3.3.1 Friction and irreversible processes

Friction converts mechanical energy into thermal energy and is a major source of dissipation. Many natural and engineered processes are irreversible, meaning they do not spontaneously run backward in the same way. Irreversibility reflects the tendency for energy to spread among many microscopic degrees of freedom.

3.3.2 Efficiency

Efficiency compares useful output energy with input energy. No device is perfectly efficient because some energy is always lost to dissipation, noise, or waste heat. Higher efficiency indicates better conversion performance, though practical limits depend on the process.

4 Energy in thermodynamics

4.1 Internal energy

Internal energy is the total microscopic energy contained within a system, including molecular motion and interactions. It excludes the macroscopic kinetic and potential energies of the system as a whole. Internal energy is central to thermodynamic analysis of gases, liquids, solids, and phase changes.

4.2 Heat and temperature

Heat is energy transferred because of a temperature difference, while temperature measures the tendency for such transfer and the average microscopic energy of particles. Heat is a process, not a stored property. Temperature helps determine the direction of thermal energy flow.

4.3 First law of thermodynamics

The first law of thermodynamics expresses conservation of energy in thermodynamic systems. It states that the change in internal energy equals heat added to the system minus work done by the system. This law provides the basis for analyzing engines, refrigerators, and chemical reactions.

4.4 Entropy and available energy

Entropy describes the dispersal of energy among microscopic states and is closely linked to irreversibility. As entropy increases, less of the system’s energy is available for useful work under given conditions. This connection explains why some energy can be conserved yet not fully converted into work.

4.4.1 Free energy

Free energy refers to thermodynamic quantities that estimate the amount of energy available to do useful work under specified conditions. The best-known forms are Gibbs free energy and Helmholtz free energy. These quantities are widely used in chemistry and physical chemistry to predict equilibrium and spontaneity.

4.4.2 Spontaneous processes

A spontaneous process occurs without continuous external intervention under the given conditions. Such processes generally proceed toward states with greater entropy or lower free energy, depending on the constraint. Spontaneity does not imply rapidity; some spontaneous changes occur very slowly.

5 Energy in modern physics

5.1 Relativistic energy

In relativity, energy is linked to momentum, mass, and the geometry of spacetime. Classical formulas remain useful at low speeds, but relativistic expressions become necessary at speeds near the speed of light. Energy and momentum are treated as components of a unified framework.

5.1.1 Mass–energy equivalence

Mass–energy equivalence states that mass can be converted into energy and vice versa according to the relation E equals mc squared. This principle underlies nuclear processes and explains the enormous energy associated with small amounts of mass. It does not mean that mass and energy are identical in every context, but that they are interchangeable in certain physical transformations.

5.1.2 Energy-momentum relation

The energy-momentum relation connects a particle’s total energy, momentum, and rest mass. It remains valid for both massive and massless particles when expressed in the appropriate form. This relation is essential in high-energy physics and relativistic particle descriptions.

5.2 Quantum energy

Quantum theory shows that energy is not always continuous at microscopic scales. In many systems, only certain energies are allowed, and transitions between them occur in discrete steps. This discrete structure explains spectra, atomic stability, and many properties of matter.

5.2.1 Quantization of energy

Quantization means that some physical systems can occupy only specific energy values rather than any arbitrary value. This appears in bound systems such as atoms, molecules, and particles in potential wells. The concept revolutionized physics by replacing classical continuous assumptions with discrete states.

5.2.2 Energy levels in atoms

Atoms possess discrete energy levels for their electrons. When an electron changes level, the atom absorbs or emits energy equal to the difference between the states. These transitions produce spectral lines and are foundational to atomic spectroscopy.

5.2.3 Photons and electromagnetic energy

Photons are quanta of electromagnetic radiation. Their energy depends on frequency, with higher-frequency photons carrying more energy. Photon behavior is central to light emission, absorption, lasers, and many quantum technologies.

5.3 Nuclear energy

Nuclear energy is associated with processes in atomic nuclei. It is much larger per unit mass than energy from chemical reactions because it involves changes in nuclear binding rather than electron bonds. Nuclear energy plays a major role in astrophysics, reactors, and particle transformations.

5.3.1 Nuclear binding energy

Nuclear binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. It reflects the stability of the nucleus and the strength of nuclear forces. Differences in binding energy explain why some nuclei release energy when transformed.

5.3.2 Fission and fusion

Fission is the splitting of a heavy nucleus into smaller nuclei, releasing energy in the process. Fusion is the combining of light nuclei into a heavier one, also releasing energy under suitable conditions. Both processes are important in nuclear physics and stellar energy generation.

6.1 Mechanics

In mechanics, energy provides a compact way to analyze motion, forces, and equilibrium. Mechanical systems are often described in terms of kinetic and potential energy, especially when dealing with oscillations, collisions, and conservative forces. Energy methods frequently simplify calculations compared with direct force analysis.

6.2 Chemistry

Chemical energy governs bond formation and bond breaking in reactions. Thermochemical data help predict reaction heat, equilibrium, and reaction pathways. Energy concepts are also crucial in electrochemistry, catalysis, and molecular design.

6.3 Biology

Living organisms obtain and use energy to maintain structure, drive metabolism, and perform work. Energy transformations occur in respiration, photosynthesis, muscle contraction, and cellular transport. Biological systems must continuously manage energy intake and release to remain functional.

6.4 Engineering

Engineering relies on energy analysis for machines, electrical networks, buildings, transport systems, and industrial processes. Designers consider input energy, losses, efficiency, storage, and conversion. Energy concepts are also central to safety, sustainability, and performance assessment.

6.5 Astronomy and cosmology

Energy plays a major role in the behavior of stars, planets, galaxies, and the universe as a whole. Stellar luminosity, orbital dynamics, and radiation balance all involve energy transfer. In cosmology, energy density and large-scale energy content are important for modeling the evolution of the universe.

7 Energy systems and resources

7.1 Energy conversion technologies

Energy conversion technologies transform energy from one usable form into another. Examples include turbines, generators, engines, solar cells, and heat exchangers. The effectiveness of these technologies depends on thermodynamics, materials, and design.

7.2 Renewable energy

Renewable energy comes from sources replenished on human time scales, such as sunlight, wind, and flowing water. These sources are converted into electricity, heat, or mechanical power. Their availability depends on local conditions and infrastructure.

7.2.1 Solar energy

Solar energy is derived from electromagnetic radiation from the Sun. It can be captured directly as heat or converted to electricity using photovoltaic devices. Solar systems are widely used in residential, industrial, and remote applications.

7.2.2 Wind energy

Wind energy is the kinetic energy of moving air. Wind turbines convert this motion into electrical power through rotating blades and generators. Output varies with wind speed, turbine design, and site conditions.

7.2.3 Hydroelectric energy

Hydroelectric energy uses the gravitational potential and kinetic energy of moving water. Dams and flowing rivers can drive turbines to produce electricity. This method has long been one of the most established forms of large-scale power generation.

7.3 Nonrenewable energy

Nonrenewable energy sources are finite on human time scales and are depleted as they are used. They include fossil fuels and nuclear fuels. Their extraction, processing, and use involve distinct technical and environmental considerations.

7.3.1 Fossil fuels

Fossil fuels such as coal, oil, and natural gas store chemical energy accumulated over geological time. Combustion releases this energy as heat, which can then be converted into mechanical or electrical power. They have been a dominant energy source in modern industrial systems.

7.3.2 Nuclear power

Nuclear power generates usable energy from controlled nuclear fission in reactors. The process produces heat, which is used to create steam and drive turbines in many power systems. It is notable for high energy density and distinctive engineering requirements.

7.4 Energy storage

Energy storage technologies preserve energy for later use and help balance supply and demand. Storage may be electrical, chemical, thermal, mechanical, or gravitational. Effective storage improves grid stability, mobility, and energy reliability.

7.4.1 Batteries

Batteries store energy electrochemically and release it as electrical current. They are used in portable electronics, vehicles, and backup systems. Performance depends on capacity, charge rate, lifespan, and materials chemistry.

7.4.2 Fuel cells

Fuel cells convert chemical energy directly into electrical energy through electrochemical reactions. Unlike batteries, they typically require a continuous external supply of fuel and oxidant. They are used in specialized power applications and transportation systems.

7.4.3 Thermal storage

Thermal storage retains energy in heated or cooled materials for later use. Common approaches include sensible heat storage, latent heat storage, and thermochemical storage. This method is useful in buildings, industrial processes, and renewable-energy systems.

8.1 Force and motion

Force causes acceleration or deformation, while motion describes the change in position of a body over time. Energy and force are related through work, but they are distinct quantities. Understanding both is essential in classical mechanics.

8.2 Momentum

Momentum is the product of mass and velocity and is conserved in isolated systems. It complements energy in the analysis of collisions and motion. Unlike energy, momentum has direction and is therefore a vector quantity.

8.3 Heat

Heat is energy transferred because of temperature difference. It differs from internal energy, which is a stored property of a system. Heat is a process variable and cannot be contained in a body in the same way as energy content can.

8.4 Power

Power is the rate of energy transfer or conversion. It indicates how quickly work is done or energy is used. Devices with the same energy output can differ greatly in power depending on the time involved.

8.5 Exergy

Exergy is the maximum useful work obtainable from a system as it comes into equilibrium with its surroundings. It measures energy quality rather than quantity alone. Exergy analysis is valuable in thermodynamics, engineering design, and efficiency studies.