Internal Energy Formula: The branch of science that deals with the study of different forms of energy and the quantitative relationship between them is known as thermodynamics. It is a well-known fact that most of the physical changes and chemical changes are accompanied by energy changes. These energy changes may take place in the form of heat, light, work, electrical energy, etc. All these forms of energy are convertible into one another, and hence they are related to each other quantitatively.

In this article, you will explore everything about internal energy, its meaning, examples, internal energy formula, its SI unit, internal energy as a state function, internal energy as extensive property, etc.

What is Internal Energy?

Every substance possesses a definite quantity of energy which depends upon factors such as the chemical nature of the substance, temperature and pressure. This is known as internal energy or intrinsic energy. It is represented by the symbol \(\rm{U}\). Earlier it was represented by the symbol \(\rm{E}\).

Internal energy is made up of kinetic energy and the potential energy of the constituent particles. The kinetic energy arises due to the motion of its particles like translational energy, rotational energy, vibrational energy, etc. The potential energy arises from different types of interaction between the particles, and it includes electronic energy, nuclear energy, energy due to molecular interaction, etc.

The total energy within a substance or a system is called its internal energy. That is the sum of electronic energy \((\rm{U}_\rm{e})\), nuclear energy \((\rm{U}_\rm{n})\), chemical bond energy \((\rm{U}_\rm{c})\), potential energy \((\rm{U}_\rm{p})\), and kinetic energy \((\rm{U}_\rm{k})\).

\(\rm{U = U}_\rm{e} + \rm{U}_\rm{n} + \rm{U}_\rm{c} + \rm{U}_\rm{p} + \rm{U}_\rm{k}\)

What is the SI unit of Internal Energy?

The SI unit of internal energy is Joule \((\rm{J})\).

\(1\,\rm{J} = 10^7\) ergs.

The CGS unit of internal energy is ergs.

Is the Amount of Internal Energy Same in All the Systems or Substance?

Different substances have different internal energies depending upon the nature of the constituent atoms, bonds, and other conditions like temperature, pressure, etc. For example, the internal energy of one mole of carbon dioxide will be different from the internal energy of one mole of sulphur dioxide under similar conditions of temperature and pressure.

The internal energy of one mole of water at \(300\,\rm{K}\) is different from that of one mole of water at \(310\,\rm{K}\) under the same atmospheric pressure.

What is a State Function?

A temperature of one litre of water can be changed either by heating or by cooling. Here, change in temperature is more important than the path in which change is brought about.

Based on this example, state function can be defined as follows, a physical quantity in which its value depends only upon the state of the system and does not depend upon the path by which this state has been attained.

In other words, a physical quantity is said to be a state function if the change in its value during the process depends only upon the initial state and the final state of the system and does not depend upon the path or route by which this change has been brought about.

How Internal Energy is a State Function?

Internal energy is a state function because the internal energy of a system depends upon the state of the system and not upon how the system attains that state.

The change in the internal energy \((\rm{ΔU})\) depends only upon the initial and final states of the system but not upon the intermediate states.

\(\rm{∆U = U}_{\rm{final}\,\rm{state}}-\rm{U}_{\rm{initial}\,\rm{State}}\)

\(\rm{∆U = U}_2 – \rm{U}_1\)

The change in the internal energy in a chemical reaction is given by

\(\rm{∆U = U}_{\rm{products}} – \rm{U}_{\rm{reactants}}\)

\(\rm{∆U = U}_\rm{p} – \rm{U}_\rm{r}\)

If the internal energy of the products is less than the internal energy of the reactants, then \(\rm{∆U}\) would be negative.

\(\rm{∆U=U}_\rm{p}-\rm{U}_\rm{r}= -\rm{ve}\) \((∵ \rm{U}_\rm{p} < \rm{U}_\rm{r})\)

If the internal energy of the products is more than the internal energy of the reactants, then \(\rm{∆U}\) would be positive.
\(\rm{U}\rm{p}-\rm{U}\rm{r}= +\rm{ve}\) \((∵ \rm{U}\rm{p} > \rm{U}\rm{r})\)

Thus, the internal energy, \(\rm{U}\) is a state function. This means that \(\rm{∆U}\) depends only on the initial and final states and is independent of the path. In other words, \(\rm{∆U}\) will be the same even if the change is brought about differently.

However, the absolute value of internal energy possessed by a substance cannot be calculated because it is not possible to find the accurate values of different types of energies such as translational, vibrational, rotational, chemical energy, etc., in a system.

First Law of Thermodynamics

The First Law of Thermodynamics, i.e., the law of conservation mass, states that energy cannot be created or destroyed, although one form of energy can be converted into the other form and vice versa.

Consider a system that has internal energy equal to \(\rm{U}_1\). If it absorbs heat energy \((\rm{q})\) from the surrounding, then its internal energy will increase and become \({{\rm{U}}_1}{\rm{ + q}}.\)

If work \((\rm{w})\) is done on the system, then its final internal energy \((\rm{U}_2)\) is

\(\rm{U}_2=\rm{U}_1+\rm{q+w}\)

\(\rm{U}_2-\rm{U}_1=\rm{q+w}\)

\(\rm{∆U = q + w}\)

Thus, change in internal energy \(=\) Heat energy added to the system \(+\) Work done on the system.

If \(\rm{w}\) is the work done by the system, then

\(\rm{∆U = q – w}\)

\(\rm{q = ∆U + w}\)

The sign of \(\rm{w}\) and \(\rm{q}\) is related to the change in internal energy \(\rm{∆U}\). In general, ‘\(\rm{q}\)’ is positive if the system absorbs the energy from the surroundings, and ‘\(\rm{q}\)’ is negative if the system releases the energy to the surroundings. The value of w is positive if work is done on the system, and \(\rm{w}\) is negative if work is done by the system.

Is Internal Energy being an Extensive or Intensive Property?

The two most important points about internal energy are:

1. The internal energy depends only upon the quantity of the substance contained in the system. Hence, it is an extensive property.
2. The internal energy of ideal gases is a function of temperature only. Hence, in isothermal processes, as the temperature remains constant, there is no change in the internal energy of an ideal gas, i.e., \(\rm{∆U = 0}\). This is because the intermolecular forces of attraction in the molecules of an ideal gas are negligible. Thus, no work is done in overcoming the intermolecular forces when the ideal gas expands. Hence, its internal energy remains constant at a constant temperature.

How is Internal Energy Stored in the System or Substance?

The internal energy is stored in the system or substance in different forms like transitional energy \((\rm{U}_\rm{t})\), electronic energy \((\rm{U}_\rm{e})\), nuclear energy \((\rm{U}_\rm{n})\), chemical bond energy \((\rm{U}_\rm{c})\), potential energy \((\rm{U}_\rm{p})\), and kinetic energy \((\rm{U}_\rm{k})\).

The Internal Energy Reserve in Autotrophs is?

Autotrophs are organisms that produce their own food. The internal energy (cellular energy) reserve in autotrophs is starch. Starch is a type of carbohydrate made up of monomers of glucose.

Summary

In the article, Internal energy formula, you have understood what is internal energy? Its formula, Units. You are also able to explain how internal energy is a state function. Why is it an extensive property? How is internal energy related to the first law of thermodynamics? etc. This article will be helpful in further studies and calculation of heat change, heat capacity, work done, etc.

FAQs

Q.1. What do you mean by internal energy?
Ans: The total energy within a substance or a system is called its internal energy. That is the sum of all type of energies like electronic energy \((\rm{U}_\rm{e})\), nuclear energy \((\rm{U}_\rm{n})\), chemical bond energy \((\rm{U}_\rm{c})\), potential energy \((\rm{U}_\rm{p})\), and kinetic energy \((\rm{U}_\rm{k})\).
\(\rm{U} = \rm{U}_\rm{e}+\rm{U}_\rm{n}+\rm{U}_\rm{c}+\rm{U}_\rm{p}+\rm{U}_\rm{k}\)

Q.2. What are the two main forms of internal energy?
Ans: The two main forms of internal energy are kinetic energy and potential energy. The kinetic energy arises due to the motion of its particles like translational energy, rotational energy, vibrational energy, etc. The potential energy arises from different types of interaction between the particles, and it includes electronic energy, nuclear energy, energy due to molecular interaction, etc.

Q.3. What is the internal energy of gas?
Ans: Internal energy of a gas is defined as the sum of the kinetic and potential energy possessed by the gas.

Q.4. What is the internal energy function?
Ans: Internal energy helps to calculate different types of energies of substances. By known value of internal energy, and heat or work done, the value of unknown quantity can be calculated from the equation \(\rm{∆U = q + w}.\)

Q.5. Does internal energy change with pressure?
Ans: The internal energy does not change with pressure. The internal energy of ideal gases is a function of temperature only.

Q.6. How is internal energy stored?
Ans: The internal energy is stored in the system or substance in different forms like transitional energy \((\rm{U}_\rm{t})\), electronic energy \((\rm{U}_\rm{e})\), nuclear energy \((\rm{U}_\rm{n})\), chemical bond energy \((\rm{U}_\rm{c})\), potential energy \((\rm{U}_\rm{p})\), and kinetic energy \((\rm{U}_\rm{k}).\)

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