Internal energy, a concept central to the study of thermodynamics, describes the total energy contained within a physical system at the microscopic level. While energy is often associated with a positive presence, internal energy can definitively be negative. This negative value is not a sign of a fundamental physical deficit, but arises because internal energy is measured relative to an arbitrary, human-chosen baseline, rather than being an absolute measure of all energy in the system.
What Exactly is Internal Energy
Internal energy, symbolized as \(U\), represents the energy stored within a system associated with the random, disordered motions and interactions of its constituent particles. This total microscopic energy excludes the kinetic energy of the system moving as a whole and any potential energy due to external forces. Instead, it focuses on the energy stored inside the substance itself.
The two main components are microscopic kinetic energy and microscopic potential energy. Kinetic energy is the energy of motion, including the translational movement, rotation, and vibration of atoms within molecules, and is directly related to the system’s temperature. Potential energy is the stored energy arising from the forces between particles, which includes the energy locked in chemical bonds and the intermolecular forces that hold the substance together.
The Role of the Reference Point in Measurement
The reason internal energy can be negative stems from the fact that it is a relative quantity, not an absolute one. In physics and chemistry, it is practically impossible to calculate the total absolute internal energy of a system because it would involve accounting for every single form of energy down to the subatomic level. Instead, scientists measure the change in internal energy, symbolized as \(\Delta U\), which is the difference between the final and initial states of a system.
Since only the change matters for thermodynamic calculations, a convenient zero point, or reference state, is established for the system’s internal energy. This zero point is entirely arbitrary and chosen for mathematical simplicity, meaning any state of the system can be assigned an internal energy of zero. If the system under study possesses less energy than this chosen reference state, its calculated internal energy value will naturally be negative. A negative internal energy value simply indicates that the system is at a lower energy level compared to the defined baseline.
This process is similar to measuring elevation, where sea level is arbitrarily assigned a height of zero. An object’s elevation is positive if it is above sea level and negative if it is below. The physical quantity of energy itself remains a positive, quantifiable property of the system, but the numerical value assigned to it is contingent on the selected zero point. The focus in thermodynamics is almost always on the energy transfer as heat or work, which dictates the change in internal energy, \(\Delta U\), and this change is independent of the arbitrary zero point.
When Internal Energy Appears Negative
Negative internal energy frequently arises when the reference state is defined as a high-energy, separated state. In chemical thermodynamics, the internal energy of atoms is often defined as zero when their constituent atoms are infinitely separated from one another. When these atoms bond to form a stable molecule, energy is released, and the resulting molecule exists at a lower energy state than the separated atoms.
Because the stable molecule has less energy than the zero-energy reference state, its internal energy is reported as a negative value. This negative sign indicates a stable, bound state, meaning energy must be added to break the bonds and return the atoms to the zero-energy separated state. A similar concept is used for gravitational potential energy, where the zero point is set at an infinite distance from a large mass. Any object closer to the mass will have a negative potential energy, reflecting that it is in a bound state.