The total energy held within an object due to the motion and arrangement of its atoms and molecules is known as Internal Energy, symbolized in thermodynamics as \(U\). This quantity represents the entire microscopic energy content of a system, distinct from any macroscopic energy the object might possess, such as the kinetic energy of the object moving as a whole or its potential energy due to its position in a gravitational field. Understanding internal energy is foundational to the study of thermodynamics. It is an extensive property, meaning its value depends directly on the amount of substance present.
The Sum of Particle Energies
Internal energy is the summation of two primary forms of energy residing within the particles of a substance: kinetic energy and potential energy. The kinetic energy component is the energy of motion at the microscopic level, arising from the constant, random movement of the constituent atoms and molecules. This movement includes translational, rotational, and vibrational kinetic energy. These forms of kinetic energy contribute to the thermal energy aspect of internal energy, which is closely linked to the object’s temperature.
The potential energy component is the energy stored in the forces that hold the particles together or influence their arrangement. This includes energy stored within the chemical bonds that link atoms to form molecules. It also includes energy associated with intermolecular forces, such as van der Waals forces. Changes in this potential energy often accompany phase transitions or chemical reactions.
Total Energy Compared to Average Energy
The distinction between internal energy and temperature lies in the concept of total versus average energy. Internal energy is the total energy of all particles in the object, encompassing every form of microscopic kinetic and potential energy.
Temperature, by contrast, is a measure related only to the average kinetic energy of the particles. A higher temperature indicates increased average particle speed. Because temperature is an intensive property, it does not depend on the size or mass of the object.
This separation means two objects can have the same temperature but vastly different internal energies. For example, a small cup of boiling water at \(100\text{°C}\) has a high temperature. However, a large swimming pool of water at \(20\text{°C}\) has a much greater internal energy overall because it contains a significantly larger number of molecules contributing to the total sum.
How Internal Energy Is Transferred
The internal energy of a system can be changed only by transferring energy across its boundary, a concept described by the First Law of Thermodynamics. This law states that the change in internal energy (\(\Delta U\)) equals the energy added as heat (\(Q\)) minus the energy lost as work (\(W\)) done on the surroundings. The two primary mechanisms for transferring internal energy are heat and work.
Heat is defined as the transfer of thermal energy between a system and its surroundings due to a temperature difference. This transfer occurs spontaneously from higher to lower temperature until thermal equilibrium is reached. Heat transfer can occur through conduction, convection, or radiation.
Work represents the transfer of energy resulting from a force acting over a distance. For a gas contained in a piston, if the gas expands and pushes the piston outward, the system performs work on the surroundings, decreasing its internal energy. Conversely, if an external force compresses the gas, work is done on the system, and its internal energy increases.
Internal Energy in Action
Changes in internal energy are responsible for many physical phenomena, most notably phase transitions. When ice melts into liquid water, the temperature remains fixed at \(0\text{°C}\) even as heat is continuously added. This added energy is not increasing the average kinetic energy of the molecules, which would raise the temperature.
Instead, the input energy, called the latent heat of fusion, is used to increase the potential energy of the water molecules by breaking the hydrogen bonds that lock them into the solid crystalline structure. This process increases the internal energy of the system without changing its temperature. The resulting liquid water, while at the same temperature as the ice, possesses a higher internal energy due to this stored potential energy.
This principle is also at play in technological applications like refrigeration and steam engines. In a refrigerator, a working fluid is repeatedly vaporized and condensed; the boiling process absorbs heat from the interior, increasing the fluid’s internal energy, while the condensation process releases that energy outside the unit. Steam engines harness the increase in internal energy that occurs when water is boiled into steam, converting a portion of this energy into mechanical work to drive a piston.