Internal Energy, Thermal Energy & Temperature

Internal Energy

Each particle within a body possesses both potential energy, associated with its state and position, and kinetic energy, stemming from its motion. The cumulative sum of these energies is referred to as the internal energy of the body.

Internal energy is an energy store that is made up of the total kinetic energy associated with the random motion of the particles and the total potential energy between the particles in the system.

While the potential energy of particles within a body tends to be relatively small and remains relatively constant, variations in the internal energy primarily result from changes in kinetic energy.

The temperature of an object serves as an indicator of its thermal intensity, indicating whether it is hot or cold; however, it does not directly quantify the internal energy content of the object.

The internal energy encapsulates the combined microscopic kinetic and potential energies of the constituent particles, which include atoms and/or molecules within the system.

$$U = \sum E_{P} + \sum E_{K}$$

  • U is a function of state(depends on state of system).
  • T increase­ $\rightarrow$ Speed increases $\rightarrow$ microscopic KE ­increase $\rightarrow$ U ­increase

To measure temperature quantitatively and objectively, a device is required.

Internal Energy Of A Box

Consider a box resting on a horizontal surface. It contains internal energy due to the molecules that make up the box having potential energy and kinetic energy. The potential energy and kinetic energy referred to are both internal. You can visualise internal potential energy as the energy to assemble the box and internal kinetic energy as the energy the molecules possess (the molecules in the box are vibrating constantly due to thermal energy).

When the box is pushed along the horizontal surface, the box acquires external kinetic energy. This external kinetic energy has nothing to do with the internal kinetic energy. In Work, energy and power, the kinetic energy that is referred to is the external kinetic energy.

Internal Energy Of A Glass Of Water

Visualize a glass of water. The water particles within the glass exhibit two distinct forms of energy – kinetic energy linked to their motion (whereby the greater their speed, vibration, or rotation, the elevated their kinetic energy) and potential energy correlated with any forces or interactions occurring between the particles (including electrostatic attraction or repulsion).

The kinetic energies of these particles are contingent upon their temperature, while the potential energies are contingent upon any intermolecular forces at play between them.

Thermal Energy

Thermal energy is a subset of internal energy and it focuses exclusively on the kinetic energy related to temperature.

  • When a body is heated, its associated atoms or molecules start to move faster. (Their kinetic energy is increased) So, in microscopic level, heat energy is stored in the form of kinetic energy in the atoms or molecules.
  • The kinetic energy of the atoms or molecules is described as random thermal energy, to avoid confusion with the kinetic energy of the body as a whole. (Distinguish between internal kinetic energy and external kinetic energy)
  • When the sum of kinetic energies in the particles increases, thermal energy, and hence, internal energy increases, temperature being a gross measure of the state of the body increases.
  • To increase the internal energy (kinetic energy) of an object by a certain amount, the amount of heat energy to be supplied depends on its type of material, rise in temperature and mass. (capacity of absorbing or releasing heat varies from substance to substance.

Thermal Energy Of A Spark Vs Boiling Water

For instance, consider a red-hot spark emanating from a fire, which maintains a higher temperature compared to the boiling water within a saucepan. While the average kinetic energy of particles in the boiling water is lower than that in the spark, the substantial quantity of water particles compensates for this difference. As a result, the total energy of the water is higher, allowing it to supply more thermal energy than the spark.

Thermal energy is transferred from a body at a higher temperature to one at a lower temperature.


Thermal energy is a form of internal energy. Thermal energy is possessed by all material matter and manifest as the random motion of atoms and small particles. The amount of thermal energy depends on the temperature of the matter.

A simplified definition for temperature:

Temperature is a measure of the degree of hotness or coldness of a body.

Thermal energy may be transferred from one region to another as a result of a difference in temperature via thermal conduction, convection and radiation. (Will elaborate more on these 3 mechanisms later) Thermal energy flows from a higher temperature object to a lower temperature object. However, this heat exchange will cease when both objects reach thermal equilibrium (same temperature).

Temperature is not the equivalent of the total energy contained in a body. The total energy contained in a body is comprised of other forms of energy as well.

Thermal Contact

  • Two objects are in thermal contact if energy can be exchanged between them.
  • Two way process

Thermal Equilibrium

Two objects, in thermal contact, are said to be in thermal equilibrium with each other if there is no net heat flow between them.

  • In thermal contact, the hotter body becomes cooler while the cooler body becomes hotter until a point is reached where no more change occurs.
  • Heat transfer will continue until thermal equilibrium is achieved. Hence, heat is the exchange of energy between two object because of differences in their temperatures.
  • The two objects are said to be at the same temperature if they are in thermal equilibrium.

Note: Objects does not have to be touching one another to be in thermal contact! Two objects are said to be in thermal contact when they can exchange heat energy between them. For instance, Earth is in thermal contact with the Sun, even though the Earth is obviously not touching the surface of the Sun. Hence, real systems (not idealised) are always in thermal contact.

Thermal contact does not mean thermal equilibrium. The Earth is in thermal contact with the Sun, but is definitely not in thermal equilibrium.

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