Every thermodynamic system possesses a definite amount of energy by virtue of the motion and interactions of its constituent particles. This energy stored within the system itself is known as internal energy and is represented by the symbol U.
Internal energy is a microscopic form of energy and arises from the kinetic energy of molecular motion as well as the potential energy associated with intermolecular forces and chemical bonds. It does not include the macroscopic kinetic energy due to the motion of the system as a whole or the potential energy due to its position in an external field.
Nature of Internal Energy
The internal energy of a system is the sum of all forms of energy possessed by its molecules. This includes translational, rotational, and vibrational kinetic energies of molecules and the potential energy arising from attractive and repulsive interactions between them.
In real gases, liquids, and solids, internal energy depends on both temperature and intermolecular interactions. In contrast, for an ideal gas where intermolecular forces are neglected, internal energy depends only on temperature.
Internal Energy as a State Function
Internal energy is a state function, which means that its value depends only on the present state of the system and not on the path by which the system has reached that state. If a system changes from an initial state to a final state, the change in internal energy is independent of the route followed.
This property distinguishes internal energy from heat and work, which are path functions. While heat and work describe modes of energy transfer during a process, internal energy represents energy stored within the system.
Change in Internal Energy
The absolute value of internal energy of a system cannot be measured experimentally. Thermodynamics therefore deals only with changes in internal energy. The change in internal energy is defined as the difference between the internal energies of the final and initial states.
\[\Delta U = U_{final} – U_{initial}\]
A positive value of ΔU indicates an increase in internal energy, whereas a negative value indicates a decrease in internal energy.
Factors Affecting Internal Energy
The internal energy of a system depends on several factors, the most important being temperature. An increase in temperature generally increases molecular motion and hence increases internal energy.
The nature of the substance also affects internal energy. Systems with strong intermolecular forces have different internal energies compared to systems with weak intermolecular interactions even at the same temperature.
Internal Energy of an Ideal Gas
For an ideal gas, intermolecular forces are assumed to be negligible and molecules are considered to be point particles. As a result, the internal energy of an ideal gas depends only on temperature and is independent of pressure and volume.
This relationship may be expressed as
\[U = f(T)\]
Therefore, for an ideal gas, any process that occurs at constant temperature results in no change in internal energy.
Internal Energy and the First Law of Thermodynamics
The First Law of Thermodynamics establishes a direct relationship between internal energy, heat, and work. According to the First Law, the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system.
\[\Delta U = q – W\]
This equation shows that internal energy acts as the central accounting quantity in thermodynamics, keeping track of all energy exchanges between the system and its surroundings.
With the concept of internal energy clearly understood, we are now prepared to study the other modes of energy transfer, beginning with heat.