# Internal Energy

## What is Internal Energy?

An energy form inherent in every system is the internal energy, which arises from the molecular state of motion of matter. The symbol U is used for the internal energy and the unit of measurement is the joules (J).

Internal energy increases with rising temperature and with changes of state or phase from solid to liquid and liquid to gas. Planetary bodies can be thought of as combinations of heat reservoirs and heat engines. The heat reservoirs store internal energy E, and the heat engines convert some of this thermal energy into various types of mechanical, electrical and chemical energies.

## Internal Energy Explanation

Internal energy U of a system or a body with well defined boundaries is the total of the kinetic energy due to the motion of molecules and the potential energy associated with the vibrational motion and electric energy of atoms within molecules. Internal energy also includes the energy in all the chemical bonds. From a microscopic point of view, the internal energy may be found in many different forms. For any material or repulsion between the individual molecules.

Internal energy is a state function of a system and is an extensive quantity. One can have a corresponding intensive thermodynamic property called specific internal energy, commonly symbolized by the lowercase letter u, which is internal energy per mass of the substance in question. As such the SI unit of specific internal energy would be the J/g. If the internal energy is expressed on an amount of substance basis then it could be referred to as molar internal energy and the unit would be the J/mol.

## Internal Energy of a Closed System

For a closed system the internal energy is essentially defined by

ΔU = q + W

Where

• U is the change in internal energy of a system during a process
• q is the heat
• W is the mechanical work.

If an energy exchange occurs because of temperature difference between a system and its surroundings, this energy appears as heat otherwise it appears as work. When a force acts on a system through a distance the energy is transferred as work. The above equation shows that energy is conserved.

The different components of internal energy of a system is given below.

 Thermal energy Sensible heat Energy change of a system associated with: Molecular translation, rotation, vibration. Electron translation and sopin. Nuclear spin of molecules. Latent heat Energy required or released for phase change, change from liquid to vapour phase requires heat of vaporization. Chemical energy Energy associated with the chemical bonds in a molecule. Nuclear energy The large amount of energy associated with the bonds within the nucleus of the atom.

The physical and chemical processes that can change the internal energy of a system is given below.

 Transferring energy across the system boundary by Heat transfer Energy transfer from a high temperature to low temperature state. Work transfer Energy transfer driven by changes in macroscopic physical properties of a system such as compression or expansion work. Mass transfer Energy transfer by mass flowing across a system boundary. Change through internal processes Mixing Heat releases upon components mixing that may lead to lower internal energy. Chemical reaction Heat required or released during a chemical reaction that changes chemical energy. Nuclear reaction Heat released during a nuclear reaction that changes nuclear energy.

## Internal Energy Change

Every substance possesses a fixed quantity of energy which depends upon its chemical nature and its state of existence. This is known as intrinsic energy. Every substance has a definite value of internal energy and is equal to the energies possessed by all its constituents namely atoms, ions or molecules.

The change in internal energy which occurs during chemical reactions. The change in internal energy of a reaction may be considered as the difference between the internal energies of the two states.

Let EA and Eb are the initial energies in states A and B respectively. Then the difference between the initial energies in the two states will be

ΔU = EB – EA

The difference in internal energies has a fixed value and will be independent of the path taken between two states A and B. For the chemical reaction, the change in internal energy may be considered as the difference between the internal energies of the products and that of the reactants.

ΔU = Eproducts – Ereactants

Thus, the internal energy, ΔU is a state function. This means that ΔU depends only on the initial and final states and is independent of the path. In other words, ΔU will be the same even if the change is brought about differently.

## Solved Example

Question:

On burning 0.5g of benzoic acid (molecular mass = 122) in excess of oxygen in a bomb calorimeter (constant volume conditions), the heat evolved is 3150cal at 25oC. Calculate U for the reaction.

C6H5COOH(s) + 7.5O2(g) → 7CO2(g) + 3H2O(l)

R = 1.987 K cal-1K-1

Solution:

Heat evolved while burning 1 mol (122g) of benzoic acid at constant volume is

$= -3150 \times \frac{122}{0.5}$

= -768,600 cal

Hence ΔU = -768.6 K cal mol-1