Thermodynamics

# Internal energy formula and examples

Internal energy is The sum of all forms of molecular energies (kinetic and potential ) of a substance. In the study of thermodynamics, a usually ideal gas is considered as a working substance. the molecules of an ideal gas are mere mass points that exert no force on one another. so the internal energy of an ideal gas system is generally the translational kinetic energy of its molecules.
since the temperature of a system is defined as the average kinetic energy of its molecules, thus for an ideal gas system, the internal energy is directly proportional to its temperature.

when we heat substance energy associated with its atoms or molecules is increase i.e , heat is converted to internal energy.

It is important to note that energy can be added to a system even though no heat transfer takes place. for example, when two objects are rubbed together, their internal energy increases because of mechanical work. the increase in temperature of the object is an indication of an increase in the internal energy. similarly, when an object slides over any surface and comes to rest because of frictional force, the mechanical work done on or by the system is partially converted into internal energy.

In thermodynamics, the internal energy is a function of the state. consequently, it doesn’t depend on the path but depends on the initial and final states of the system. consider a system which undergoes a pressure and volume change from Pa and Va to Pb and Vb respectively, regardless of the process by which the system changes from initial to final state. by experiment it has been seen that the change in internal energy is always the same and is independent of paths C1 and C2.

Thus internal energy is similar to the gravitational potential energy. so like the potential energy, it is the change in internal energy and not its absolute value, which is important.

### Internal energy variation

The internal energy of particle systems can vary, regardless of their spatial position or acquired shape (in the case of liquids and gases). For example, when introducing heat to a closed system of particles, thermal energy is added that will affect the internal energy of the assembly.
However, the internal energy is a state function, that is, it does not attend to the variation that connects two states of matter, but to the initial and final state of it. That is why the calculation of the variation of the internal energy in a given cycle will always be null since the initial and final states are one and the same.
The formulations to calculate this variation are :
ΔU = U B – U A, where the system has gone from state A to state B.
ΔU = -W, in cases where a quantity of mechanical work W is carried out, which results in the expansion of the system and the decrease of its internal energy.
ΔU = Q, in the cases in which we add caloric energy that increases the internal energy.
ΔU = 0, in cases of cyclical changes in internal energy.
All these cases and others can be summarized in an equation that describes the Principle of Conservation of Energy in the system:
ΔU = Q + W

## Internal Energy Examples in everyday life?

Here’s the List of Some Examples of internal energy:

• Batteries. In the body of the charged batteries, there is using internal energy, thanks to the chemical reactions between acids and heavy metals inside. Said internal energy will be greater when its electric charge is complete and less when it has been consumed, although in the case of rechargeable batteries this energy may increase again by introducing electricity from the outlets.
• Compressed gases. Considering that gases tend to occupy the total volume of the container in which they are contained since their internal energy will vary as this amount of space is greater and will increase when it is less. Thus, a gas dispersed in a room has less internal energy than if we compress it into a cylinder since its particles will be forced to interact more closely.
• Increase the temperature of matter. If we increase the temperature of, for example, one gram of water and one gram of copper, both at a base temperature of 0 ° C, we will notice that despite being the same amount of matter, ice will require a greater amount of total energy to reach the desired temperature. This is because its specific heat is greater, that is, its particles are less receptive to the energy introduced than those of copper, adding heat much more slowly to its internal energy.
• Shake a liquid. When we dissolve sugar or salt in water or promote similar mixtures, we usually stir the liquid with an instrument to promote further dissolution. This is due to the increase in the internal energy of the system produced by the introduction of that amount of work (W) provided by our action, which allows greater chemical reactivity between the particles involved.
• Water vapor. When boiling water, we will notice that the steam has higher internal energy than the liquid water in the container. This is because, despite being the same molecules (the compound has not changed), to induce the physical transformation we have added a certain amount of caloric energy (Q) to the water, inducing a greater agitation of its particles.

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