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Physics Formulas

Internal Energy Formula

To understand and perform any sort of thermodynamic calculation, we have to be very clear about the fundamental laws and concepts of thermodynamics. For example, work and heat are dependent terms with interrelated concepts. Heat is the transfer of thermal energy between two objects which are at different temperatures, and also not equal to thermal energy. Work is the force used to transfer energy between the system and its surroundings. It is needed to create heat and the transfer of internal energy. In this article, we will see the concept of internal energy formula with examples. Let us learn things!

The relationship between heat and work, the two concepts can be analyzed through the topic of Thermodynamics, which is the scientific study of the interaction of heat and other types of energy.

Internal Energy Formula

Concept of Internal Energy

To understand the relationship between work and heat, we need to understand the factor of linking factors. This is the change in internal energy. We cannot create nor destroy energy but we can convert or transfer it. Internal energy refers to the energy within a given system, which includes the kinetic energy of molecules and the energy stored in all of the chemical bonds between the molecules.

With the interactions of heat, work and internal energy, there is a transfer of energy and conversions every time. But, no net energy is created or lost during these transfers. This is the main theme of the first law of thermodynamics.

According to the First Law of Thermodynamics energy can be converted from one form to another with the interaction of heat, work, and internal energy. But no one can create nor destroy it, under any circumstances.

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Internal Energy Formal Definition

The energy accumulated within the system associated with random motions of the particles along with the potential energies of the molecules due to their orientation.

The energy due to random motion includes many forms as translational, rotational, and vibrational energy. We represent it as U. Therefore, we can say that internal energy is a state function and in all the processes in internal energy from one state to another state will be the same.

The Formula of Internal Energy

Mathematically, we can represent it,

\( \Delta U=q+w \)


\( \Delta U \) total change in internal energy of a system,
q heat exchanged between a system and its surroundings
w work done by or on the system

Solved Examples

Q.1: A system has constant volume and the heat around the system increases by 45 J. Then,

(i)  What will be the sign for heat (q) for the system?

(ii)  What will be \( \delta U\)  equal to?

(iii)  Find out the value of the internal energy of the system in Joules?


Since the system has constant volume, so \( \delta V=0. \)

i.e. -P  \( \delta V=0. \)

So, Work is equal to zero.

Thus, in the equation

\( \delta U=q+w \)

Put w=0, then

\( \delta U=q. \)

Therefore, the internal energy is equal to the heat of the system. The surrounding heat increases, then the heat of the system decreases because heat is not created nor destroyed. Therefore, heat is taken away from the system making it exothermic and hence negative. So, the value of Internal Energy will be the negative value of the

(i)  Negative (q<0)

(ii)  \( \delta U=q + w \)

= q+ 0

= q

(iii)   \( \delta U = -45 J \)

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