# Internal Energy in Thermodynamics In thermodynamics, the system's internal energy is called the total energy that a system contains.

This energy can be modified by exerting work on it or by the transfer of energy. The system's energy can change by transferring heat or work (or both) between the system and its surroundings. If positive work is applied, the system gains energy.

The first law of thermodynamics postulates that the increase in internal energy is equal to the total heat added plus the work done by the environment. If it is an isolated system, it remains constant.

Internal energy is a state function. Its value depends only on the current state of the system. It is also an extensive property.

The unit of measurement, according to the International System, is the joule (J).

## Internal Energy on a Microscopic Scale

On a microscopic scale, this form of energy includes internal kinetic and potential energy:

• Internal kinetic energy is the sum of all kinetic energies of each system's element concerning its center of mass. (translations, rotations, and vibrations of atoms and electrons).

• The internal potential energy. That is, the potential energy associated with each of the interactions of these elements. It is associated with the static constituents of matter.

For example, a bottle of water at room temperature has no apparent energy. But on the microscopic scale, water molecules travel at hundreds of meters per second, vibrating and rotating.

## How Does It Relate to Ideal Gases?

Thermodynamics often uses the concept of the ideal gas. It is an approximation of the real systems that are used for educational purposes.

The ideal gas is a gas of particles considered as point objects that interact only by elastic collisions. Here the kinetic energy consists only of the translational energy of the individual atoms.

Therefore, internal energy changes in an ideal gas are only due to changes in its kinetic energy. In this case, the energy solely depends on its pressure, volume, and thermodynamic temperature. The value is proportional to its mass (number of moles), temperature, and the specific heat at the gas's constant volume.

Heat capacity is the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature. It is assumed that the heat capacity at constant pressure is related to the heat capacity at constant volume.

## How Is Internal Energy Measured?

Total internal energy measurement is not possible. Its variation is measured and expressed by ΔU.

This variation depends on thermal energy, light energy, or similar energies transmitted. You can also calculate the amount of work done by the system or work done in the system.

When a thermodynamic system transfers energy from heat to another system, the two systems' internal energy varies. Also, other of its state variables can be altered.

If there is an alteration in the atomic or molecular structure, there is a variation in the internal chemical energy.

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Published: April 4, 2017
Last review: August 30, 2020