Internal energy (E or U)

Internal energy is an important concept in thermodynamics. All the energy present in a system, including the kinetic energy of molecules due to translational, vibrational and rotational motion and the potential energy due to intermolecular forces held in every chemical link between molecules, is referred to as internal energy. Every time a system is changed, there are energy transfers and conversions due to the interplay of heat, work, and internal energy. The total energy stored in a substance by virtue of its chemical nature is called internal energy.

E = E_{translational} + E_vibrational + E_rotational + E_kinetic + E_potential + …

Change in internal energy is given by;

If  then internal energy is positive.

If  then internal energy is negative.

Characteristics of Internal Energy

Internal energy is a state function, meaning it is based only on the system's current state and not on the steps required to accomplish it. It is measured in units of joules (J) or calories (Cal) and is denoted by the sign U.

Changes in a system's volume, pressure and temperature can have an impact on its internal energy. The system's molecules will move more quickly as their temperature rises. As a result, an increase in temperature, pressure, or a decrease in volume causes a system's internal energy to increase. On the other hand, a system's internal energy diminishes as temperature, pressure, or volume increase (Shanthini R,2006).

                              Fig 2: Showing internal energy in three states of matter

The internal energy-affecting factors

Temperature, pressure, and volume are a few variables that can have an impact on a system's internal energy. The most significant factor influencing a system's internal energy is probably temperature. The internal energy of a system grows together with the system's temperature. This is due to an increase in the internal energy caused by the system's molecules' increased kinetic energy.

A system's internal energy may also be impacted by pressure. A system's internal energy rises in direct proportion to its pressure. Because of the system's molecules' increased potential energy as a result of compression.

The internal energy of a system can also be impacted by volume, which is the third factor. An increasing amount of internal energy is present in a system as its volume shrinks. Because they must fit into a smaller area, the molecules in the system's molecules have more potential energy    (Hahn A. et al.,2007).

 

Internal energy used in several processes

i. Internal energy is inversely correlated with absolute temperature for a given system.

ii. The amount of heat provided to a system is equal to the increase in internal energy while the volume remains constant.

iii. During adiabatic expansion, a gas cools because its internal energy is reduced.

iv. The change in internal energy is zero in cyclic processes.

v. Internal energy is negative for exothermic reactions because E_R>E_P.

vi. Internal energy in exothermic reactions is positive because E_R > E_P.

References

Arendsen, A. R. J., & Versteeg, G. F. (2009). Dynamic thermodynamics with internal energy, volume, and amount of moles as states: Application to liquefied gas tank. Industrial & engineering chemistry research, 48(6), 3167-3176.

Erlichson, H. (1984). Internal energy in the first law of thermodynamics. American Journal of Physics, 52(7), 623-625.

 Hahn A. et al., A_Thermodynamics-_Atoms_Molecules_and_Energy_Internal_Energy,2007

Shanthini R., Thermodynamics for Beginners - Chapter 4 INTERNAL ENERGY & ENTHALPY,  pp.29 – 34, University of Peradeniya

Smith, D. E., & Haymet, A. D. J. (1993). Free energy, entropy, and internal energy of hydrophobic interactions: Computer simulations. The Journal of chemical physics, 98(8), 6445-6454.