What is total energy made up of?

November 20, 2025 •

3 min read

According to the first law of thermodynamics, the total energy of an isolated system remains constant; energy is not created or destroyed, but merely converted from one form to another. This means a system's total energy is a sum of its many constituent parts, but what is total energy made up of specifically?

Quick Summary

Total energy is the sum of all energy forms within a system. This includes macroscopic kinetic and potential energies, as well as the system's microscopic internal energy and the energy equivalent of its mass.

Key Points

Fundamental Equation: Total energy ($E$) is the sum of a system's macroscopic kinetic energy ($KE$), macroscopic potential energy ($PE$), and its internal energy ($U$) ($E=KE+PE+U$).
Macroscopic Energy: This encompasses the system's external kinetic energy from overall motion and external potential energy from its position relative to external forces, like gravity.
Internal Energy: A microscopic component, internal energy is the total kinetic (molecular movement) and potential energy (intermolecular forces, chemical bonds) of all particles within the system.
Mass-Energy Equivalence: Albert Einstein's $E=mc^2$ reveals that mass is a form of potential energy, contributing significantly to a system's total energy, especially in nuclear reactions.
Forms of Energy: A system's total energy is distributed across various forms, including thermal, chemical, electrical, radiant, and nuclear energies.
Conservation of Energy: The total energy of an isolated system is a conserved quantity; it can change from one form to another but is never created or destroyed.

The Core Components of Total Energy

In its broadest sense, the total energy ($E$) of a system is the sum of its external kinetic energy ($KE$), external potential energy ($PE$), and its internal energy ($U$). This provides a comprehensive view, combining the observable motion and position of the system as a whole with the unobservable, microscopic energy of its constituent particles.

Macroscopic Kinetic Energy

Kinetic energy is the energy an object or system possesses due to its motion. This can be translational or rotational motion. The classical formula is $KE = \frac{1}{2}mv^2$. Relativistic effects alter this formula at high speeds.

Macroscopic Potential Energy

Potential energy is stored energy based on position or configuration. Examples include gravitational potential energy ($PE = mgh$) and elastic potential energy.

Internal Energy

Internal energy ($U$) is the sum of microscopic energies within a system, linked to random molecular motion and intermolecular forces. It relates to temperature and phase. For ideal gases, internal energy is purely kinetic; for real substances, it includes kinetic energy (translation, rotation, vibration) and potential energy (intermolecular forces, chemical bonds).

Deeper Dive: Internal Energy Components

Internal energy is a combination of microscopic kinetic and potential energies.

Microscopic Kinetic Energy: Includes translational, rotational, and vibrational motion of particles.
Microscopic Potential Energy: Energy from forces between particles, including intermolecular forces and chemical bonds.

The Role of Mass-Energy Equivalence

Total energy also incorporates rest energy, described by Einstein's $E = mc^2$, where mass and energy are interchangeable. Mass represents significant potential energy, particularly evident in nuclear reactions.

Nuclear Energy: The Ultimate Component

Nuclear energy is potential energy in the atomic nucleus. Nuclear fission or fusion releases vast amounts of energy.

How Different Energy Forms Contribute

Various specific forms contribute to total energy:

Thermal Energy: Kinetic energy of atoms and molecules.
Chemical Energy: Potential energy in chemical bonds.
Nuclear Energy: Potential energy in atomic nuclei.
Electrical Energy: Kinetic energy of electrons.
Radiant Energy: Kinetic energy of electromagnetic waves.
Sound Energy: Kinetic and potential energy of particles in waves.

Internal Energy vs. Total Energy: A Comparison

Internal energy and total energy are distinct concepts.


Feature	Internal Energy ($U$)	Total Energy ($E$)
Scope	Microscopic energy of particles relative to center of mass.	Macroscopic and microscopic energy, including motion and position.
Frame of Reference	Relative to the system's center of mass.	Relative to an external inertial frame.
Components	Microscopic kinetic and potential energies.	$U + KE{macroscopic} + PE{macroscopic}$.
Dependence on Motion	Independent of overall motion.	Dependent on overall motion and position.

The Principle of Conservation of Energy

The first law of thermodynamics states that the total energy of an isolated system is constant. Energy transforms within the system but the sum is conserved. A roller coaster demonstrates potential converting to kinetic energy. Real systems lose energy to surroundings (e.g., heat from friction), but total energy of the system and surroundings is conserved. For further reading on related concepts, see resources like the Stanford Encyclopedia of Philosophy's entry on the Equivalence of Mass and Energy.

Conclusion: The Holistic View of Energy

Total energy is a fundamental concept encompassing all energetic components. It includes macroscopic kinetic and potential energies, microscopic internal energy, and mass-energy equivalence. This holistic view, supported by the conservation of energy, is vital in physics.

Frequently Asked Questions

Total energy includes a system's macroscopic kinetic energy (from overall motion), macroscopic potential energy (from its position), and its internal energy. Internal energy only accounts for the microscopic kinetic and potential energy of the system's particles relative to its center of mass.

Yes. Einstein's famous equation shows that mass is a form of energy. The rest mass of an object represents a massive store of potential energy ($E_0=m_0c^2$) that is a fundamental component of its total energy, even when the object is at rest.

The main types of potential energy are gravitational potential energy, based on an object's position in a gravitational field, and elastic potential energy, stored in compressed or stretched objects like springs.

Thermal energy is a form of internal energy, and therefore a component of total energy. It refers specifically to the microscopic kinetic energy of a system's particles due to their random motion, which is what we measure as temperature.

Chemical energy is a form of potential energy stored in the bonds of molecules. When a chemical reaction occurs, these bonds are rearranged, releasing or absorbing energy. This chemical energy is a component of a system's internal energy.

The total energy of an isolated system is always conserved. This means that within a closed system, energy can only be converted from one form to another. In practice, real-world systems like a car or an engine are not perfectly isolated, so energy may dissipate to the surroundings, such as through friction or heat loss.

Yes. Internal energy is not determined solely by temperature. For example, a larger mass of water at the same temperature as a smaller mass will have more internal energy because it contains more particles. Also, a substance can have higher potential energy depending on its state (solid, liquid, or gas), giving it more total internal energy even at the same temperature.

In special relativity, the total energy ($E$) of a particle is related to its momentum ($p$) and rest mass ($m_0$) by the equation $E^2=(pc)^2+(m_0c^2)^2$. For a particle at rest, momentum is zero, and the equation simplifies to $E=m_0c^2$. For massless particles like photons, the equation becomes $E=pc$.