# Internal Energy as a State of System

• Last Updated : 29 Nov, 2021

The various forms of energy are interconnected, and they can be converted from one form to another under certain conditions. The field of science known as thermodynamics is related to the study of various kinds of energy and its conversion. In thermodynamics, the system refers to the part of the universe that is being observed, whereas the surrounding refers to the rest of the universe that isn’t part of the system. Every substance has a specific amount of energy that is determined by the substance’s type, such as, temperature, and pressure. Internal energy is the terminology for this. The internal energy change as a state function or as a state of the system is described further down.

### What is the State of a System?

A system’s state is defined as its state of existence when its macroscopic characteristics have definite values. The state of the system is said to change if any of the system’s macroscopic characteristics change. State variables are the measurable properties needed to describe a system’s state. The state variables are temperature, pressure, volume, composition, and so on. Consider the case of a system formed of an ideal gas. Only three variables, such as temperature, pressure, and volume, may define the state of this system.

A state function is a system property whose value is solely determined by the system’s state and is unaffected by the path or method by which that state is attained. The initial and final states of the system, not the path by which they are obtained, determine the change in the value of these properties.

The system’s thermodynamic state is a crucial term. The system is in some particular state at any given time, which may be described using values of macroscopic properties that are relevant to our objectives. The current state of the system is defined by the values of these characteristics at any given time. The state changes whenever the value of any of these properties changes. If it can be later discovered that each of the important properties has the same value as it did at a previous point in time, it can be observed that the system has reverted to its previous state.

The state of the system should not be mixed up with the type of physical state or phase aggregation state. A change of state refers to a shift in the system’s state rather than a phase transition.

### Internal Energy

Every substance has a specific amount of energy that is determined by factors like the chemical nature of the substance, temperature, and pressure. The term “intrinsic energy” or “internal energy” refers to this type of energy. The letter U is used to signify it (earlier it was represented by the symbol E). It is made up of the individual particles’ kinetic energy and potential energy.

Translational energy, rational energy, vibrational energy, and other forms of kinetic energy emerge from the motion of its particles. Electronic energy, energy due to molecular interactions, nuclear energy, and other types of interactions between particles all contribute to potential energy.

Although traditional thermodynamics is concerned with the macroscopic characteristics of materials, such as temperature, pressure, and volume, thermal energy is understood at the microscopic level as a rise in the kinetic energy of motion of the molecules that make up a substance. The translational kinetic energy of gas molecules, for example, is proportional to the temperature of the gas, the molecules can rotate around their centre of mass, and the constituent atoms can vibrate with respect to each other.

Chemical energy is also stored in the bonds that hold molecules together, and weaker long-range interactions between molecules require even more energy. The total internal energy of a substance in a particular thermodynamic state is the sum of all these kinds of energy. A system’s total energy contains its internal energy as well as any external sources of energy, such as kinetic energy from the system’s overall motion, and gravitational potential energy from its elevation.

Internal energy is the sum of all forms of energy stored in atoms or molecules.

Depending on the nature of the constituent atoms, bonds, and various temperatures, pressure, and other conditions, different substances have varying internal energies. Even under equal temperature and pressure conditions, the internal energy of 1 mole of carbon dioxide will differ from the internal energy of 1 mole of sulphur dioxide. Furthermore, under the same atmospheric pressure, the internal energy of one mole of water at 300K differs from that of one mole of water at 310K.

### Internal Energy as the State of System

A variety of thermodynamic characteristics, such as pressure, volume, temperature, internal energy, and enthalpy, can be used to define a thermodynamic system. These are grouped into two categories: state functions and path functions. A state function is a property of a system whose value is determined by the system’s initial and final states.  These types of functions explain a function’s equilibrium state and are unaffected by how the system got there. Internal energy, for example, is a state function that is independent of the path taken to change the system’s state.

It is a system’s overall energy. This consists of a number of components, including molecule translational kinetic energy, bond energy, electronic energy, and the intermolecular interaction energy of the system’s constituents’ particles, among others. Internal energy is affected by factors such as pressure, volume, and temperature. All of the variables in this list are state functions. Mass, volume, pressure, temperature, density, and entropy are all examples of state functions. Some factors are influenced by the amount of matter present. Intensive properties are factors that are independent of the amount of matter present.

Density is an example. A state function is a property of a system that is dependent only on the system’s state and not on the process by which it is achieved. Internal energy is independent of the path used to get from one condition to the next. It depends on the system’s current state.

Since accurate values of different types of energies are stored in a system, such as translational, vibrational, rational, chemical, and so on, it is impossible to compute the absolute value of internal energy possessed by a substance. The difference between the internal energies of the two states can be used to calculate the change in the internal energy of a reaction.

Let’s denote the internal energies in states A and B as UA and UB, respectively. The difference in internal energy between the two states will be,

∆U=UB – UA

The internal energy difference (∆U) has a set value and is unaffected by the path followed between two states A and B. The difference between the products’ and reactants’ internal energies, i.e. the change in internal energy, can be considered for chemical reactions.

∆U=Uproducts – Ureactants

∆U =Up – Ur

where Up denotes the internal energy of the products, Ur denotes the internal energy of the reactants, and ∆U denotes the internal energy change.

∆U is positive if the internal energy of the products is greater than the internal energy of the reactants.

This means that if Up > Ur, then ∆U =Up – Ur = positive.

If the internal energy of the products is smaller than the internal energy of the reactants, then ∆U will be negative.

This means that if Up < Ur, then ∆U =Up – Ur = negative.

As a result, the internal energy, U, is a state system, that is, the internal energy is a property of the system whose value is solely determined by the system’s state. This means that the difference in internal energy U is independent of the path and only depends on the initial and final states.

### Sample Questions

Question 1: What significance does internal energy have?

Since the possible energies between molecules and atoms are crucial, the internal energy is important for understanding phase shifts, chemical reactions, nuclear events, and many other microscopic phenomena. In a vacuum, both objects have macroscopic and microscopic energy.

Question 2: What affects internal energy?

Internal energy can be changed by altering the temperature or volume of an object without changing the number of particles inside. As the temperature of a system rises, the molecules move faster, resulting in higher kinetic energy and hence an increase in internal energy.

Question 3: Is internal energy a state function?

A state function describes the equilibrium state of a system, as well as the system itself. Since the internal energy U is defined by the quantities that determine the state of the system at equilibrium, it is called a state function because any change in energy is entirely determined by the system’s initial and final states.

Question 4: Is the internal energy affected by the system’s path?