The first principle is a law of conservation of energy and, in turn, a precise definition of heat. It states that, since energy cannot be created or destroyed (leaving aside the subsequent ramifications of the equivalence between mass and energy) the amount of energy transferred to a system in the form of heat plus the amount of energy transferred in the form of work on the system must be equal to the increase in the internal energy ( U ) of the system. Heat and work ar mechanisms by that systems exchange energy with one another.

Q + L = U (1)

or more precisely:

DeltaQ + DeltaL = DeltaU (2)

When a system contacts another one with a lower energy level than it does, a process of matching the energy levels of both takes place. The first principle of thermodynamics identifies heat, as a form of energy. It can become mechanical work and be stored. Experimentally it was shown that heat, which was originally measured in units called calories , and work or energy, measured in joules, were completely equivalent.

In any machine, a certain amount of energy is needed to produce work; It is impossible for a machine to perform work without the need for energy. A hypothetical machine of these characteristics is called the first-kind perpetual motive. The law of conservation of energy rules out that such a machine can be invented. Sometimes, the first principle is enunciated as the impossibility of the existence of a perpetual motive of the first kind.

Heat, like work, corresponds to energy in transit (energy exchange process), heat is a transfer of energy and can cause the same changes in a body as work. Mechanical energy can become heat through friction, and the mechanical work necessary to produce 1 calorie is known as mechanical heat equivalent. According to the law of conservation of energy, all mechanical work done to produce heat by friction appears in the form of energy in the objects on which the work is performed. James Prescott Joule was the first to prove it reliably in a classic experiment: he heated water in a closed container by spinning paddle wheels and found that the increase in the energy level of the water was proportional to the work done to move the wheels.

When heat is converted into mechanical energy, as in an internal combustion engine, the law of conservation of energy is also valid. However, energy is always lost or dissipated in the form of heat because no motor has perfect efficiency.

Q = mc e. Delta T °(3)

Replacing (3) in (1):

mc e. Delta T °+ L = U (4)

The first principle of thermodynamics is rigorously expressed with the following equation:

dQ = dW + dU (5)

the general representation of the equation and the signs can take the figures (1) or the (2) or some combination.

Equation (5) and figures (1) and (2) are valid in any system, conceptually it is the synthesis of the principle of conservation of energy in a closed system. Recall that the thermodynamic system (STD) is a set of elements with known characteristics and also known relationships that have a continent of known geometry and properties through which exchanges of different types with the environment occur or not.

Our theme is in all cases the determination of which is the STD, for which we must have perfectly defined continent and contents.

Next we will analyze the following cases:

**1. Case 1**: An ideally elastic ball that is the STD and that is at a distance **h** from a comparison plane, to apply equation (2) to this case we take into account the following considerations:

**i.**We despise friction with air and therefore:

**DeltaQ =0**

And we have:

**0= DeltaW + DeltaU (6)**

**ii.**As there are no applied forces, there is no work on the system or the system on the environment, therefore DeltaW =0 and the expression of the first principle is:

**DeltaU =0**

**iii. **dU is the mathematical expression of the variation of energy between two infinitesimally distanced points, its integration between point 1 and 2 gives us the following expression:

**Delta dU = U _{2} U _{1}**(7)

**iv.]**From (7) it appears that:

**U _{2}= U _{1}**

**v.**The analyzed STD may possess in the terms set forth **E _{MT}**. This type of energy in position (1) is only potential from rest, and in (2) it is only kinetic because it is the distance to the reference axis equal to zero, therefore remembering the expressions of the Ep and the Ec, we can write:

**½.mv ²= mgh**(8)

**saw.**If we wanted to analyze conceptually what happens if there is an exchange of thermal energy between the STD and the medium, we must do another analysis, before we observe that the described system is absolutely reversible and the ball lowers-bounces-ups, lowers-bounces-ups…

Let’s analyze below a sequence of the same case considering friction, we highlight that it is verified in two ways:

a) external: there is friction of the STD in the path (1)-(2) that causes a thermal contribution to it.

b) internal: occurs at the moment of shock in which a storage of the kinetic energy is recorded in the potential elastic of the STD, which is used almost instantaneously to change the direction of movement, in the period in which accumulation and return begins of energy in the ball produces intramolecular friction that generates thermal energy that is supplied to the environment. With all these considerations the sequence would be:

**i.**In the descent the STD receives a certain? Q (consider that, if it receives it also emits).

**ii.**In the? T of shock-accumulation of energy-inversion of the route, a? Q partially or totally transformed takes place. We clarify that the transformations in the route and in the crash are functions closely linked to the speed of the process.

**iii.**The expression (2) is in this case:

**DeltaQ = DeltaU**

**iv.**Making the same considerations as in the preceding example we can write:

**U _{1}– U _{2}= DeltaQ**

Without entering into the detailed analysis of the value from where the DeltaQ was produced, we can deduce the expression:

**U _{1}=? Q + U _{2}**

which is telling us that E _{MT1} becomes E _{MT2} plus thermal energy, in this case we observe that we will have to reverse the path of an energy, in this case kinetic, less than the one that the STD had at the beginning, therefore , it is clear that you will not be able to reach the original height, even if you do not have a new friction in the path (2)-(1), therefore we could represent what happens in the following approximate form:

In the graph we represent schematically the bounce height that is tending **0** after **n** cycles, the graph also indicates that the total energy remains constant, having been transformed in the case of the irreversible process in thermal energy.

**2. Case 2**: Students do it.

**3. Case 3**: In this case, the system is a bar that we assume does not have any type of restriction, since it does not have a restriction, it cannot have a value? First principle leads us to the expression:

**DeltaQ = DeltaU**

When we talk about U as internal energy, we are really referring to the variations with respect to a basic energy level that contains another type of energy (molecular and nuclear), therefore the DeltaU refers only to the variation of thermal energy and this symbolic expression It is encompassing of the expression already known:

**Q = mc **_{e.}** Delta T °**

In the case of explosion engines, the STD is constituted by a gas contained in known and variable volumes, which receives and delivers thermal energy from the medium and on which it performs a positive work, part of this mechanically stored constitutes the energy resource for complete the cycle