**The birth of thermodynamic**

Thermodynamic is born along with the steam engine, in 1824 in Paris, when Sadi Carnot (the uncle of the future french President) published his *Reflections on the Motive Power of Fire and own machinery to develop this power* .The idea was to improve the steam engine performance. The thermodynamic term did not yet exist, but it was found later perfectly suited, since it means the « mouvent generated by fire (or heat). »

« The driving power is due, to a steam engine, not to an actual consumption of caloric (heat), but transport of a warm body to a cold body. It is therefore not sufficient to give rise to the motive power to produce heat; we must still get cold. »

Sadi Carnot

# Brief history of thermodynamic

### The steam engine, thermodynamic machine

The idea of the steam engine was probably born in a kitchen where a physicist found that the lid of a pot was periodically raised by the pressure of the steam produced by the boiling water. The cover, desperately, fell, because the pressure at each opening, billowing in the air, losing his strength and vigor by diluting the atmosphere. If there were a way to prevent this unfortunate leak, so the cover could rise up to heaven! The piston principle had been described. The heat could be tamed and transformed into mechanical energy to generate movement. : Thermodynamics, moving through the fire!

### The heat (Q) – Brownian motion

A system contains no heat, in exchange with the outside! It is clear that represents **the temperature** . It is less clear that represents **heat**. When two systems are in contact (a swimmer in a lake), they do not exchange the temperature, but heat! The lake pump heat swimmer and vice versa. Heat
is an energy that can be transmitted from one body to another (in our
example above, it flows from the firebox coal (coal) to water. At a
microscopic level, the heat is the consequence of the agitation of atoms
and molecules (Brownian motion). They move in a disorderly manner and
impinge on the walls of the vessel containing them. the sum of all these
shocks produced at macroscopic level, pressure. the Brownian motion is
completely chaotic. Yet, when we go to the macroscopic level, its result
(the transfer of heat or pressure) is perfectly ordered and can be put
into equations.

### Work

A system contains no work, in exchange with the outside! The heat helps put things in motion. As in the case of a steam locomotive: the heat generated by burning coal heats water that eventually vaporize. Pressure mounts in the « phase » always powered steam to heat the home. The
water molecules are still agitate and collide with the wall of the
piston: they exert on it a force F F is equal to the product of the
pressure by the surface on which it applies: F = P x S. This force **F** allows movement of the piston by a distance **dx** .

**The work W** (Work English) exerted by the steam on the piston is the product of the force F by the movement (dx) of the piston:

**= W – F dx**

The heat is transformed into work. Work is negative, because it is provided by the steam engine to the piston. In contrast, when a tire is inflated using a hand pump, the work done (by the inflator) is positive. The work is an energy such as heat and is expressed in Joules.

We have seen that **F = P × S** (force equals the product of the pressure P by the surface S).

So :

W = – P × S × dV dx = -P

(DV is the change in volume (S × dx) induced by the movement of the piston).

### The energy of the system (U)

The energy variation ΔU of a system is the sum of the transfer of energy between it and the outside, expressed in the form:

- of heat Q
- of work W

Δ **U = W + Q **

The total energy U of the system remains constant if the system is in **equilibrium with the external environment** . To
take the example of the pump, the energy supplied to the gas in the
form of work results in a rise in temperature of the compressed gas. The heat is then discharged to gradually return to balance. Going back to the initial point (the gas is expanded by folding the pump), the energy of gas remained constant.

## The first law of thermodynamics

The first principle justly said that the total energy U of a closed system (the gas content in the pump) is constant (if it is in equilibrium with the outside). The energy changes form, but can not appear ex nihilo or disappear into oblivion without a trace.

« Nothing is lost, nothing is created, everything is transformed. » Lavoisier

ΔU = W + Q

If the pump is insulated, the system is no longer in equilibrium with the outside. The energy that I bring in the form of work is not discharged as heat and internal energy of the system increases.

Statement of the first principle: « During any transformation of a closed system (without exchange of matter with the outside), the variation of its energy is equal to the amount of energy exchanged with the external environment, in the form heat and in the form of work. « Mayer – 1845

## The second law of thermodynamics

One has the Carnot himself. This principle states that certain transformations (compression of a gas) are reversible. For others, the rollback is not possible.

**The entropy S**

This second principle leads to introduce a new concept: **the entropy S**. It reflects the fact that certain reactions are irreversible. If you put a mint syrup tasted in a glass of water. The
system will evolve naturally (without exchange with the outside): mint
will spread until the mixture is homogeneous: its entropy is then
maximum. Both substances (water and mint) are closely related. Both substances can not return to their original state: entropy can only increase. The reaction is irreversible. Note, however, that nothing physically preventing the two substances separate again. But it’s so unlikely that we consider that it is not possible. This applies also to our universe: the sum of its internal energy remains constant. Part of this energy is transformed. Entropy increases irreversibly toward greater disorder.

« I prefer to borrow from the ancient languages the names of important scientific quantities, so they can stay the same in all living languages; I would propose to call the quantity S the entropy of the body, from the Greek word η τροπη (transformation). It is by design that I have formed this word entropy, so that it is as close as possible to the word energy; since these two quantities have such an analogy in their physical meaning that naming analogy seemed useful. » Rudolf Clausius – 1865.

**Any work into heat transformation is irreversible**

Imagine a system (a hot water bottle) exchanging heat with a second (lake). The lake remains at temperature **T** constant (for mass). However, the bottle cools. During a time interval, the bottle receives:

- a quantity of heat dQ from the lake;
- an entropy S = ΔQ / T

Note dS = ΔQ / T

complete statement of the second lawA closed system is defined by a function

Sof said extensive state ‘entropy’. DS variation (when the system turns) of the entropy of a system is the sum of the variation of entropy:

dS = oF + diSIf the transformation is reversible

Entropy is extensive: if we mix two systems S1 and S2, we obtain a third entropy S. The system is the sum S1 + S2 of the first two.

### Enthalpy

**If a transformation isobaric (constant pressure)**

The enthalpy of a system occupying a volume V, at pressure P is:

- Energy that allows it to exist! It has an internal energy (U), but must also make its way into the world through the work of its pressure forces (POS).

**We denote H = U + PV**

- also « releasable » heat from the system, that it is capable of releasing the form of work. For example, the combustion of methane follows the following reaction: CH
_{4}+ 2 O_{2}→ CO_{2}+ 2 H_{2}O. This reaction releases heat (enthalpy) of .DELTA.h °_{combCH4}= – 778 kJ / mol. It will therefore provide 778 kcal / mol to go the other way (replenish methane).

### The thermodynamic engine – the Carnot cycle

### principle

We need a hot source and a cold source. Both sources will exchange heat QH and QC during a cycle (compression and relaxation) with the system (gas for compression). This heat will be converted into work. This is the steam engine principle.

It is a cycle so the internal energy change of the system is zero ΔU = 0.

**A to B: Isothermal expansion (PV = RT = constant)**

The starting point A. The system (the gas to be compressed) is at a pressure PA and a temperature Th (as hot). It provides a source of heat that will transfer a QH amount of heat to the system. As the piston is free, it will rise. The volume will increase from VA to VB. In B, the temperature is still Th.

- Relaxation is isothermal, so PV = RT = constant.
- V increases, so P must decrease from PA to PB.

On the path AB, heat progressively from the reservoir to the system by dQH small package. We dQH = POS (because ΔU = 0) = RT dV / V. Therefore QH = ∫dV RT / V = RT ln VB / VA

QH = RT ln VB / VA

**B to C: adiabatic (** PV ^{γ }**= constant: see further this relationship Laplace)**

The heat source was removed QH. The piston descends providing a job to the system. The volume therefore increases the pressure decreases.

Th / Tc = (VB / VC)^{γ-1}

**yield**

The yield equals η = -W / QC (that is the ratio between the obtained work and the amount of heat needed provided by the heat source).

W = QC + QH / QC = 1 + QC / QH = 1 – Tc / Th

It is therefore necessarily less than 1 showing that perpetual motion is impossible. It also shows the need for Tc and Th are different if the yield zero.

## Energy BRODE – (explosion in a pressure equipment (PSE))

Imagine a pressure vessel. When the wall gives way, the accumulated pressure is released suddenly. It then decreases to atmospheric pressure.

The example below illustrates the explosion of a liquefied gas chamber pressure (e.g. LPG). Pressure rises with the temperature. When the tank wall gives way, the energy is released. The last image (out of about developed here) is inflammation of the gas released in the form of a fireball (BLEVE).

**What is the energy released E at the opening of the tank ?**

It is equal to the energy that can accumulate in the blowing chamber, the atmospheric pressure (Pa) to break its pressure (Pr). The ΔU energy accumulates in the form of work and heat (Q).

**U = W + Q = -P.dV + m.Cv.ΔT**

In our case dV = 0, because the volume to rupture remains constant.

- Thus
**U = Q = m.CV.ΔT**

Imagine that the gas is perfect.

**PV = nRΔT (n: number of moles of the gas constant R and ideal gas)**- is P.dV + V.dP = nRΔT
- is V.dP nRΔT = (dV = 0)

n = m / M (mass / molar mass)

- is V.dP = m / M. (Cp-Cv) .ΔT (Mayer relationship below)
- is V.dP = m / M. (γ-1) .CV .DELTA.T with γ = Cp / Cv
- is V.dP = m / M.Cv.ΔT. (γ-1)
- or v dP = Q (γ-1)
**E = V dP / γ-1 (energy BRODE)**

**Relationship MAYER**

- H = U + PV
- dH = dU + V P + dP dV
- m Cp .DELTA.T = .DELTA.T cV m + m R .DELTA.T
- Cp – Cv = R

Cv = R (γ-1)

Relationship MAYER

## Laplace

Assume now an adiabatic transformation: there is no exchange of heat thus Q = 0. The change of energy will be equal to the work dU = W = -PdV

We start from the enthalpy

- H = U + PV
- dH = dU + POS + VdP
- dH = VdP

the gas is assumed as perfect:

- dU = Cv.dT
- dH = Cp.dT

So :

- Cp.dT = VdP
- Cv.dT = – POS

and:

- dT = VdP / Cp = -PdV / Cv
- Cp.Cv dV / V = - dP / P

then introduced the coefficient Υ Laplace = Cp / Cv:

- Υ dV / V = - dP / P
- Υ ∫ dV / V = - ∫ dP / PV
- Υ = LNV – InP
- PV
^{γ}= constant that is the law of Laplace

PV^{γ}= constant

Laplace

### The free energy or energy or Gibbs free energy

Very useful in chemistry, the energy released by Gibbs lets us know if a reaction occurs and where is its equilibrium. During the reaction, it is known that the entropy will increase or otherwise: **Scréee = + ΔSsytème ΔSextérieur> 0**

**The exterior receives entropy qIlluminated / T**

Or, the reaction being at constant pressure, it was for the system: ΔHsystème = dU + d (PV) = W + Q + d (PV) = Q system. So :

- Scréée = ΔSsytème – qIlluminated / T> 0
- Scréée = ΔSsytème – ΔHsystème / T> 0
- if my multiplies -T
- -TScréée = -TΔSsytème + ΔHsystème <0
- or ΔHsystème -TΔSsytème <0
- G = .DELTA.h -TΔS <0 is the free energy

The reaction takes place only if it is negative. Balance is attenteint when G is at a minimum.

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