# First law of Thermodynamics Equation & Definition

A law on energy conservation and, in exchange, a definite description of heat is the first law of thermodynamics. 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 internal energy(U) of the system, because energy can not be produced or destroyed (leaving aside the subsequent implications of mass-energy equivalence). Mechanisms by which systems exchange energy with each other are heat and work.

Q + L = U (1)

or more precisely:

Delta Q + Delta L = DeltaU (2)

Thermodynamics’ first law defines heat as a source of energy. It may become mechanical and be stored.

On any machine, it takes a certain amount of energy to produce work; it is impossible for a machine to do work without the need for energy. A hypothetical machine of these characteristics is called a **perpetual** motion machine. The energy conservation law rules out that such a machine can be invented. Sometimes the first law of thermodynamics is stated as the impossibility of the existence of a *perpetual* motion machines.

Heat, like work, corresponds to *energy in transit* (energy exchange process). Heat is an energy transfer and can cause the same changes in a body as the work. Mechanical energy can be converted to heat through **friction** and the mechanical work needed to produce 1 calorie is known as mechanical heat equivalent.

According to the energy conservation law, all mechanical work done to produce frictional heat appears in the form of energy in the objects on which the work is performed. James Prescott Joule was the first to prove it in a classic experiment: he heated water in a closed container by turning a pair of paddle wheels and found that the increased energy level of the water was proportional to the work done to move the wheels.

## First law of thermodynamics definition

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

Q = m.ce.Delta T ° (3)

Replacing (3) in (1):

m.ce.Delta T ° + L = U (4)

The following equation rigorously expresses the first law of thermodynamics:

dQ = dW + dU (5)

The figures (1) or (2) or any combination may be used for the general representation of the equation and the signs.

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

Our theme is in all cases the determination of what is the S T D, for which we must have a perfectly defined continent and contents.

Next we will analyze the following cases:

**1. Case 1**: An ideally elastic ball that is the S T D and which is at a distance **h** of 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 forces applied, there is no work on the system or the system on the medium, therefore DeltaW 0 and the expression of the first law of thermodynamics remains:

**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 = U2 – U1 (7)

**iv.** From (7) it arises that:

**U2 = U1**

**v.** The S T D analyzed may possess in the terms raised **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.m.v ² = m.g.h (8)

**vi.** If we would like to analyze conceptually that it happens if there is exchange of thermal energy between the S T D and the middle, we must do another analysis, before that we notice that the system described is absolutely reversible and the ball – low-bounce-ups, low-bounce-up…

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

a) external: there is friction of the S T D 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 elastic potential of the S T D, which is used almost instantly to change the direction of movement, in the period in which the accumulation and return of energy in the pelletation begins intramolecular frictions that generate thermal energy that is provided to the medium. With all these considerations the sequence would be:

**i.** On the descent the S T D receives true ? Q (consider that, if it also receives issues).

ii. In the shock-accumulation of energy-inversion of the path, partially or totally transformed? Q is produced. We clarify that the transformations in the path 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:

**U1– U2 = DeltaQ**

Without going into the detailed analysis of the value of where the DeltaQ occurred, we can infer the expression:

**U1 = deltaQ + U2**

that is telling us that the E MT1 becomes E MT2plus thermal energy, in this case we note that we will have when we reverse the path of an energy, in this case kinetic, less than that provided for the S T D at the beginning, therefore, it is clear that it will not be able to reach the original height, even if it does not have a new friction in the trajectory (2) – (1), therefore we could represent what happens in the following approximate form :

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

When we talk about U as internal energy we actually refer to variations with respect to a basic energy level containing another type of energy (molecular and nuclear) therefore the DeltaU refers only to the variation of thermal energy and this symbolic expression is comprehensive of the expression already known:

**Q = m.ce.Delta T °**

In the case of explosion engines, the S T D is composed of a gas contained in known and variable volumes, which receives and delivers thermal energy from the medium and on which it performs positive work, part of this mechanically stored constitutes the energy resource to complete the cycle.

Introduction to the Thermodynamics of Materials 6th Edition

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