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The phase space interpretation of the Le Chatelier‐Braun principle and its generalization as a principle of natural philosophy

  • Orta Dogu Teknik Universitesi (Middle East Technical University), Ankara, Turkey


The well-known Le Chatelier principle in chemistry describes how a system behaves when subject to an external effect. The way this principle works in conservative and dissipative systems was discussed within the framework of phase space. The Le Chatelier principle was restated in a more generalized form in such a way that it now becomes an underlying principle of many natural phenomena. The Lenz law in electromagnetism and deformations of materials were treated within this context. The increase of entropy and the adaptability of biological organisms in evolution were also discussed from the standpoint point of view of the generalized principle.
The phase space interpretation of the Le Chatelier–Braun principle
and its generalization as a principle of natural philosophy
¨zdog˘an Gu¨ndu¨z
and Gu¨ngo¨r Gu¨ndu¨z
Gu¨ zelyalı Mah., 331.So. 9/2, Go¨lbası, Ankara 06830, Turkey
Kimya Mu¨ hendislig˘i Bo¨lu¨mu¨ , Orta Dog˘ u Teknik U
¨niversitesi, Ankara 06800, Turkey
(Received 10 September 2013; accepted 16 July 2014; published online 12 August 2014)
Abstract: The well-known Le Chatelier principle in chemistry describes how a system behaves
when subject to an external effect. The way this principle works in conservative and dissipative
systems was discussed within the framework of phase space. The Le Chatelier principle was
restated in a more generalized form in such a way that it now becomes an underlying principle of
many natural phenomena. The Lenz law in electromagnetism and deformations of materials
were treated within this context. The increase of entropy and the adaptability of biological
organisms in evolution were also discussed from the standpoint point of view of the generalized
principle. V
C2014 Physics Essays Publication.[]
Re´ sume´: En chimie, le principe bien connu de Le Chatelier de´ crit la fac¸on dont un syste`me se
comporte lorsqu’il est soumis a` un effet externe. La manie`re dont ce principe fonctionne dans les
syste`mes conservatifs et dissipatifs a e´te´ discute´e dans le cadre de l’espace des phases. Le principe
de Le Chatelier a e´te´ reformule´ dans une forme plus ge´ne´ ralise´ e de manie`re a` devenir un principe
sous-jacent a` de nombreux phe´nome`nes naturels. La loi de Lenz en e´lectromagne´tisme et les de´ for-
mations de mate´riaux ont e´te´ traite´es dans ce contexte. L’augmentation de l’entropie et l’adaptabi-
lite´ des organismes biologiques dans l’e´volution ont aussi e´te´ discute´es du point de vue du principe
Key words: Le Chatelier–Braun; Chemical Equilibrium; Lenz Law; Entropy; Deformation; Adaptability; Evolution.
The Le Chatelier principle describes the behavior of a
chemical system at equilibrium subject to an external force.
It briefly says:
(i) “If any of the variables such as pressure, volume, tem-
perature, and concentration under which a chemical
system sustains its stability is forced to change, the
system shifts its equilibrium to a new state to counter-
act the imposed change.”
It is sometimes stated in more general terms as:
(ii) “Any change in current situation generates an oppos-
ing reaction in the system.”
A better definition is:
(iii) “An external interaction which disturbs the equilib-
rium brings about processes in the body which tend to
reduce the effects of this interaction.”
The explanation of this principle is usually done using a
reversible gas phase chemical reaction system.
The two-way arrows designate the reversibility of the sys-
tem. Let us assume this reaction to be at equilibrium. If some
more A or B is added the reaction shifts to the right and pro-
duces more C, such that the equilibrium is re-established.
The newly addition of A or B actually increases not only the
concentration but also the pressure, so the system moves in
the direction to reduce it. If an external pressure is applied
on the system without introducing new A or B the system
again behaves in the same way, shifts to the right, and pro-
duces more C to relieve the external pressure applied. If heat
is supplied to the system the shift occurs in a direction to
absorb the given heat. If A þB!C direction is exothermic,
some C decomposes to give C !AþB such that the given
heat is absorbed for the decomposition of C, or if the reaction
is endothermic, heat is absorbed to produce more C.
The principle underlying these chemical changes can be
extended to other natural phenomena of all kinds no matter
whether it is in physical world or in human relations,
economics etc.
The principle was introduced by Le Chatelier in 1884 as
a qualitative statement, and Braun established a scientific
framework in 1887–1888; and it is also known as the Le
Chatelier–Braun principle.
All changes in chemical equilibrium systems can be
interpreted by using the Gibbs–Duhem equation that can be
easily derived from the Gibbs free energy equation and the
Maxwell relations. Its derivation can be found in physical
chemistry and thermodynamics textbooks. It is given as
dG ¼VdP SdT þX
0836-1398/2014/27(3)/404/7/$25.00 V
C2014 Physics Essays Publication404
PHYSICS ESSAYS 27, 3 (2014)
where G is free energy, V, P, S, and T are volume, pressure,
entropy, and temperature, respectively. The last term is due
to chemical change, and l
and n
denote the chemical poten-
tial and the number of molecules of the ith species, respec-
tively. The change in any of the terms of Eq. (2) changes the
others as expected to keep dG ¼0. This equation involves
the mutual effects of all moments, i.e., (i) zeroth moment,
(or n), (ii) first moment, mv
(or P), and (iii) second
moment, 1
(or T).
Chemical equilibrium is a very dynamic system. The
experiments showed that an infinitesimal addition of a radio-
active isotope of reactant (A or B) which is so small that it
cannot disturb equilibrium, in fact, caused the formation of a
radioactive product (e.g., radioactive C molecules). The
chemical equilibrium constant K for Eq. (1) is simply given
where the brackets designate the equilibrium concentrations.
At the equilibrium, K ¼1; and according to the Le Chatelier
principle an increase in the value of concentration either in
numerator or denominator changes to keep K ¼1. It is usu-
ally difficult to understand what really happens dynamically;
and the change in mass balance is interpreted in a trivial way
as “if concentration is changed in one side, the concentration
in the other side also changes to keep the system at equi-
librium.” The change in pressure or temperature affects the
concentrations but they are related to each other by some
other relations such as ideal gas law.
Besides the chemical change, all other equations involv-
ing flow have the same mathematical form such, as
Jq¼dq=dt ¼krTðheat flow;Fourier’s lawÞ;(4)
JC¼dm=dt ¼DrCðmass flow;Fick’s lawÞ;(5)
Je¼dQ=dt ¼KrUðelectric current;Ohm’s lawÞ;(6)
Jch ¼dN=dt ¼r
nGðchemical changeÞ:(7)
These equations can be put into a general form so-called the
Onsager relation,
where X is the gradient of the driving force or affinity and J
is flux or reaction rate; L is a coefficient not depending on ei-
ther X or J. X creates J according to Eq. (8), which actually
represents “cause-effect” relation. Equations (4)(7) were
derived from experimental facts, therefore the constants L
are known as phenomenological coefficients. When there are
numerous processes occurring simultaneously, Eq. (8) can be
generalized as
The entropy change in time (dS/dt) can be expressed also in
terms of X and J, such that
dt ¼r¼X
where the summation is done over all extensive variables
such as energy or volume; and ris called dissipation
function. The combination of Eqs. (8) and (10) gives
As the thermodynamic forces X
are arbitrary, and r>0 for
a nonequilibrium system the diagonal kinetic coefficients are
always positive, that is,
Lii >0:(12)
If a stationary state is slightly disturbed, it returns to its ini-
tial state after a while. Let us assume that the system which
is under the balance of forces X1;X2; ::::Xkis disturbed by a
small external force dXi;ði>kÞ. The flux given by Eq. (9)
which is zero in the stationary state becomes dJi¼LiidXiin
the perturbed state as can be easily deduced from Eq. (9).
Then, Eq. (11) gives
According to this relation, an increase in dXiincreases the
flux dJi. However, the increase in flux always decreases the
force which causes it. This is nothing but the Le Chatelier
principle; the increase in dJidecreases dXiand restores the
stationary or equilibrium state.
The entropy of a steady-state system exchanging mass
and heat with the surrounding medium can be simply written
as follows by using Eq. (11):
where the subscripts H and M denote heat and mass, respec-
tively, and
JH¼L11XH;JM¼L22 XM:(15)
Consider a stationary state with the conditions of
The deviation from this state may be possible due to a small
variation of the force X
by dX
, such that
Then the entropy production r
before the perturbation
changes by a small additional term,
The r
is the minimum entropy production term and the
deviation from it will be positive,
dr ¼L22ðdXMÞ2>0:(18)
Since ðdXMÞ2>0, it is clear that L22 >0 in conformity with
Eq. (12).
The insertion of Eq. (16) into Eq. (18) yields
Physics Essays 27, 3 (2014) 405
dr ¼dJMdXM>0:(19)
This inequality designates the Le Chatelier–Braun principle.
The variation of the force (i.e., dXM) gives rise to a variation
in current (i.e., dJM) of the same sign. It means the variation
in current reduces the effect of variation in force.
The traditional interpretation of the Le Chatelier princi-
ple is somehow restricted although some interesting applica-
tions are found in economics and in biology. The economist
Samuelson introduced Le Chatelier’s principle into economy
in 1947 to explain the price equilibrium.
The Le Chatelier
principle finds many applications in a diverse variety of
fields, even in cosmological physics.
It is also applied in
biology to explain homeostasis which is defined as the prop-
erty of a system to regulate its internal parameters to coun-
teract environmental changes to maintain its stability. The
living organisms have to show adaptation to the changing
conditions to survive. In fact, only those species which ex-
hibit adaptability can survive and give offsprings, which,
then look for future stability. In fact only those species which
have stability at varying conditions can have a chance to
multiply. It is worth to note that this stability needs to be
dynamic stability to cope with the multiparameter conditions
of environment.
However, there had also been severe criticisms of this
principle in the past led by De Heer based on the statements
of Ehrenfest and Raveau about the ambiguity of the principle
as quoted in his work.
De Heer suggests “to replace the Le
Chatelier–Braun principle by a small number of rules each
of which has a limited range of applicability and is less am-
bitious (such as the ones given by van’t Hoff).” There have
been numerous studies to define it in a more explanatory
way and to understand its meaning, and to explain the condi-
tions of its applicability.
De Heer strictly concentrated on
the state of chemical equilibrium and claimed that the system
did not have to oppose or relieve the applied perturbation,
and he supported his argument by some examples from phys-
ical chemistry.
An external effect forces the system to change in certain
directions; however, the system develops a negative feed-
back to this change in accordance with the Newton’s third
law. The new equilibrium state can be far away from the for-
mer one, and it may take a long time to arrive at it. The fun-
damental action–reaction principle of Newton can also be
explained by the Le Chatelier principle, and its importance
should not be undervalued. Rather than “replacing the Le
Chatelier–Braun principle by a small number of rules”itis
much more meaningful to re-express it in a larger conceptual
context to cover much broader phenomena in nature. The
Ehrenfest’s question on differentiation of thermodynamic
properties of nonequilibrium states from those of equilibrium
states has been answered to some degree by Prigogine.
Actually nonequilibrium thermodynamics shifts the para-
digm from equilibrium states to processes. Processes should
be considered as autonomous entities and they cannot be
defined as the changes in the state of objects.
The concepts
of nonequilibrium thermodynamics dispute the De Heer’s
arguments to weaken the importance of Le Chatelier princi-
ple, and instead trigger its use in more general sense.
In fact there is no perfect equilibrium in nature as stated
by the “continuous creation–destruction (corruption)” princi-
ple of Aristotle;
and all states are transient as also stated by
chaos theories.
Molecular and biological evolutions also
occur according to this natural principle.
The chemical equilibrium as a dynamic process can be
defined as a state where forward and backward rates
(i:e:; r!and r ) are equal, i.e.,
r!¼r or r!r ¼0:(20)
In this form, it looks like a flow equation, and the Gibbs–
Duhem equation (i.e., Eq. (2)) then can be written as
G!G ¼ðP!P ÞSðT!T Þ
ðlin!ljn Þ:(21)
The change in A þB!
C due to change in concentration,
temperature, or pressure is actually a distortion in the phase
space of the system. That is, the kinematic and the potential
energy states of molecules change if the system is distorted.
In other words, positions, velocities, and also vibration, rota-
tion, and electronic configurations of molecules change to
attain new equilibrium. The system moves out from a previ-
ous equilibrium state to a new equilibrium state via the gen-
eration of material and energy fluxes; and it can reach
stability only if the external causes are counteracted by
absorbing the external energy input in the form of kinematic
and potential energies at molecular level. Such systems are
known as dissipative systems,
and energy dissipation goes
extinct if fluxes (or currents) of material and energy stop
feeding the system. The system then finally arrives at its new
equilibrium state. Dissipative systems have a kind of order in
their structure, and can sustain it only at the expense of
increasing the entropy of a “larger system” in which the dis-
sipative system is embedded. The change from an equilib-
rium state to a dissipative state or to another equilibrium
state takes place only through fluxes. As the great philoso-
pher Heraclitus said in the Ancient times, “everything occurs
through fluxes.
The creation of fluxes naturally involves
entropy production or irreversibility, because, fluxes distort
the surrounding environment. In other words, the persistent
change in nature can be achieved only by increasing the irre-
versibility. The change from one equilibrium state to another
one can be accomplished only through the creation of gra-
dients which are the driving forces that generate the fluxes.
In this respect, the initial and the final equilibrium states
behave like attractors connected by fluxes; or like opposite
electric charges connected by electric field lines, or magnetic
poles connected by magnetic flux.
The physical laws can be categorized in two groups, (i)
those which are nonmathematical and do not involve the
concepts of space and time, and (ii) and those stated by
mathematical relations between the properties of matter,
space and time.
Although the Le Chatelier–Braun principle
406 Physics Essays 27, 3 (2014)
is stated in a nonmathematical form, it involves space and
time in its applications. There is no space and time concept
in chemical equilibrium, but they are involved when equilib-
rium is perturbed.
According to the very fundamental principles of classi-
cal physics, the motion of an object occurs in the direction of
applied force, i.e., an applied force induces a movement (or
flux) in its own direction. The term “current” is used instead
of “flux” in the physical equations such as the Fourier’s heat
conduction law, the Fick’s law, and the Ohm’s law; all of
which have the same mathematical structure. This Newto-
nian approach to describe action–reaction phenomenon in
nature purely depends on interactions of rigid bodies which
do not deform on collisions where causality principle works
perfectly. It is well-known that in quantum mechanics cau-
sality principle fails because interactions are not rigid body
interactions, and an object subject to an external force is no
more the one before interaction, because, the previous wave
function collapses after the interaction and the system is then
described by a new wave function. No matter whether we
describe chemical reactions in terms of classical or quantum
mechanics the molecules are always subject to deform per-
manently after the reaction, i.e., they change into another
persistent shape, or into a state described persistently by a
new wave function.
In phase space, molecules are described by their posi-
tions and velocities, and only the changes in positions and
velocities of molecules are of concern for dynamical descrip-
tion. The chemical reactions or phase transitions both change
the phase space. Since the definition of phase space is based
only on position and velocity the flux (or current) due to
deformational change as in chemical reaction (i.e., change of
shapes of molecules) cannot be explicitly expressed simulta-
neously with dynamical changes within the context of con-
served phase space. In fact, the perturbation of phase space
by any cause yields a change in entropy which is a measure
of deformation or of degradation.
Whether phase space is conserved or not the question is
in what way it reacts against an external force; in other
words, how reaction reveals within the context of action–
reaction principle. Since phase space (C) has two compo-
nents as space (position) and momentum (velocity) the
change in one of them influences the other. The change in
phase space (dC) can be simply given in terms of the change
in space (ds) and the change in momentum (dp), such that
dC¼ds dp:(22)
In a conservative system, phase space is conserved and the
change in the magnitude of one of the components inversely
affects the other to keep dCconstant. In dissipative systems
dCis not conserved but the inverse dependence is still valid
though it is not one to one. In conservative systems one of
the components of dCacts as the potentiality of the other in
the Aristotelian sense.
That is, if ds contracts dp expands
or vice versa. For instance, in a “cylinder-and-piston” system
the contraction of space (e.g., volume, V, or ds) is due to the
increase in pressure P (or momentum, dp). This is actually
the well-known Boyle–Mariotte law (i.e., PV ¼constant).
The physical deformation (contraction or expansion, or
decrease or increase) in either one is reversible in conserva-
tive systems. In the case if temperature also changes, we
may have dissipative system, but still ds and dp behave in a
similar manner. If one of the variables is changed the system
reorganizes itself by readjusting the variables of the phase
space. The adjustment can finally yield reversible or irrevers-
ible state depending whether the phase space is maintained
or is degraded.
In dissipative and chemically reacting systems, dCis not
conserved and a flux is created at the expense of the irrevers-
ible decomposition of dC. The reversible deformation of ds
and dp (i.e., the change of the magnitudes of ds and dp) in
conservative systems signifies a reversible transient state,
and it becomes irreversible only if dCdecomposes to a new
value, say dC0. Every new input can change the phase space
into new forms, i.e., dC!dC0!dC00 !dC000:::.
Any parameter which can sustain itself against the long-
term reactive changes (or permanent changes) in the course
of evolution can be carried into future. This is what is known
as adaptability in biological evolution. Adaptability is
actually the persistence of some of the appropriate parame-
ters of the system but allowing relatively small changes in
some other parameters. What is apt to change or to evolve is
what cannot resist the forces affecting because of being at a
lower stability state. What perishes and what comes in new
both provide the new potentiality for the adaptability of the
nonperishing parameters of the system.
The dissipative process increases entropy and reveals
persistency or irreversibility of a new state which is sup-
posed to be more stable than the former state under new con-
ditions. In other words, the newly evolved system can be
persistent only if the former phase space is degraded and
rebuilt. However the new state is also transient in the long
run and forced to change by oncoming processes. All these
reveal through the partial changes caused by the generation
of fluxes. In this sense, whether the system is conservative or
dissipative the system always tries to adjust itself against the
external effects. So the Le Chatelier principle can be modi-
fied and generalized to the following form:
“If any of the variables under which a system sustains its
stability is forced to change, the system adjusts itself to the
new conditions by changing its equilibrium to a new state
which fits to the changed (new) conditions.”
The reason why ds and dp act in an inverse manner has
roots in the very basic definition of velocity; the instantane-
ous velocity is always tangential to trajectory as it denotes
the slope. In fact phase space is nothing but a simple tangent
space. An opposing or relieving type of reaction revealed
according to the Le Chatelier–Braun principle takes place
through the changes taking place in the tangent space. Any
effect produced in the coordinate space due to an external
cause can also induce another effect in the velocity space, or
vice versa.
The tangent space (or phase space) interpretation of Le
Chatelier principle can be best understood by considering the
Physics Essays 27, 3 (2014) 407
law of induction in electromagnetism. According to the Lenz
An induced current is always in a direction to oppose
the motion that causes it.”
This definition is in perfect agreement with the definition
of the Le Chatelier principle given in “(ii)” in the introduc-
tion part. In more specific terms it can be restated as
An induced electromotive force generates a current
whose magnetic field opposes the original magnetic flux.
An induced electromotive force (e) and the change in
magnetic flux (UB) are related to each other by
where N is the number of loops in a coil.
The Faraday equation given by the following equation
describes how electric and magnetic fields induce each
The induced magnetic field inside any loop behaves in a way
to keep the magnetic flux in the loop constant. The minus
sign indicates the direction of electromotive force. If the
magnetic field is increased, the induced field acts in opposi-
tion and decreases it; and if the magnetic field is decreased,
the induced field acts in the direction of the applied field to
increase the magnetic flux to keep it constant.
Here, electrical and magnetic fields act as if they are two
components of a phase space perpendicular to each other, the
positional change (i.e., r) concerns the change in electrical
field whereas the change involving the rate (i.e., @=@t) con-
cerns the change in magnetic flux. The change in one of the
components induces an effect in the other (i.e., vertical)
component to counteract the imposed change. This is so,
because electromagnetic field is a vector field, and the two
components (E and B) are perpendicular to each other. The
Le Chatelier principle works perfectly here, and the Lenz
law is its excellent application in electromagnetism.
The Lenz law can be used to understand how Newton’s
third law can be interpreted in electromagnetism. However
neither the third law nor the Lenz’s law explicitly explains
the mechanism of “deformational type of reaction” of a sys-
tem in terms of changes in tangent space (or phase space)
even though the Faraday equation is clearly defined in this
space. In Newton’s third law, acting and reacting objects are
involved in rigid collisions and nothing is said about the ver-
tical direction as the material objects remain undeformed.
The Lenz law considers changes in both components of tan-
gent space; but the system is implicitly conservative. How-
ever, this is not the case in the deformation of material
Now, we can consider the most general case where the
system does not inherently possess two vertical components
as in electromagnetic fields, and in addition, the change (or
deformation) may be dissipative. There are two fundamental
laws which describe the dynamical behavior of material
objects at two extreme states. These are the Hooke’s law for
rigid systems and the Newton’s law for viscous flow. The
Hooke’s law finds applications in material science describing
conservative so-called linear elastic deformations. Viscous
deformation is an irreversible process and not well recover-
able. The materials which exhibit partial recovery are said to
exhibit “plastic deformation.” The “elastic deformation
such as tension or compression of a metallic, ceramic, or
polymeric specimen is given by
where “E
” denotes the Young’s modulus. This equation is
of the same form with the Hooke’s law, and the stress “r
denotes the force applied per unit cross sectional area. The
fractional change in length “e” corresponds to the displace-
ment and “E
” corresponds to the spring constant in the
Hooke’s law. In tension or compression the deformation
occurring along the axis also causes deformation in the verti-
cal direction. All these deformations go extinct upon the re-
moval of the stress applied. The system undergoes
deformation along axial and vertical directions to oppose the
externally applied stress. In case if shear stress is applied
(i.e., stress applied parallel to the cross section), the shear
stress “s” causes a deformation “c” expressed by
where the constant “G” is called the shear modulus. Both the
moduli E
and G can be expressed in terms of complex vari-
such that
The real and complex components correspond to elastic and
dissipative terms, respectively. By the same token the modulus
G0and G00 are called “storage”and“loss” modulus, respec-
tively. In fact the stress “s” can be split into two components,
where s0and s00 are stress components applied along the par-
allel (i.e., in-phase) and the vertical (i.e., out-of-phase) direc-
tions to the cross section of the specimen. If a specimen is
subject to a cyclic deformation given by
c¼c0sin xt;(30)
the elastic energy W
(or stored energy) and the dissipative
energy W
(or loss energy) can be given by
These energy expressions are similar to the field energies of
electrostatic (W
) and magnetic (W
) fields, such that
408 Physics Essays 27, 3 (2014)
where E and H represent the electrical, and the magnetic
fields, and eand lrepresent the permittivity, and the perme-
ability constants, respectively.
In electromagnetic fields, E
and H propagate perpendicular to each other similar to the
components of s(i.e., s0and s00). In both the electromagnetic
field and the material stress field the parallel and vertical
components store energy by the same natural phenomena so
that the mathematical expressions are of the same structure
as seen from Eqs. (31) and (32) to Eqs. (33) and (34). How-
ever, the second components (i.e., Eqs. (32) and (34)) differ
in their physical behavior; the magnetic and the electrical
fields are bound to each other and they copropagate in space,
one induces the other according to the Faraday’s induction
law. In material science, the Hooke’s law for rigid systems
and the Newton’s law for viscous flow do not induce each
other when an external force acted on a viscoelastic material.
This is the point where the entropy is substantiated in sys-
tems where there is not a one-to-one dependence (or correla-
tion) between the components of the system, or when the
phase space cannot maintain its stability due to weakening of
correlations between its components. The degradation of
phase space brings in an increase of entropy and thus a
change in the information content which actually originates
from the change of the configurations of the molecules, or
the extents of correlations within the system.
there exists an analogy between electromagnetism and
hydrodynamics, and the behavior of electromagnetic and
hydrodynamic systems may resemble each other in some
The degraded new system can survive only if it is adapt-
able to new conditions, or if it is not reacted by whatever sur-
rounds it. At molecular level, a new molecule bounced into a
new surrounding medium can survive only if it maintains its
stability. For instance, an oxygen molecule given off in a
chemical reaction can survive at atmospheric conditions, but
a hydroperoxide molecule easily reacts with other molecules
in the environment or degraded by solar radiation and thus it
cannot survive for sufficiently long time. In biological world,
the process is same; any newly born organism is said to be
adaptable to the existing environment and multiply itself if it
can maintain its stability for sufficiently long time which is
the maturation time at minimum. So the stability of either
chemical molecules or biological organisms leads to adapta-
bility in the long run.
The continuous change of entropy
and the new information gained in time by complex systems
cause reorganization in molecular configurations. In other
words, the time dependent Kolmogorov–Sinai entropy and
the associated information content of an evolving system de-
velop in time in the resultant direction of the forces acting on
the system. These forces are always counteracted by the sys-
tem according to the generalized Le Chatelier–Braun princi-
ple, and the final form of the system maintains its structure
and stays stable; or it survives if it is a biological organism.
The adaptability concerns with how evolution develops from
the actions and reactions of forces according to the general-
ized Le Chatelier–Braun principle.
The Le Chatelier–Braun principle applied to chemically
reacting systems can be generalized to all other natural phe-
nomena. Its interpretation in tangent or phase space brings in
a unified view of the behavior of electromagnetic fields and
deformation dynamics of materials. The generalized concept
also helps to analyze the importance of entropy and adapta-
bility in evolutionary systems.
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... This implies an inverse relationship, which is associated with the disproportionate rise in sorption sites (at higher dosages) in the face of constant adsorbate concentration (Mohamed et al. 2021a). According to Le Chatelier's principle (Gündüz and Gündüz 2014), at a fixed initial adsorbate concentration (in this case, 20 mg/L), the concentration-induced adsorption driving force diminishes at increasing dosage (from 0.2 to 2.0 g/L), thus, leading to decreased uptake. Previous studies (Banisheykholeslami et al. 2021;Grabi et al. 2021;Putri et al. 2021) also showed that with increasing dosage, no significant increase in the dye uptake was recorded because the number of unoccupied sites on the respective adsorbents exceeded the number of dye molecules in the liquid phase at a constant initial concentration (C o ). ...
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In this study, a novel Lepidium sativum seed powder (L-seed) was investigated for the adsorptive uptake of acid orange 142 dye. The different L-seed biosorbent samples were characterized via the Fourier transform infrared (FTIR), scanning electron microscopy (SEM), energy dispersion X-ray (EDX), X-ray diffraction (XRD) and Brunauer–Emmett–Teller (BET) surface area and pHPZC approaches. The effect of the process variable on the process was investigated via batch adsorption mode. The FTIR measurement revealed the presence of functional groups necessary for dye uptake, while the surface micropores observed from the SEM micrographs were further confirmed from the pore size distribution result. The BET surface area, pore volume and average pore size of L-seed are estimated as 90.86 m²/g, 0.072 cm³/g and 1.93 nm, respectively. Batch adsorption investigations showed the following optimum process conditions: pH 4.0, 0.2 g/L adsorbent mass and time of 120 min. The experimental equilibrium and kinetic data were properly described by the Freundlich isotherm and pseudo-first-order kinetics model, respectively. The thermodynamics studies confirmed the occurrence of external energy-driven adsorption. Therefore, the experimental results showed that the L-seed is an efficient and alternate low-cost biosorbent for acid orange 142 dye from aqueous media.
... This principle is not only restricted to the chemical world, but it arises as a natural philosophy, and¯nds applications in electromagnetism through the Lenz's law, and in materials through the laws of viscoelastic theory. 16 The existence of dissipative events within a complex system results in irreversibility, which increases the entropy, and thus, the system stabilizes itself in a new equilibrium state. The magnitude of dissipative phenomena in a complex system plays a predominant role in¯xing the new equilibrium (or quasi-equilibrium) states, and thus also the new boundaries of the system. ...
A new methodology was introduced to investigate the pattern formation in time series systems due to their viscoelastic behavior. Four stochastic processes, uniform distribution, normal distribution, Nasdaq-100 stock market index, and a melody were studied within this context. The time series data were converted into vectorial forms in a scattering diagram. The sequential vectors can be split into its in-line (or conservative) and out-of-line (or dissipative) components. Thus, one can define the storage and loss modulus for conservative, and dissipative components, respectively. Instead of using the geometric Brownian equation which involves Wiener noise term, the changes were taken into consideration at every step by introducing "lethargy" concept and the deviation from it. Thus, the mathematics is somehow simplified, and the dynamical behavior of time series systems can be elucidated at every step of change. The viscoelastic behavior of time series systems reveals patterns of the viscoelastic parameters such as storage and loss modulus, and also of thermodynamic work-like and heat-like properties. Besides, there occur some minima and maxima in the distribution of the angles between the sequential vectors in the scattering diagram. The same is true for the change of entropy of the system.
... In material science, BE and DE correspond to in-phase and out-of-phase components, while they correspond to electrical and magnetic¯elds, respectively, in electromagnetism. 45 In other words, G 0 is associated with conservative component whereas G 00 is associated with dissipative component. ...
The rise of empires can be elucidated by treating them as living organisms, and the celebrated Verhulst or Lotka–Volterra dynamics can be used to understand the growth mechanisms of empires. The fast growth can be expressed by an exponential function as in the case of Macedonian empire of the Alexander the Great whereas a sigmoidal growth can be expressed by power-law equation as in the case of Roman and Ottoman empires. The superpowers Russia and the USA follow somehow different mechanisms, Russia displays two different exponential growth behaviors whereas the USA follows two different power-law behaviors. They did not disturb and mobilize their social capacity much during the course of their rise. The decline and the collapse of an empire occur through a kind of fragmentation process, and the consequently formed small states become rather free in their behavior. The lands of the new states formed exhibit a hierarchical pattern, and the number of the states having an area smaller than the largest one can be given either by an exponential or power-law function. The exponential distribution pattern occurs when the states are quite free in their pursuits, but the power-law behavior occurs when they are under the pressure of an empire or a strong state in the region. The geological and geographical conditions also affect whether there occurs exponential or power-law behavior. The new unions formed such as the European Union and the Shanghai Cooperation increase the power-law exponent implying that they increase the stress in the international affairs. The viscoelastic behavior of the empires can be found from the scattering diagrams, and the storage (Formula presented.)and loss modulus (Formula presented.), and the associated work-like and heat-like terms can be determined in the sense of thermodynamics. The (Formula presented.) of Ottomans was larger than that of Romans implying that they confronted severe resistance during their expansion. The (Formula presented.) of Russia is also larger than that of the USA; in fact the USA did not face severe resistance as they had an overwhelming superiority over native Americans. The (Formula presented.) indicates solidity in the social structure and Romans, Ottomans, and Russians all have (Formula presented.) larger than (Formula presented.). The (Formula presented.) is slightly larger than (Formula presented.) for the USA indicating that they have had a very flexible social structure. By the same token the ratio of the work-like term to the internal energy is larger for Ottomans than that of Romans, and larger for the USA than that of Russia. That means the fraction of the total energy allocated to improve the social capacity is larger for Romans than that of Ottomans, and is larger for Russians than that of the USA.
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In simple, reversible, chemical reactions of the type A ⇋ B, chemical equilibrium is related to chemical kinetics via the equality between the equilibrium constant and the ratio of the forward to the reverse rate-constant, i.e., Keq = kf/kr, where Keq is the equilibrium constant and kf and kr denote the rate constants for the forward (A → B) and reverse (B → A) reactions, respectively. We review and examine the relation between the number of forward and reverse reactions required to take place for the aforementioned system to reach equilibrium and the ratio of the forward to the reverse rate constant. Each cycle of reactants becoming products and the products becoming reactants is defined as the transfer cycle (TC). Therefore, we underscore the relation between the number of TCs required for the system to equilibrate and kf/kr. We also vary the initial concentrations of the reactants and products to examine their dependency of the relation between the number of TCs required to reach equilibrium and kf/kr. The data reveal a logarithmic growth-type relation between the number of TCs required for the system to achieve equilibrium and kf/kr. The results of this relation are discussed in the context of several scenarios that populate the trajectory. We conclude by introducing students and researchers in the area of chemistry and biochemistry to physical phenomena that relate the initial concentrations of the reactants and products and kf/kr to the number of TCs necessary for the system to equilibrate.
Chemical equilibrium is one of the most important concepts in chemistry. The changes in properties of the chemical system at equilibrium induced by variations in pressure, volume, temperature, and concentration are always included in classroom teaching and discussions. This work introduces a novel, geometrical approach to understanding the chemical system at equilibrium with the example of a simple two-component system and shows how the equilibrium changes under the influence of external perturbations. The paper discusses how thermodynamic factors (contained in the equilibrium constant K) and the conservation of mass principle govern the equilibrium state. The equilibrium and its changes are described using the geometrical representation in concentration space. The goal of this work is to help students better understand the basis behind the well-known Le Châtelier’s principle and equilibrium in general.
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Employing quaternionic Newton’s law, we have found that the energy conservationequation is the analog of Lorenz gauge in electromagnetism. This Newton’s law yields directly theEuler equation and other equations governing the fluid motion. With this formalism, the pressurecontributes positively to the dynamics of the system in the same way mass does. Hydrodynamicequations are derived from Maxwell’s equations by adopting an electromagnetohydrodynamicsanalogy. In this analogy the hydroelectric field is related to the local acceleration of the fluid and theLorenz gauge is related to the incompressible fluid condition. The equations governing the fluidmotion are analogous to those governing the motion of a charged particle. An analogous Lorenzgauge in hydrodynamics is proposed. We have shown that the vorticity of the fluid is developedwhenever the particle local acceleration of the fluid deviates from the velocity direction. We havealso shown that Lorentz force in electromagnetism corresponds to Euler force in fluids. Moreover,we have obtained Gauss, Faraday, and Ampere-like laws in hydrodynamics. The analogy between electromagnetism and hydrodynamics. Available from:
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We explicate the nature of physical law by examining the implications of a fundamental law hypothesis, which states that fundamental laws of nature (physics) do exist independent of the human mind. That we do by exploring, from the physical law perspective, the concepts of space and time and the role of mathematics in physics. We show that the fundamental law hypothesis implies two kinds of laws in physics: (i) fundamental laws of physics, which are nonmathematical and do not incorporate the concepts of space and time and (ii) physical laws devised by physicists, which are stated as mathematical relations between the properties of matter, space, and time. We also show that according to that hypothesis, a theory of everything cannot exist. Without further assumptions, the fundamental law hypothesis leads to the conclusion that both the fundamental laws of physics and their executions are simple in the extreme. It also allows for explaining some mysteries of today's physics, including the ratio of gravity to electrostatic forces, Mach's principle, the principle of relativity, and the equivalence principle. (C) 2012 Physics Essays Publication. [DOI: 10.4006/0836-1398-25.4.590]
The creators of equilibrium and irreversible thermodynamics developed a conception of processes which bears on metaphysical discussions of change, occurrents, and continuants and merits the attention of contemporary analytic metaphysicians. It concerns the macroscopic domain, from which metaphysicians normally take their examples, and is unjustly ignored on the grounds that it is not ‘fundamental science’. Why this often-voiced view should disqualify just thermodynamics, and not the broad range of considerations normally raised, is a moot point. But even if there were an adequate reductive argument, that wouldn’t eliminate the ontological claims. It is argued that processes cannot be defined as changes in the state of enduring objects, but should be considered autonomous entities. The relational character of processes involving several continuants is developed, alongside their mereological features and their relation to space and time. Some aspects of the historical development of the notions of reversible and irreversible processes in thermodynamics are taken up in the course of the discussion, but the paper is not concerned with the mathematical foundations of equilibrium and irreversible thermodynamics. • 1 Introduction • 2 Change • 3 Distinguishing Processes from States • 4 Causings • 5 The Relational Character and Mereological Structure of Processes • 6 Concluding Comments
In a recent article, Torres presents a thermodynamic analysis of the response of a system initially at chemical equilibrium to an infinitesimal perturbation. While the analysis is correct in this context, Torres argues incorrectly that the general rule so obtained is also valid for finite perturbations.
Examples of multiple chemical equilibria are considered, illustrating responses of systems which cannot be treated by direct application of the Le Chatelier principle. In order to rationalize these unusual responses, a general treatment of sensitivity coefficients of complex chemical equilibria, both in the gas phase and in solution, is elaborated. The sensitivity coefficients may be given as sums of contributions coming from certain well defined reactions, which we name response reactions. The concept of response reactions enables us to give the sensitivity coefficients a clear chemical meaning and to arrive at a simple and efficient algorithm for the analysis of the sensitivity of complex chemical equilibria.
An experiment and a computer simulation are presented to address a counterintuitive situation often encountered when teaching chemical equilibria. This is prompted by the question "How can the subdivision of a solid reactant affect the reaction rate and not the composition of the equilibrium state?"