Internal Energy

[7.1] Energy Of a System

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.

[7.1.1] Macroscopic and Microscopic Forms of Energy of a System

When you are determining the different forms of energy within a system you will need to look at the system at a macroscopic level as well as a microscopic level. A macroscopic level represents system processes as a whole in respect to an outside reference frame. Potential as well as kinetic energy occur at the macroscopic level. On the other hand, microscopic forms of energy represent the energy that effects the molecular structure of the system. The total energy of a system Utot, is the sum of its macroscopic Umac, and microscopic Umic, forms of energy

Utot = Umac + Umic

Macroscopic Energy

Macroscopic forms of energy contain an overall system energy with respect to a reference frame, for instance, kinetic and potential energies. The macroscopic energy of an object increases with rising velocity and elevation. Hence, the macroscopic energy of a system is associated with motion and the influence of external effects such as gravity, magnetism, electricity, and surface tension [4]. The energy available as a result of its motion is called kinetic energy. The total potential energy of a system is the summation of the gravitational, centrifugal, electrical, and magnetic potential energies. The energy available as a result of its elevation in a gravitational field is called gravitational potential energy. Since the changes of other subtypes of potential energy are mostly minor or neglected, it is commonly referred to as potential energy. Potential energy can be transformed into other forms of energy such as kinetic energy. Kinetic and potential energy quantities are dependent on the environment in which the system exists.

Microscopic Energy

Internal energy involves energy on the microscopic scale. It may be divided into microscopic potential energy, U_pot, and microscopic kinetic energy, U_kin, components:

U = U_pot + U_kin

where the microscopic kinetic energy, U_kin, involves the motions of all the system’s particles with respect to the center-of-mass frame. For an ideal monatomic gas, this is just the translational kinetic energy of the linear motion of the atoms. Monoatomic particles do not rotate or vibrate. The behavior of the system is well described by kinetic theory of gases. Kinetic theory is based on the fact that during an elastic collision between a molecule with high kinetic energy and one with low kinetic energy, part of energy will transfer to the molecule of lower kinetic energy. However, for polyatomic gases there is rotational and vibrational kinetic energy as well.

The microscopic potential energy, U_pot, involves the chemical bonds between the atoms that make up the molecules, binding forces in the nucleus and also the physical force fields within the system (e.g. electric or magnetic fields).

[7.2] Internal Energy of a Thermodynamic System(Uint)

The internal energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state. It does not include the kinetic energy of motion of the system as a whole, nor the potential energy of the system as a whole due to external force fields, including the energy of displacement of the surroundings of the system. It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. The internal energy is measured as a difference from a reference zero defined by a standard state. The difference is determined by thermodynamic processes that carry the system between the reference state and the current state of interest.

The internal energy is an extensive property, and cannot be measured directly. The thermodynamic processes that define the internal energy are transfers of matter, or of energy as heat, and thermodynamic work. These processes are measured by changes in the system's extensive variables, such as entropy, volume, and chemical composition. It is often not necessary to consider all of the system's intrinsic energies, for example, the static rest mass energy of its constituent matter. When matter transfer is prevented by impermeable containing walls, the system is said to be closed and the first law of thermodynamics defines the change in internal energy as the difference between the energy added to the system as heat and the thermodynamic work done by the system on its surroundings. If the containing walls pass neither matter nor energy, the system is said to be isolated and its internal energy cannot change.

Uint = Umic

[7.2.3] Change in the Internal Energy

The change in the internal energy of a system is the sum of the heat transferred and the work done.

∆U = Ufinal − Uinitial