BASICS OF THERMODYNAMICS OF LIVING SYSTEMS

Thermodynamics deals with mutual conversion ofdifferent types of energy, the direction of physicaland chemical processes and of equilibria. It alsostudies systems composed of many parts.

As a system

we consider any region of space separated from itssurroundings

According to the interaction of the system with itssurroundings we discriminate systems:

isolated – do not exchange matter or energy with surroundings

closed – exchange only energy with surroundings, not matter

open – exchange both matter and energy with surroundings

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 thesystem (concentration of chemical components,temperature, electrical potential)

The studies of the relationship between extensive and intensiveparameters create the basis for the formulation of thermodynamiclaws. 

The basic laws of thermodynamics are:

law of conservation of mass

I. law of thermodynamics

II. law of thermodynamics

III. law of thermodynamics

I. law of thermodynamics

If a system is doing a work or the surroundings is doinga work on the system, its internal state is changed.E.g. if we compress a gas in a cylinder with a pistonthe temperature of the gas increases. Similarly, if there isa chemical reaction between the components of thesystem, its temperature changes. Or, if you consider aniceberg moving on rocky surface, the friction producesheat and the iceberg changes its phase – it melts. Thecause producing the change of the state is called energy.

Energy can be thus defined as the ability to change given(equilibrium) state of matter.

Initial experimets indicated an equivalence between heatand mechanical work (the work produces heat and heatcan 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 energyfrom nothing. That means it is not possible to produce aperpetuum mobile of the first kind.In a more general formulation:The total energy of isolated system is constant during allprocesses.

So we can expres the I. law of thermodynamics in this wayThe total energy that a system exchanges with surroundings in any process is dependent only onthe 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 toenergy exchanged between the system and surroundings.This function is calledinner energy of the system and is labelled as U.

ΔU = 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 andfinal state of the system

The I. law of thermodynamics implies that total heatreleased in a chemical reaction will be the same if thereaction 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

This conclusion is known as the Hess law.

Now we can introduce new thermodynamic function.It is called enthalpy, labeled H, and defined by anequation:

H = U + PV where P is pressure and V volume of the system

Now we can calculate the amount of heat released inthe system under constant pressure:

qP = H2 - H1 = ΔH

This expression says that the change of enthalpy inany process is dependent only on the initial and finalstate 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 thereaction.

Reaction heat is the amount of heat exchanged by thesystem 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 asendothermic process.

If the reaction proceeds under constant volume, the reactionheat 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. 

II. law of thermodynamics By the beginning of 19th century Carnot studied theefficiency of heat machines. He created a concept ofcyclically working heat machine, in which the volume inthe cylinder was changed by interaction with two heatexchangers having different temperature. Theoreticalwork out of this concept led to the formulation of the theorem:

All the reversible machines working between the same heatexchangers have the same efficiency in spite of thecomposition of the exchangers.

Related formulation was stated by Clausius: It is not possible to construct an equipment that would donothing else than transfer heat from the colder body to awarmer body.

This implies that it is not possible to create the so calledperpetuum mobile of the second kind.

 These formulations are the expressions of the II. law of thermodynamics

The studies of the efficiency of heat engines revealedthe existence of a new state function called entropy labeled S 

dS = dq/T (4) According to Carnot theorem the efficiency of reversiblemachine is maximum. Thus, the irreversible machineshave always lower efficiency. For the irreversible process we get:

dS > dq /T (5) 

If the system does not exchange heat with surroundingswe get for irreversible process: 

dS > 0 (6) and for reversible process: 

dS = 0 (7) It means that entropy is growing under irreversibleprocesses and in equilibrium, when only reversible processes can proceed, it does not change. Entropy can be looked upon as a measure of spontaneousness, as itincreases during spontaneous processes.

Energy functions F and G For the case of reversible process we get from theI. law of thermodynamics: 

dU = dqrev - dwrev

For dqrev we substitute from the definition of entropyTdS:

 dU = TdS - dwrevFrom this equation we can deduce that work done by the

system under reversible conditions can be expressed usingbasic thermodynamic parameters T, U, S.

We can substitute for TdS : 

TdS = d(TS) - SdT  In the case of a process under constant temperaturedT = 0 and TdS = d(TS), and the equation can be rewritten

dU - d(TS) = d(U - TS) = -dwrev  

For a finite change we get: 

Δ(U - TS) = -dwrev

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

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 processunder 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

And for the finite change: 

Δ(U - TS + PV) = -w,rev

 We can see another state function (U - TS + PV), thedecrease of which indicates maximum useful work thatcan be done by the system under constant pressure andtemperature. It is called Gibbs function and labeled G: 

G = U + PV - TS = H - TS

III. law of thermodynamics The formulation was developing in time. As a definitiveversion is considered the formulation by Planck from1912:

Entropy of every chemically homogenous condensed phaseapproaches 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. 

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 isolatedfrom surroundings and let suficient time to evolve until it isnot changing any more. This final state will correspond tothe most probable arrangement, characterized by thehighest degree of disorganization, when entropy reachesits maximum value.

Chemical reactions are characterized by equilibriumconstant K, which describes the composition of the reaction mixture under situation when the reactionrate from left to right equals the rate from right to left.

For the change of Gibbs function in equilibrium statewe obtain:

- ΔG = RT ln K.

Living systems are open systems. In the living biologicalsystem taken as a whole we can not expect thermodynamicequilibrium, as the system in equilibrium can not do work.However, the ability to do work is essential for themaintenance 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.

The total entropy of an open system can be changedeither 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 bothpositive and negative values,diS/dt is only positive.

Under stationary state the rate of entropy production is constant, thus dS/dt = 0, and therefore│deS/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 entropyfrom the system equals the rate of entropy productioninside the system.

Development and growth of organisms is accompanied byan increase in the complexity of their organization. Fromthe point of view of classical thermodynamics it appearsas spontaneous decreasing of entropy of living systems,which is evidently in contradiction with II. law ofthermodynamics.

However, the decrease of the total entropy of living organisms appears under conditions of  deS/dt < 0

and │deS/dt│ > diS/dt.

It means that the decrease in entropy inside the livingsystem runs at the expense of increased entropy in the surroundings.

Let us consider open system in equilibrium under constant temperature and pressure with no irreversibleprocesses running, such as heat transfer etc. In such asystem entropy increases only as the result of chemicalreactions, mass transfer between phases of the systemand generally in processes characterized by a change ofchemical potential. We shall consider the heat exchangeto proceed only by reversible processes and then we getfor entropy change:

dS = dqrev/T + diS

We can calculate the entropy production inside the systemdiS = 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 decreaseof the Gibbs function of the system.

If we will study the changes of the state parameters inchemical reactions, when changes in the number of molesappear, 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

The relationship between entropy increase, decrease ofGibbs energy, change in composition and in chemical potentials in open system can be expressed like this:

diS = - dG/T = - 1/T Σ μidni

 

diS/dt = - 1/T (dG/dt) = - 1/T Σ μi (dni/dt)

dni = υi dλ

and dλ = 1/ υi dni

 The reaction rate is given: 

v = 1/ υi (dni/dt)

 After substituting for dni we get:

 v = dλ/dt

For the change of mols of reacting substance we get: 

dni/dt = υi v = υi (dλ/dt)

And we obtain expression for the increase of entropyin the system:diS/dt = - 1/T Σ μi υi (dλ/dt) = - 1/T Σ μi υi v

 As the reaction rate is equal for all components i, we get: 

diS/dt = - 1/T (v) Σ μi υi

we introduce:

W = - Σ μi υi = (dG/ dλ)T,P

 which represents work done by the system after allreactions run through

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 underconstant temperature and pressure is given by product ofreaction rate and the work done by the system. 

Now we introduce expression for the rate of entropyproduction in unit volume:

Θ = 1/V (dS/dt)  and function Ψ: 

Ψ = T Θ The functionΨ is proportional to the rate of entropy inunit volume and is called dissipative function

We can rewrite it in general expression: 

Ψ = T Θ = Σ Ji Xi > 0

where Ji ...... rate of flux of the process

Xi ..... driving force of the process

 Ψ depends on the rate of flux and driving force of theprocess, which are time-dependent parameters, thereforeΨ is also a function of time: 

Ψ(t) = Σ Ji(t) Xi(t)

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

J = J(X) and it holds:

J(X) = L(X) This equation represents linear phenomenologicalrelationship between the parameters of generalizedfluxes and forces, and the coefficient L is calledlinear phenomenological coefficient

If we have a linear system close to equlibrium, we can writeexpression for the rate of entropy production in the system: 

diS/dt = 1/T Σ Jj Xj > 0 In agreement with II. law of thermodynamics this changemust be positive. Although the overall sum must bepositive, inside system can proceed one ore more processesfor which we can write: 

diS'/dt = 1/T Σ Jk Xk ≤ 0

i.e. there are processes during which the entropy ofthe system decreases

These conclusions in such a simple form holds trueonly for linear relationships close to equilibrium. Livingsystems, however, are nonlinear systems far fromequilibrium, in which irreversible processes proceed.

In agreement with II. law of thermodynamics anyirreversible 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

Analogicaly with the preceding situation we havefunction Ψ:

Ψ = Ψn + Ψd

where Ψn ..... function of bound dissipation

Ψd ..... function of outer dissipation

 According to the principle of the least outer dissipationof energy:

In the stationary state of any thermodynamics system, thefunction of outer dissipation reaches the least possiblevalues. 

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 isbasal metabolism.

Basal metabolism measured as the rate of heat productionor breathing represents the lowest metabolism of an animalin rest. It is thus characterized by minimal rate of heatproduction (minimum of the function of outer dissipationof energy), that corresponds the concept of stationarystate.

The stationary state of living systems differs from thestationary state of sipmple physical-chemical systems. Thisdifference consists in the fact, that in the simple systems thestationary state is given by the outer parameters and stayesstable only under maintained outer conditions. On the other hand, living systems are able to resist the changes ofthe outer environment by means of regulation and controlof the inner processes. Thus to describe the stationary state of living systems it is more appropriate to use theterm homeostasis, introduced by Cannon.

As homeostasis we describe the ability of living organismsto 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 thermodynamicequilibrium. They are controlled and regulated. Exactthermodynamic theory of such systems has not beencreated yet.