Thermodynamics. Thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature,

Thermodynamics

Thermodynamics

Thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature, volume and pressure.

A thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration. A hypothetical boundary separates the system from the rest of the universe.

A useful classification of thermodynamic systems is based on the nature of the boundary and the quantities flowing through it, such as matter, energy, work, heat, and entropy. A system can be anything, for example a piston, a solution in a test tube, a living organism, an electrical circuit, a planet, etc.

Isolated systems are completely isolated in every way from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system would be an insulated rigid container, such as an insulated gas cylinder.

Closed systems are able to exchange energy (heat and work) but not matter with their environment. A greenhouse is an example of a closed system exchanging heat but not

work with its environment. Whether a system exchanges heat, work or both is usually thought of as a

property of its boundary.

Open systems: exchanging energy (heat and work) and matter with their environment. A boundary allowing matter exchange is called permeable. The ocean, human body, cells would be examples of open thermodynamic systems.

A macrostate and a microstate are two very different ways of looking at a system. (Admittedly, a macrostate always has to involve an amount of matter large enough for us to measure its volume or pressure or temperature, i.e. in “bulk”.

But in thermodynamics, a microstate isn't just about a smaller amount of matter', it is a detailed look at the energy that molecules or other particles have.) A microstate is one of the huge number of different accessible arrangements of the molecules' motional energy for a particular

macrostate.

A macrostate is the thermodynamic state of any system that is exactly characterized by measurement of the system's properties such as p, V, T, H and number of moles of each constituent. Thus, a macrostate does not change over time if its observable properties do not change.

• In contrast, a microstate for a system is all about time and the energy of the molecules in that system. In a system its energy is constantly being redistributed among its particles. In liquids and gases, the particles themselves are constantly redistributing in location as well as changing in the quanta (the individual amount of energy that each molecule has) due to their incessantly colliding, bouncing off each other with (usually) a different amount of energy for each molecule after the collision..

• Each specific way, each arrangement of the energy of each molecule in the whole system at one instant is called a microstate.

How can we find out how many microstates are accessible for a macrostate? (Remember, a macrostate is just any system whose thermodynamic qualities of P, V, T, H, etc. have been measured so the system is exactly defined.) Fortunately, Ludwig Boltzmann gives us the answer in

S = kB ln W,

where S is the value of entropy in joules/mole at T,

kB is Boltzmann's constant of 1.4 x 10-23 J/K and W is the number of microstates, called the thermodynamic probability.

Spontaneous events occur only when energy spreads out and entropy increases.

• Entropy increase predicts what physical and chemical events will happen spontaneously - in the lab and everywhere in the world since its beginning.

• That's why entropy increases can be called "time's arrow". Energy continually disperses and spreads out in all natural spontaneous events. (It's our experience all our lives with spontaneous natural events that gives us our psychological feeling of "time" passing

• The internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of atoms within molecules or crystals.

• It includes the energy in all of the chemical bonds, and the energy of the free, conduction electrons in metals.

First law of thermodynamics

The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy (Q) supplied to or removed from the system and the work (W) done on or by the system.

ΔU = W + Q

Heat energy (Q) supplied to the system and the work (W) done on the system are positive.Heat energy (Q) removed from the system and the work (W) done by the system are negative.

Second law of thermodynamics

• Not all processes, that theoretically might occur according to the first thermodynamic law, will ever occur in nature. .e. g. .:

• When we touch together a hot and a cold object, we observe that energy is passed away from the wormer to the cooler object. We never observe opposite situation.

• Substance dissolved in solvent diffuses from the areas with higher concentration to the areas with lower concentration. The direction of difusion is never from lower to higher concentration.

• All thermodynamic processes can occur spontaneousely in specified direction only – from more ordered states to less ordered states.

• The processes are irreversible.

A

BA

B

S2

S1

S2 > S1

• It is not possible for the system to become spontaneousely ordered again. Gas particles will not gather again in containar A, while containar B will not become spontaneousely empty.

• It is possible to empty containar B, but this process will not be spontaneous. If we perform the process, then the entropy of the system will be decresed.

Second law of thermodynamics, about entropy(S):

• The total entropy of any isolated thermodynamic system always increases over time, approaching a maximum value.

• ΔS >= Q / T

• In order to discribe thermodynamic functions phisicists use a concept of an ideal gas.

• An ideal gas is a theoretical gas composed of a set of randomly-moving particles that do not have any volume (points) and that do not interact (except through elastic collisions).

• It means that internal energy of an ideal gas is equal to sum of kinetic energies of all its particles.

• The internal energy of a gas is hard to measure, but the

temperature of a gas is easy to measure, thus to measure internal energy of an ideal gas we use temperature:

• U = f (T)

• (p V) / T = const

• An ideal gas can undergo following processes:– isothermal process,

– isobaric process,

– isochoric process,

– adiabatic process.

Isothermal process• An isothermal process is a change of a

system, in which the temperature remains constant:

ΔT = 0.

• In isothermal processes internal energy remains constant:

Q + W = 0

Let us consider 2 states of a system, which went through isothermal process:

• The system in both states has the same internal energy.• The spontaneous change from state 1 to state 2 is possible, thus

S2 > S1.

• It means it is less probable that the system in state 2 will do work.• Even though the internal energy stays unchanged, capability of

doing work has decreased.• Thus we observe here degradation of internal energy.

p1V1

p2V2

T

T U

U

• Another thermodynamic function is enthalpy H enthalpy (H), which is defined to be the sum of the internal energy (U) plus the product of the pressure (p) and volume (V):

H = U – p V

• Enthalpy of the system in state 1 is:

H1 = U - p1V1

• Enthalpy of the system in state 2 is:

H2 = U – p2V2 • Since p1V1 = p2V2 , thus H1 = H2

Enthalpy (H)• A partial measure of the internal energy of a

system. Enthalpy cannot be directly measured, but changes in it can be. If an outside pressure on a system is held constant, a change in enthalpy entails a change in the system's internal energy, plus a change in the system's volume (meaning the system exchanges energy with the outside world).

• For example, in endothermic chemical reactions, the change in enthalpy is the amount of energy absorbed by the reaction; in exothermic reactions, it is the amount given off.

• In spontaneous processes entropy incresses. Thus disorder in the system incresses, while capacity of a system to do work decresses.

• Internal energies of two systems may be equal, while their degrees of disorder may be different. That is the reason for using other thermodynamic quantities: Helmholtz free energy (F) and Gibbs free energy(G)

• F = U – TS• G = H – TS, H = U + pV, • H – enthalpy

• Helmholtz free energy (F) = „free energy”

• Gibbs free energy(G) = „free enthalpy”

• F = U – TS, G = H – TS• Since S1 < S2 , thus functions F and G will be different for

state 1 and state 2.

• F1 = U – TS1, F2 = U – TS2 => F1 > F2

• Likewise G1 > G2 • Even though internal energy stayed unchanged, both free energy and

free enthalpy decreased.

p1V1

p2V2

T

T U

U

• In spontaneous processes free energy and free enthalpy decreas.

• Δ F < 0

• Δ G < 0

• These 2 functions shows ability of a thermodynamic system to do work.

• F – the part of internal energy that can be changed into work.

• G – the part of enthalpy that can be changed into work.

fetal stage death

fertilizationdeath

birth

birth

old age

adult

• The picture shows changes of entropy during human life: from fertilization till death.

• During the fetal stage entropy per unit of mass decresses. It means that the processes of human development is not a spontaneous process. Structures that are created are more and more ordered.

• Entropy still drops in postnatal growth, babyhood, childhood and youth. Then it doesn’t change for many years.Finally it incresses again leading to death.

disease

diseasedisease

• A disease causes entropy to increase. When a person will get healthy again, the level of entropy will decrease back.

• Since F = U – TS, thus increase of entropy is associated with dicrease of free energy.

• This fact can be confirmed with your experience: while a human is ill, entropy is big, which means that free energy is small and the ability to work by a sick person is small.

Multicomponent systems

• Introduction of an additional particle to a multicomponent system leads to change in Gibbs free energy of the system.

• Change of free energy caused by adding 1 mole of i-th substance is called chemical potential of i-th substance.

• Such change also causes change of internal energy of the system.

• The chemical potential of a thermodynamic system is the amount by which the energy of the system would change if an additional particle were introduced, with the entropy and volume held fixed.

• If a system contains more than one species of particle, there is a separate chemical potential associated with each species, defined as the change in Gibbs free energy when the number of particles of that species is increased by one.

• The chemical potential is a measure of how much the free enthalpy (or the Gibbs free energy) of a system changes (by dGi) if you add

or remove a number dni particles of the particle

species i while keeping the number of the other particles (and the temperature T and the pressure p) constant:

• i =  G/ ni  ·  dni

• Δ G = i Δ ni

• The fist law of thermodymanics for open systems:

ΔU = W + Q + Σ i Δ ni

W – mechanical workQ – heatΣ i Δ ni - chemical work

• How does Gibbs free energy change, when

Δ ni moles of a certain substance is

moving form area with chemical potential ’i for the substance, to area

where its potential is ”i ?

’i”i

• ΔG1 = - ’i Δ ni

• ΔG2 = + ”i Δ ni

• ΔG = ΔG1 + ΔG2 = (- ’i + ”i) Δ ni (1)

• If the process is spontaneous, then ΔG<0. Thus

’i > ”i

• Ability to do work depends on difference between chemical potentials.

’i”i

• The equation:

• ΔG = ΔG1 + ΔG2 = (- ’i + ”i) Δ ni (1)

lets us formulate condition in which exchange of substances is possible.

In isothermal and isobaric processes condition for thermodynamical equilibrium is when ΔG = 0, thus

(- ’i + ”i) Δ ni = 0

’i = ”i

• If in two species we have i different substances, then the system is at thermodynamic equillibrium, when chemical potential of each substance separately is the same in every point.

Chemical potential of extremely diluted solutions

• μi = μ0 + RT ln xi + Vip + zi FUe

• μ0 – standard chemical potential

• xi - i-th substance concentration, where

xi = ni / (n1 + n2 + ...) precisely it is molar fraction of i-th substances

• Vi - molar volume

• Ue - electrical potential caused by ions in

dilution

• Non-electrolyte solution:

μi = μ0 + RT ln xi + Vip

• Electrolyte solution, p=0:

μi = μ0 + RT ln xi + zi FUe

• Non-electrolyte solution and p=0:

μi = μ0 + RTln xi

• The change of the chemical potential of i-th substance while flowing from one space to another:

• Δμi = μ”i – μ’i = = RT ln (x”i / x’i) + ViΔP + zi FΔUe

• [J/mol] – unit of chemical potencial

• Condition for flow of i-th substance is Δμi <> 0

RT ln (x”i / x’i) + ViΔP + zi FΔUe <> 0• condition for thermodynamical equilibrium is

Δμi = 0

Koniec

• W procesach zachodzących samorzutnie rośnie entropia (tzn. maleje stopień uporządkowania układu) i zmniejsza się zdolność układu do wykonania pracy.

• Układ może mieć taką samą energię wewnętrzną, a różnić się stopniem uporządkowania, dlatego wprowadza się kolejne funkcje termodynamiczne: energię swobodną Helmholtza (F) oraz enrgię swobodną Gibbsa (G).

• F = U – TS• G = H – TS, H = U + pV, H – entalpia• F – ta część energii wewnętrznej, która może być

zamieniona na pracę.• G – ta część entalpii, która może być zamieniona na

pracę.

• Rysynek przedstawia jak zmienia się entropia w czasie życia człowieka: od momentu poczęcia do śmierci.

• Z rysynku widać, że w okresie płodowym entropia przypadająca na jednostkę masy maleje. Oznacza to, że proces tworzenia człowieka nie jest procesem samorzutnym. Oznacza to też, że tworzone są struktury coraz bardziej uporządkowane.

• W okresie niemowlęcym, dzieciństwie i młodości entropia w dalszym ciągu maleje. Utrzymuje się na stałym poziomie w okresie dojrzałości, zaczyna rosnąć, gdy zaczyna się okres starości.

• Kolejne rysunki pokazują, że w stanie choroby entropia rośnie. Gdy człowiek wyzdrowieje, entropia ponownie zmaleje.

• Ze wzoru F = U – TS wynika, że wzrostowi entropii towarzyszy spadek energii swobodnej. Jest to zgodne z życiowym doświadczeniem: w stanie chorobowym entropia duża, co oznacza małą energię swobodną, a także małą zdolność do wykonywania pracy przez człowieka chorego.

ENERGY• In the mechanical sense, work was originally defined in terms of

lifting a weight to a certain height. The quantity of work was defined as the product of the weight and the height. This definition was then generalized, so that work was considered to be done whenever any kind of force is exerted through some distance. The quantity of work is the force multiplied by the distance. When two physical systems interact, one of them may do work on the other. We find it convenient to assign to each physical system a quantity called energy, with the same units as the units of work. Whenever a system does work on its surroundings, we say its energy has been reduced by the amount of work done, and whenever a system has work done on it (by some other system) we say its energy has been increased by that amount of work. By the law of action and re-action, all work that is done by one system is done on another system. It follows that the total amount of energy is conserved. (Notice that we haven’t established the absolute value of energy, we have merely discussed changes in the energy levels.)

• The starting point for most thermodynamic considerations are the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work.

• They also postulate the existence of a quantity named entropy, which can be defined for any isolated system that is in thermodynamic equilibrium.

• In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of system and surroundings. A system is composed of particles, whose average motions define its properties, which in turn are related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.

• Classical thermodynamics is founded on two principles, both of which involve the concept of energy. The first principle asserts that energy is conserved, i.e., energy can neither be created nor destroyed, and the second principle asserts that the overall distribution of energy tends to become more uniform, never less uniform. These two principles are called the first and second laws of thermodynamics.

Laws of thermodynamics

• First law of thermodynamics, about the conservation of energy:

• The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to or removed from the system and the work done on or by the system.

• Second law of thermodynamics, about entropy: • The total entropy of any isolated thermodynamic system always

increases over time, approaching a maximum value.

• Third law of thermodynamics, about the absolute zero of temperature:

• As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value; also stated as: "the entropy of all systems and of all states of a system is zero at absolute zero" or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

• Multicomponent systems

• all systems tend toward disorder• Direction of evolution of a system