Prezentace aplikace PowerPoint

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BASICS OF THERMODYNAMICS OF LIVING
SYSTEMS
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Thermodynamics deals with mutual conversion
of different types of energy, the direction of
physical and chemical processes and of
equilibria. It also studies systems composed of
many parts. As a system we consider any
region of space separated from its surroundings



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According to the interaction of the system with
its surroundings we discriminate
systems isolated do not exchange matter or
energy with surroundings close
d exchange only energy with surroundings,
not matter open exchange both
matter and energy with surroundings
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Thermodynamics studies two types of
parameters extensive parameters characterize
thermodynamic
system as a whole (mass, volume, total
electric charge) intensive parameters they
have different values
in different parts of the system
(concentration of chemical components, temperature
, electrical potential)


The studies of the relationship between extensive
and intensive parameters create the basis for the
formulation of thermodynamic laws.  
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The basic laws of thermodynamics are law of
conservation of mass I. law of
thermodynamics II. law of thermodynamics III.
law of thermodynamics
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I. law of thermodynamics If
a system is doing a work or the surroundings is
doing a work on the system, its internal state is
changed. E.g. if we compress a gas in a cylinder
with a piston the temperature of the gas
increases. Similarly, if there is a chemical
reaction between the components of the system,
its temperature changes. Or, if you consider
an iceberg moving on rocky surface, the friction
produces heat and the iceberg changes its phase
it melts. The cause producing the change of the
state is called energy. Energy can be thus
defined as the ability to change
given (equilibrium) state of matter.
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Initial experimets indicated an equivalence
between heat and mechanical work (the work
produces heat and heat can be used to do a
work) This studies led to the formulation
of principle of energy conservation. This
principle can be formulated in different ways,
e.g. It is not possible to construct a machine
generating energy from nothing. That means it is
not possible to produce a perpetuum mobile of the
first kind. In a more general formulation The
total energy of isolated system is constant
during all processes.
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So we can expres the I. law of thermodynamics in
this way The total energy that a system exchanges
with surroundings in any process is dependent
only on the initial and final state of the
system, and not on the way this change was
achieved. This means there is an energetic
function, whose difference between initial and
final state corresponds to energy exchanged
between the system and surroundings. This
function is called inner energy of the system and
is labelled as U. ?U U2 - U1 q - w
here q indicates heat accepted by the system from
surroundings, w is a work done by the system,
indexes 1 a 2 indicate initial and final state of
the system
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The I. law of thermodynamics implies that total
heat released in a chemical reaction will be the
same if the reaction proceeds in one step or in
more steps. E.g. the amount of heat released
during reaction C O2
CO2 equals the sum of heat produced in the
following reactions C 1/2O2 CO
CO 1/2O2 CO2
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This conclusion is known as the Hess law. Now we
can introduce new thermodynamic function. It is
called enthalpy, labeled H, and defined by
an equation
H U PV

where P is pressure and V volume of the system
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Now we can calculate the amount of heat released
in the system under constant pressure qP
H2 - H1 ?H
This
expression says that the change of enthalpy
in any process is dependent only on the initial
and final state of the system. In the case of
chemical reaction it is the state of the
reactants at the beginning of the reaction and
the state of products in the end of the reaction.
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Reaction heat is the amount of heat exchanged by
the system with surroundings during the chemical
reaction. If the heat is released we speak of an
exothermic process, if the heat is consumed by
the system, it is referred to as endothermic
process.
If the reaction proceeds under constant volume,
the reaction heat corresponds to the change of
inner energy of the system. If the reaction
proceeds under constant pressure, the reaction
heat corresponds to the change of enthalpy.  
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II. law of thermodynamics   By
the beginning of 19th century Carnot studied
the efficiency of heat machines. He created a
concept of cyclically working heat machine, in
which the volume in the cylinder was changed by
interaction with two heat exchangers having
different temperature. Theoretical work out of
this concept led to the formulation of the
theorem All the reversible machines working
between the same heat exchangers have the same
efficiency in spite of the composition of the
exchangers.
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Related formulation was stated by Clausius   It
is not possible to construct an equipment that
would do nothing else than transfer heat from the
colder body to a warmer body. This implies that
it is not possible to create the so
called perpetuum mobile of the second
kind.   These formulations are the expressions
of the II. law of thermodynamics
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The studies of the efficiency of heat engines
revealed the existence of a new state function
called entropy labeled S   dS
dq/T

(4)   According to Carnot theorem the efficiency
of reversible machine is maximum. Thus, the
irreversible machines have always lower
efficiency. For the irreversible process we
get dS gt dq /T

(5)  
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If the system does not exchange heat with
surroundings we get for irreversible
process   dS gt 0

(6)   and for reversible
process   dS 0

(7)   It means that entropy is growing
under irreversible processes and in equilibrium,
when only reversible processes can proceed, it
does not change. Entropy can be looked upon as a
measure of spontaneousness, as it increases
during spontaneous processes.
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Energy functions F and
G   For the case of reversible process we get
from the I. law of thermodynamics   dU
dqrev - dwrev For dqrev we substitute from the
definition of entropyTdS   dU TdS - dwrev
From this equation we can deduce that work done
by the system under reversible conditions can be
expressed using basic thermodynamic parameters T,
U, S.
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We can substitute for TdS   TdS d(TS) -
SdT
  In the case of a process
under constant temperature dT 0 and TdS
d(TS), and the equation can be rewritten dU -
d(TS) d(U - TS) -dwrev
 
For a finite change we get   ?(U - TS)
-dwrev
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It is evident there is a state function (U - TS),
the decrease of which indicates maximum (i.e.
reversible) work that the system can do under
constant temperature. It is known as Helmholtz
function and labelled F  
F U - TS
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We can discern between volume work wvol (wobj
PdV) and an useful work w,rev, comprising all
other kinds of work (electrical, transport, etc.)
Then we can rewrite the equation dU TdS -
PdV - dw,rev
  In the case that in
the system proceeds reversible process under
constant pressure and temperature, we have dT
0, TdS d(TS) dP 0, PdV d(PV) Substituting
in the above equation we get   dU - d(TS)
d(PV) d(U - TS PV) -dw,rev
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And for the finite change   ?(U - TS PV)
-w,rev
  We can see another state
function (U - TS PV), the decrease of which
indicates maximum useful work that can be done by
the system under constant pressure
and temperature. It is called Gibbs function and
labeled G   G U PV - TS H - TS
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III. law of thermodynamics   The
formulation was developing in time. As a
definitive version is considered the formulation
by Planck from 1912 Entropy of every chemically
homogenous condensed phase approaches with
decreasing temperature zero.    Another
formulation explains it more clearly It is not
possible to cool a physical body to absolute zero
in a finite number of steps.  
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Changes of entropy in living
systems For the description of internal
processes in the system we consider the states
of the system as a whole. Equilibrium state is
reached by a system that is isolated from
surroundings and let suficient time to evolve
until it is not changing any more. This final
state will correspond to the most probable
arrangement, characterized by the highest degree
of disorganization, when entropy reaches its
maximum value.
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Chemical reactions are characterized by
equilibrium constant K, which describes the
composition of the reaction mixture under
situation when the reaction rate from left to
right equals the rate from right to left. For
the change of Gibbs function in equilibrium
state we obtain -
?G RT ln K.
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Living systems are open systems. In the living
biological system taken as a whole we can not
expect thermodynamic equilibrium, as the system
in equilibrium can not do work. However, the
ability to do work is essential for
the maintenance of living functions. Open systems
are able to generate certain stationary state,
under which the parameters of the system
preserve constant levels of exchange of matter
and energy with surroundings.
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The total entropy of an open system can be
changed either due to exchange with external
surroundings deS, or due to internal processes in
the system diS   dS deS diS
For the rate of entropy change we
obtain   dS/dt deS/dt diS/dt

deS/dt corresponds to the exchange of
entropy between the system and surroundings and
it can reach both positive and negative
values, diS/dt is only positive.
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Under stationary state the rate of entropy
production is constant, thus dS/dt 0, and
thereforedeS/dt diS/dt   dS/dt deS/dt
diS/dt 0 If we rewrite this equation

  dS/dt (-deS/dt) diS/dt

  We can express it in words Under stationary
state the sum of the rate of entropy production
in the system and the rate of emerging
entropy from the system equals the rate of
entropy production inside the system.
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Development and growth of organisms is
accompanied by an increase in the complexity of
their organization. From the point of view of
classical thermodynamics it appears as
spontaneous decreasing of entropy of living
systems, which is evidently in contradiction with
II. law of thermodynamics. However, the decrease
of the total entropy of living organisms appears
under conditions of  deS/dt lt 0 and deS/dt gt
diS/dt. It means that the decrease in entropy
inside the living system runs at the expense of
increased entropy in the surroundings.
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Let us consider open system in equilibrium under
constant temperature and pressure with no
irreversible processes running, such as heat
transfer etc. In such a system entropy increases
only as the result of chemical reactions, mass
transfer between phases of the system and
generally in processes characterized by a change
of chemical potential. We shall consider the heat
exchange to proceed only by reversible processes
and then we get for entropy change
dS dqrev/T diS
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We can calculate the entropy production inside
the system diS dS - dqrev /T and after
aritmetical rearrangement we get
diS - dG/T

That can be expressed in
words   The increase in entropy of open system
due to internal nonequilibrium processes is
proportional to the decrease of the Gibbs
function of the system.
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If we will study the changes of the state
parameters in chemical reactions, when changes in
the number of moles appear, we obtain expressions
for the chemical potential µ   (dU/dni)S,V
(µi)S,V (dH/dni)S,P (µi)S,P (dG/dni)T,P
(µi)T,P (dF/dni)T,V (µi)T,V

Concomitantly  
(µi)S,V (µi)S,P (µi)T,P (µi)T,V
µi
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The relationship between entropy increase,
decrease of Gibbs energy, change in composition
and in chemical potentials in open system can be
expressed like this diS - dG/T - 1/T S
µidni
  diS/dt - 1/T (dG/dt)
- 1/T S µi (dni/dt)
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dni ?i d?

and d? 1/ ?i dni

  The reaction rate is
given   v 1/ ?i (dni/dt)

  After substituting for dni we get   v
d?/dt
For the change of mols of reacting substance we
get   dni/dt ?i v ?i (d?/dt)
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And we obtain expression for the increase of
entropy in the system diS/dt - 1/T S µi ?i
(d?/dt) - 1/T S µi ?i v
  As the reaction rate is equal for all
components i, we get   diS/dt - 1/T (v) S
µi ?i
we introduce
W - S µi ?i (dG/ d?)T,P
  which
represents work done by the system after
all reactions run through
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and for the rate of entropy production we
get   diS/dt Wv/T

This can be expressed in words the rate of
entropy production in open system under constant
temperature and pressure is given by product
of reaction rate and the work done by the
system.  
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Now we introduce expression for the rate of
entropy production in unit volume T 1/V
(dS/dt)
  and
function ?   ? T T

The function? is
proportional to the rate of entropy in unit
volume and is called dissipative function
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We can rewrite it in general expression   ?
T T S Ji Xi gt 0
where
Ji ...... rate of flux of the process
Xi ..... driving force of the process   ?
depends on the rate of flux and driving force of
the process, which are time-dependent parameters,
therefore ? is also a function of time   ?(t)
S Ji(t) Xi(t)

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In equilibrium X equals J, as it holds under
equilibrium that X 0, J 0. We can thus assume
that close to equilibrium there is a linear
relationship between fluxes and forces and flux
is a function of force   J J(X)

and it holds J(X)
L(X)
This equation
represents linear phenomenological relationship
between the parameters of generalized fluxes and
forces, and the coefficient L is called linear
phenomenological coefficient
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If we have a linear system close to equlibrium,
we can write expression for the rate of entropy
production in the system   diS/dt 1/T S Jj
Xj gt 0
In agreement with II. law of
thermodynamics this change must be positive.
Although the overall sum must be positive, inside
system can proceed one ore more processes for
which we can write   diS'/dt 1/T S Jk Xk
0 i.e. there are processes during which
the entropy of the system decreases

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These conclusions in such a simple form holds
true only for linear relationships close to
equilibrium. Living systems, however, are
nonlinear systems far from equilibrium, in which
irreversible processes proceed.
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In agreement with II. law of thermodynamics
any irreversible process is accompanied by heat
of dissipation. In open system it is possible
that this heat leaves the system and the total
entropy of the system stayes constant, or even
decreases.
We can write for the rate of entropy production
in non- linear systems dS/dt deS/dt
diSn/dt diSd/dt
where diSn/dt ..... part of
entropy production bound in the
system diSd/dt ...... part of
entropy production crossing the
boundaries of the system
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Analogicaly with the preceding situation we
have function ? ? ?n
?d
where
?n ..... function of bound dissipation
?d ..... function of outer dissipation   Accordi
ng to the principle of the least outer
dissipation of energy In the stationary state
of any thermodynamics system, the function of
outer dissipation reaches the least
possible values. 
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Physiology has been using long time the term,
which is very close to the concept of the
stationary state in the thermodynamics of
irreversible processes. It is basal metabolism.
Basal metabolism measured as the rate of heat
production or breathing represents the lowest
metabolism of an animal in rest. It is thus
characterized by minimal rate of heat production
(minimum of the function of outer dissipation of
energy), that corresponds the concept of
stationary state.
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The stationary state of living systems differs
from the stationary state of sipmple
physical-chemical systems. This difference
consists in the fact, that in the simple systems
the stationary state is given by the outer
parameters and stayes stable only under
maintained outer conditions. On the other hand,
living systems are able to resist the changes
of the outer environment by means of regulation
and control of the inner processes. Thus to
describe the stationary state of living systems
it is more appropriate to use the term
homeostasis, introduced by Cannon.
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As homeostasis we describe the ability of living
organisms to maintain the stability of inner
medium during occurence of random changes in the
outer environment.
Living organisms are, from the point of view of
thermodynamics, open systems far away from
thermodynamic equilibrium. They are controlled
and regulated. Exact thermodynamic theory of such
systems has not been created yet.