The internal energy can be defined as the sum of all possible kinds of energies that a system possesses. Every chemical reaction is associated with heat change. Heat is either evolved or absorbed.  This is possible only when every substance involved in chemical reaction possess certain fixed amount of energy which is called internal energy. Every substance is composed of molecules, atoms and subatomic particles.  The position and motions of the molecules, atoms and subatomic particles is the origin of internal energy.

Constituents of Internal Energy:

Kinetic or Thermal Energy:

The energy that a body possesses due to its movements is called as kinetic energy. Since kinetic energy depends upon the temperature it is called thermal energy.  Thermal energy is directly proportional to the temperature. K.E. is of three types

Translational Energy (E_trans):

The energy associated with the molecules due to the continuous, rapid, random movements along straight line path is called translational energy. Molecules of gases or liquids are in a state of constant random movement. Hence the molecules of gases and liquids have translational energy.

Vibrational Energy (E_vibr):

The energy associated with the molecules due to atomic vibrations is called vibrational energy.

There is a repulsive force between nuclei of two atoms, and electrons of two atoms.  There is an attractive force between the nucleus of one atom and electrons of other atoms and vice versa. As a result of these attractions and repulsions, atoms are in a state of to and fro movement.  Vibrations are of two types viz. stretching and bending vibration.

Rotational Energy  (E_rot):

The energy associated with the molecules by virtue of their rotations about their axes is called as rotational energy. All diatomic and polyatomic molecules rotate about an axis perpendicular to the axis of molecule.

Thus   the total kinetic energy of the system is given by

K.E.  = E_trans + E_vibr +  E_rot

Potential or Bonding Energy:

The energy associated with the body by virtue of its position is called is potential energy. Potential energy is independent of temperature.  It arises due to the bonding between atoms in a molecule. It is classified into two types.

Intermolecular Energy (E_intermole):

The amount of energy required to separate molecules from each other is called as intermolecular energy. In solids and liquids, molecules are held together by means of weak physical forces of attraction called Vander Waals forces. These forces are strong in solids hence intermolecular energy is more in solids than in liquids.

Intramolecular Energy (E_intramole):

The energy required to break the molecule into its constituent atoms is called as intramolecular energy. Atoms are held together in the molecule by certain electrostatics force of attraction called the chemical bond.  So intramolecular energy is nothing but the energy required to break chemical bonds so as to isolate constituent atoms from each other.

Thus the total potential energy of the system is given by

P.E. =   E_intermole + E_intramole.

Total Internal Energy of a System:

Internal energy is the sum of K.E. and P.E. The absolute value of it cannot be determined but the change in it can be determined.

Significance of Internal energy:

• It depends on the quantity of a substance, hence it is extensive property.
• Change in it represents the heat evolved or absorbed in a reaction at constant temperature and constant volume.
• For isothermal process change in it is zero.
• For the process involving the evolution of energy change in it is negative and for the process involving absorption of energy change in it is positive.

Characteristics of Internal energy:

• The internal energy of a system is extensive property.
• It is a state property. The change in internal energy is independent of the path followed.
• Change in it of a cyclic process is zero.

Notes:

• In practice, the absolute value of internal energy (U) is not known and cannot be measured because it is very difficult to determine accurately the most of the quantities that contribute to the internal energy of a system. But in thermodynamics, the quantity internal energy (U) is not important while the change in it (ΔU) is important.
• The quantity change in internal energy (ΔU) is associated with many other thermodynamic quantities by simple mathematical relations. Using those relations the change in internal energy (ΔU) can be determined. Such relations are ΔH = ΔU   +  PΔV  and ΔH = ΔU   + ΔnRT Hence  the change in internal energy (ΔU) can be determined.

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