The internal energy (\(U\)) of a thermodynamic system is the total energy contained within the system at the microscopic level of its constituent particles, such as atoms and molecules. This energy is stored due to the random, disordered motion and interactions of these particles, making it an intrinsic property of the substance itself.
Internal energy excludes the energy related to the system’s motion as a whole, such as its overall velocity or its position in an external field like gravity. For example, a glass of water sitting still has no macroscopic kinetic or potential energy, but it possesses significant internal energy due to the constant movement of its molecules. Since internal energy depends on the total amount of matter, it is classified as an extensive property.
The Energy Within: Kinetic and Potential Components
Internal energy is composed of two primary microscopic forms: kinetic energy and potential energy. The kinetic component is the energy of motion of the individual particles and is directly related to the system’s temperature. This microscopic motion includes the linear movement of particles (translational energy), which is present in all states of matter.
For molecules containing multiple atoms, the kinetic energy also includes the rotational movement of the entire molecule and the vibrational energy from the stretching and bending of chemical bonds. As temperature increases, the intensity of these microscopic motions rises, increasing the kinetic part of the internal energy. In an ideal gas, where intermolecular forces are negligible, internal energy is purely kinetic and depends only on temperature.
The potential energy component is the energy stored in the forces between the particles. This includes energy held within chemical bonds and energy from intermolecular forces, such as van der Waals forces, that hold molecules together in liquids and solids. Changes in this potential energy are responsible for the energy absorbed or released during phase changes (like melting or boiling) or during chemical reactions.
When water boils, the heat supplied does not change the temperature; instead, it goes entirely into overcoming the intermolecular forces. This increases the potential energy component of the water’s internal energy.
Defining Internal Energy Versus Heat and Work
A distinction in thermodynamics is separating internal energy (\(U\)) from heat (\(Q\)) and work (\(W\)). Internal energy is categorized as a state function because its value depends only on the current state of the system, defined by properties like temperature, pressure, and volume. A system at a specific state will always have the same internal energy, regardless of the path taken to reach that state.
In contrast, heat and work are process functions, meaning they are mechanisms for energy transfer across the system boundary, not properties contained within the system. We say a system possesses internal energy, but it exchanges heat or performs work. The amount of heat transferred or work done depends entirely on the specific path taken to change the system from an initial state to a final state.
For example, a gas can be taken from one state to another by heating it at a constant volume or by compressing it adiabatically (no heat transfer). Although the change in internal energy (\(\Delta U\)) will be the same in both scenarios, the amount of heat and work involved will be different. Heat is the transfer of energy driven by a temperature difference, while work involves a force acting through a distance, such as a gas expanding against a piston.
The First Law: How Internal Energy Changes
The mathematical relationship governing changes in internal energy is established by the First Law of Thermodynamics, which is the principle of energy conservation applied to a thermodynamic system. This law states that the change in a system’s internal energy (\(\Delta U\)) is equal to the energy added as heat (\(Q\)) plus the energy added as work (\(W\)). This is represented by the equation \(\Delta U = Q + W\).
When energy is transferred into the system, \(\Delta U\) increases. For example, \(Q\) is positive when heat is added (e.g., placing a cold block in an oven), and \(W\) is positive when work is done on the system (e.g., compressing a gas).
Conversely, when energy leaves the system, \(\Delta U\) decreases. If the system loses heat or performs work on its surroundings (e.g., an expanding gas), both \(Q\) and \(W\) are negative. The change in internal energy reflects the net balance of these two forms of energy exchange.
Real-World Examples of Internal Energy in Action
The concepts of internal energy and its changes are constantly at play in everyday life and technology. When a person rubs their hands together, friction converts macroscopic mechanical work into microscopic kinetic energy. This increases the internal energy of the skin, resulting in a feeling of warmth, demonstrating work converted directly into internal energy.
The process of boiling water on a stove demonstrates how heat transfer affects internal energy. Initially, added heat increases the water’s temperature, raising the kinetic component. Once the boiling point is reached, the continued addition of heat (latent heat) increases the potential energy component as intermolecular bonds are overcome to form steam, without further temperature increase.
In a car engine, the internal combustion process illustrates these energy transformations. Chemical potential energy stored in the fuel is converted into a large amount of internal energy during combustion. This rapid increase in internal energy raises the pressure and temperature of the gas, which then pushes the piston outward, performing mechanical work and causing a subsequent decrease in the gas’s internal energy.