5_a Thermodynamics and Heat

8/3/2019 5_a Thermodynamics and Heat

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Thermodynamics

Content of Lecture1. Scope and use of thermodynamics macroscopic system

2. Energy, thermodynamic variables, state and non-state functions3. Reversible and irreversible processes4. Heat, temperature and the zero t h law of thermodynamics5. The first law of thermodynamics6. Adiabatic process and the closed System versus open system7. The second law of thermodynamics and the entropy8. The third law of thermodynamics9. Thermodynamic cycles and Carnot engine

10. The microscopic basis of thermodynamics

11. The second law and equilibrium, temperature scales and thermometers12. Latent heat and heat transfer13. Calorimtrie (Bunzen ice-calorimeter, thermostat, thermocouple and Stefan law

of heat radiation)14. Newton Cooling Law15. Thermal expansion and determination of heat conductivity coefficient

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A sketch that gives a rapid summary of the types of thermodynamic process

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Meaning of the word and scope of the fieldThe word thermodynamics comes from the Greek words therme (heat)

and dynamis (force). The formal study of thermodynamics began in the earlynineteenth century, through consideration of the motive power of work (capacityof a body to do work). Today, the scope includes energy and its relationship with

the MACROSCOPIC properties of matter. Engineers use the principles ofthermodynamics to conceive and analyze natural processes and designing

devices and equipment to meet human needs.Studying thermodynamics is studying energy and its transformations.

More appropriately stated: thermodynamics governs what's possible and what'snot. In fact, thermodynamics is the field of physics that describes and correlates the

physical properties ofmacroscopic systems of matter and energy.The principles of thermodynamics are of fundamental importance to all

branches of science and engineering since they are expressions of global rolesgoverning the behavior of natural systems.

If any of the laws of thermodynamics is violated, you can rest assured theinventor (either knowingly or unknowingly) is misrepresenting his discovery. Thelaws of thermodynamics are descriptions of some of thefundamental phenomena ofnature as observed and concluded by scientists.

Three laws (first, second and third), have been formulated, and there is astatement that is sometimes referred to as the zeroth law of thermodynamics.

Thermodynamic provides a link between several sciences and engineeringdisciplines (physics, biophysics, chemistry, geochemistry, astronomy, physicalchemistry, oceanography, soil science, hydrology, engine designetc.).

It is may be studied in standalone courses, that are normally written to tacklethe major requirements and interests of each of those fields.We will deal only with the broad concepts considered as the main

introductory common parts on any account on thermodynamics in general.Phase change of matter and the chemical and physical reactions (processes)

involve exchange of energy. Consequently, we apply thermodynamics to know,follow and predict the output of processes and the state of matter.

Thermodynamics may be used to predict the temperature at which certainprocess may occur, to understand the sequence of reaction progress and to follow thenature of the reactants and products.

In particular, thermodynamics deals with studying systems at (or close to)equilibrium, assuming that the process is reversible. Thermodynamics neitherdeal with the pathways the system follows to carry out the change, nor with themechanism of reaction. Despite this limitation, thermodynamics is used in studyingequilibrium in the natural systems in geology, soils, water resources, and recently in

biology. Since equilibrium is not reached in most cases on the Earth crust (orreached very slowly), this could seem contradictory. However, kinetics help tounderstand how equilibrium is reached (or why it is not reached!), i.e. there isclose connection between thermodynamic and kinetics.

Purposes and use of thermodynamics1. Following up and understanding the processes that include energy transfer.

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2. Predicting what should result from the change of state in terms of globalparameters; like mass, temperature, pressure, chemical potential, Gibbs freeenergy, entropy, and enthalpy (which refers to the sum of work & internalenergy change), i.e. predicting system behavior.

3. Carrying out virtual experiments when it is difficult to carry them in reality.

4. Generalization of conclusions that we may arrive at, from experimental work.5. Through thermodynamics we can study the natural systems. We know thatequilibrium may not actually be realized, and the natural processes areirreversible and difficult to study. However, we assume equilibrium and anyirreversibleprocess is composed of smallreversibleprocesses to be able tosolve it. This is admissible since the change in internal energy andentropy are independent of pathway (since they are state functions)whereas work and heat depend on the pathway (since they arenon-statefunctions) and the system does not contain work or heat, considering that thethermodynamic process is an action leading to shift of the situation from

one equilibrium to another.In brief, the Uses of Thermodynamics are:

- It has a general applicability in the prediction ofthe behavior of systems underdifferent temperatures, pressures and chemical compositions.

- Ifwe cannot carry out certain experiments (due to very slow rate of reaction,high costs) we may use thermodynamic predictions.

- It is used for the generalization of the output of experimental work.

The macroscopic system

The macroscopic nature of thermodynamics means that we are dealing withthe characteristics of the system as a whole (for dealing with its temperature,volume, temperature capacity, etc.) but we do not deal with the impact of thesecharacteristics on the internal structure and/or arrangement of atoms. Inaddition, we do not deal with the rate of reaction or its mechanism.

The macroscopic system is a central concept of thermodynamics. It is thereason behind the interest in thermodynamics and source of its authority. Themacroscopic system is a geometrically isolated system within an infinite,unperturbed environment. The so-called infinite environment is a mathematicalabstraction of what we can also call a thermal reservoir.

In reality, the environment need only be large enough relative to thestudied system. Thermodynamics is concerned only with the study of systems atequilibrium, When some perturbation takes place, thermodynamics can predictthe new equilibrium (but cannot predict the pathway or the mechanism nor therate of reaction).

However, there is a field of non-equilibrium thermodynamics that will not bedealt with here. In addition, some aspects that cannot be covered bythermodynamics can be covered by kinetics. In fact, there is a close relationship

between kinetics and thermodynamics.

Energy - meaning and typesIt is the capacity for doing work. Energy can exist in many forms:

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1. Radiation, 2. Kinetic (vibration, oscillation, translocation) , 3. potential, 4.chemical, 5. atomic (nuclear) energy, 6. electromagnetic, 7. electric and 8. heat(thermal) energy .

Thermodynamic properties and variables

At equilibrium ,the state of a macroscopic system can be described interms of some measurable properties (temperature pressure volume) known as

thermodynamic variables.Meanwhile, other variables (such asdensity -specific heat- compressibility -

coefficient of thermal expansion) can also be identified and correlated to producecomplete description of a system, and its relationship to its surroundings.

The thermodynamic variables are eitherintensive orextensive.Intensive, i.e. it does not change with the number of moles of matter- Density (kg/m3)- Temperature (K)- Pressure (N m-2)- Chemical potential, = = (J mol-1)Known also as the molar Gibbs free energy

Extensive, i.e.it changes with the number of moles of matter- Gibbs free energy, G (J K-1)- Entropy, S (J K-1)- Enthalpy, H (= Work+ Internal Energy) (J K-1)- Volume (m3)- Mass (kg)

State Functions, and Non-State Functions

State Functions(A function that does not depend on the pathway = trajectory the system willfollow to realize a change. A state function has exact differentials)

- 1- Volume, V

- 2- Internal energy, U- 3- Entropy, S- 4- Enthalpy (H = U + W)

- 5- Gibbs free energy, G- 6- EquilibriumNon-state Functions(A function that depends on the pathway the system will follow to realize a change.A non-state function has inexact differentials)

- 7- Work, W- 8 Heat, Q

Thermodynamic Processes

When a macroscopic system shifts from an equilibrium to another, a process issaid to be taking place. There are two types:

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- reversible (like thawing and freezing). In many processes the idea ofirreversible process is just an idealization. In fact, it may be approached, but not

perfectly achieved. However, its formula is very useful for solving problems when wecannot directly use the formula of an irreversible process, in particular when thestudied variable is a state function (i.e. independent on pathway) since the irreversiblemay be replaced by a series of imaginary reversible steps (that starts from the sameinitial condition, and ends-up at the same final condition as the irreversible process),hence an integration procedure leads to calculating the change that takes placeduring the irreversible process of interest.

- irreversible (evaporation, dissolution, diffusion, gas seepagethrough openings from a high pressure reservoir to a law pressure one, mixing ofsolutions, gas mixing, weathering, rusting of iron, coagulation, aging (growingolder), heat flowfrom a hotter to a colder reservoir, also saline solutions (or ink andwater) do not separate by itself into salt (ink) and water. These one-directional

processes can be studied by the second law of thermodynamics.

Definition of Heat

Heat is defined through thermal energy transfer (for example, from a hotsolid-phase body to a cold liquid; in this case, heat is the energy transferred fromthe first body to the second). That is to say, heat can only be determined when itflows across the boundaries of the hot to the cold body (heat transfer starts only

upon the contact of the two bodies, whereas we consider that neither of these twobodies contain heat before this start). So, heat definition is:

Energy that flows across system boundaries due to their differenttemperatures i.e. heat - just like work - is a transient phenomena, i.e. it canonly be observed during system change. Heat and workhave a common feature:they bothdepend on the pathway,(i.e they are non-state functions).

Laws of thermodynamics

These laws were discovered in the 19th century through painstakingexperimentation. They govern the thermodynamic processes and put limits onthem.

The Zeroth

Law

When two bodies (A) and (B), in thermal equilibrium, are in equilibriumwith a third body (C), the two bodies (A) and (B) will have the sametemperature.

When each oftwo systems is in thermal equilibrium (no heat flow) with a thirdone, the first two systems must be in equilibrium with each other.

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Simple application: you may use a thermometer to measure temperature!Note that for some unknown reason the Zeroth Law came after the First Law.

The First law

This is a law that denies the possibility of creating or destroying energy (andthis is generally known as the energy conservation principle

The Second law

This is a law that denies the possibility of utilizing energy in a particular way(work can be dissipated completely into heat whereas heat cannot be converted100% into work.

This principle reflects the one-sidedness (one directional progress) of thespontaneous - natural - processes.

Definition of Temperature

Difficult to define (since it is related to our sensation of hot and coldbodies). Consequently, we better refer to the equity of temperatures . Thisequity idea leads to the Zeroth law of thermodynamics, and it is the basis of

temperature measurement.

For gases, temperature is a measure of the average kinetic energy of gasmolecules.

In fact, the law of ideal gas can be used to design a thermometer.

Also, there is an implicit idea in this law saying that there is a definiteminimum value of the absolute temperature (i.e. the absolute zero) at which the

volume of the ideal gas is zero (note that real gas should have a given volume atthe absolute zero.)

Temperature definition using the Zero t h Law

The vocabulary of empirical (experimental) sciences is often borrowed fromdaily language. Thus, although the term temperature appeals to common sense, itsmeaning suffers from this imprecise non-mathematical language.

A precise, though empirical, definition of temperature is provided by

the zero

th

lawof thermodynamics.

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From what we previously stated about this law, it is understood that when twosystems are in thermal equilibrium, they share a certain property. This propertycan be measured, and a definite numerical value ascribed to it.

In other words the zeroth law is a consequence of the statement:

Temperature is the shared property of systems in thermal equilibrium.

If any system is placed in contact with an infinite environment or reservoirthat exists at some lower temperature, the system will eventually come intoequilibrium with that environmentthat is, it reaches the same temperature as thesurroundings (we will soon study Newtons Cooling Law that mathematicallydescribes this phenomenon using the first-order kinetic law). Temperatures aremeasured with devices called thermometers (some types of thermometers aredescribed later in an optional part, where we present the basic ideas behind majortypes of thermometer designs).

A thermometer contains a substance with conveniently identifiable andreproducible states, (such as the normal boiling and freezing points ofpure water).

If a graduated scale is marked between two such states, the temperature ofany system can be determined by bringing that system into thermal contact with thethermometer, provided that the system is large enough, relative to the thermometer.

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The First Law of Thermodynamics

Energy can be transferred from one "system" to another in many forms.However, it cannot be created nor destroyed.

Thus, the total amount of energy available in the universe is constant. This

is an expression of the principle ofConservation of Energy.

The first law states that the change of the internal energy, U, isequal to the algebraic sum of the transferred heat, Q and the work done,W:

U= Q - WThis is equivalent to saying that the supplied heat Q is contributing to both theincrease of the internal energy by Uand the work done W, i.e.

Q = U+ WFormulas of the First Law & Thermodynamic Processes

1. adiabaticprocess where there is no heat transfer (Q = 0) and net work(done on or by the system) is the same as the change in internal energy.

U2 - U1= U= -Wi.e.

Enthalpy = (U2 - U1) + W = 0

2.

isochoricprocess, there is no way to carry out work

(so,

W= 0), and

U= Q3. isobaric process, the change of internal energy, heat transferred and work

done could not be zero, so the general formula of the first law is directlyapplicable (like under the atmospheric conditions),

U= Q - WWork can easily be calculated from the relationship:

W=P (V2 - V1)For gases W=P.V = CV

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4. isothermal process, the internal energy (and temperature) does not change,( U= 0) and

Q = WNote:The work done by the system is positive, (so the internal energy decreases),whereas the work done on the system is negative, (so the internal energyincreases),

Adiabatic process - the meaning

A process in which heat does not enter or leave a system. In the atmosphericsciences, adiabatic processes are often used to model internal energy changes inrising and descending parcels of air. When a parcel of air rises in expands (becauseof a reduction in pressure). If no other non-adiabatic processes occur (likecondensation, evaporation and radiation), expansion causes the parcel ofair to coolat a rate of 0.98 degrees per 100 meters. The opposite occurs when a parcel ofairdescends in the atmosphere. The air in a descending parcel becomes compressed.Compression causes the temperature within the parcel to increase at a rate of 0.98degrees per 100 meters.

The adiabatic system can exchange energy with the surroundings in the form ofwork but it does not exchange thermal energy nor matter with them, since its

boundary are thermally isolated.

Adiabatic System

A system that exchanges energy with its surroundings in the form of workbutnot in the form of heat or matter transfer, that is to say its boundaries areconsidered thermally isolated (no heat flow). This is a thermodynamic imaginaryconcept, but it has many important applications since many of the natural systemcould be considered as having good thermal isolation to the extent that it couldbe considered as adiabatic systems.

Closed SystemA system that does not exchange matter with its surroundings, but can

exchange energy with these surroundings (in the form of heat and work).

Open SystemA system that exchanges both matter and energy with its surroundings.

Notes

- Einstein's famous equationE = M C2

(describing the relationship between energy and matter)

supports the credibility of the first law of thermodynamics.- Historically, work units were erg and joule, whereas heat unit is calorie.

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- One calorie is equivalent to 4.186 107 ergs, or 4.186 joules.- We can also, say that

the first law of thermodynamics presents a definition of heat.

A common example of an adiabatic process is the drop in temperature of an

aerosol can, when some of the can's contents are released. Energy was used-up as thegases expanded too quickly for significant heat transfer to occur, hence the dropin temperature. A reverse effect oftemperature rise is seen when a gas iscompressed quickly. In addition, various familiar systems, such as automobileengines, exhibit adiabatic phenomena.

How the 1st law has enhanced the conservation of energy principle ?

1. It has extended the scope of the conservation of energy principle to covermechanical work and heat transfer.

2. It has introduced the concept of internal energy and reveals the distribution ofheat between work and internal energy.

3. It provides a practical measurement of the change of internal energy (so, theinternal energy may be indirectly measured knowing its reference level for thestandard state). So, we avoid the details internal energy related to microscopicstructure of matter.

4. It assures that there is only one value for the internal energy for any system in agiven case.

5. It indicates that the total changes that may take place in internal energy in a

cycle made-up of several thermodynamic processes is zero ( U = 0). Also, theinternal energy of an isolated system will stay constant (U = 0) (provided thatthat it does not do work).

6. It indicates that the internal energy of the ideal gas depends only on itstemperature (but for other systems it also depends on pressure).

7. This law is open to include other types of energy and its transfer methods.8. It prevents the invention of an illusionary perpetual machine of the first kind,

which is a machine that does not need heat to do mechanical work.

A perpetual machine of the first kind is a machine that doesnot need heat to perform work. The law of energy conservation (the 1st law ofthermodynamics) rules out = denies the possibility of this imaginaryperpetual machine ever being invented.

The Second Law of Thermodynamics

Heat can never pass spontaneously from a colder to a hotter body.

As a result the natural process that involves energy transfer must have one

direction and all the spontaneously natural processes are irreversible.

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This law also predicts that the entropy of an isolated system left toitself (without human intervention) will always increase with time (if allcomponents are taken into account ).

This law can also be expressed in several ways as follows:

- If we let a natural system to its own, the only change will be towards the statethat has a maximum probability (usual with much more disorder).

- It is impossible to introduce wastes through a discharge point, to produce

nutrients at an input point!

- It is impossible to build an engine capable of heat transfer in continuous circulationfrom a reservoir at low temperature to another one at higher temperature

spontaneously (without work done by an external engine). It is impossible to cool-down the air space inside a refrigerator, or a room, spontaneously and, on thecontrary, we need work to do that task.

- Heat can never be extracted, and completely transformed, into work (since there issomething, which we call the increase of entropy).

This means that engine efficiency can never by 100% . (however, the bestmethod - as stated by Carnot cycle - to improve engine efficiency is to keep thehot end of the system at high temperature, while keeping the cool end at lowtemperature; that is why car engine is cooled down by a water circuit and a fan,while fuel ignition is carried out at high temperature).

- Entropy is ever increasing in the universe due to the progress of the naturalirreversible spontaneous processes.

The second law summarizes some of our familiar daily observations like:

- We cannot use the cow to produce Alfalfa (if we can feed it with its

excretions), only the inverse is possible

- You can never introduce waste gases (CO2 and water) into an engine to get anew non-ignited fuel while pushing the car backward on the road. Only theinverse is possible - that is to say, fuel ignition is an irreversible process.

- If you open a wall that separates two gas chambers each containing differentgas, the two gases mix and you never get the two gases spontaneouslyseparated again, by their own, and return back to their respective originalreservoirs, if you insert again the wall to its original position.

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- Water mixes with salt in a closed vessel (dissolving it), but the mixture neverreturns back to its original state (pure water and salt apart from each other).

- People get older but never the inverse.

- Heating a broken egg, you get an omelet, but you can never use an omelet toget an egg.

In fact, examples of the natural (irreversible) processes are end-less. Allthese observations (feeding cows with Alfalfa and getting excretions, fuel ignitionin an engine and getting wastes, mixing of gases, salt dissolution into water,

people get older, getting an omelet from eggs) are so familiar that their inverse is just a completely funny idea that can never be realized. In reality there isnothing in the fist law of thermodynamics which stands against realizing thisinverse processes (the only condition that is imposed by the fist law is that the

number of joules on both sides is similar). However, the second law presents anadditional condition on the natural process; this is the condition of the directionof the process: natural process has a direction that can never be inverted ; this isthe unidirectional character of nature, and it is the reason behind the ever

increase of entropy in nature.

With the progress of these processes, energy becomes more and moreunavailable. Energy is not lost in these processes, but the opportunity is lost (the

opportunity to covert a portion of the heat flowing out of hot water, for example,

to mechanical work); we say the universe is run-down to that extent, and this isthe true significance of the term irreversible . The tendency of all naturalprocesses is to bring about a uniformity of temperature, pressure, composition,

etc., at all points. One may visualize a distant future in which, as consequence ofthese processes, the entire universe has attained a state of absolute uniformitythroughout. When, and if, such a state is reached, although there would be nochange in the energy of the Universe, all physical, chemical, and presumably

biological processes would have to cease . This goal toward which we appearheaded has been described the heat death of the universe .

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- Entropy (J K-1) - the meaning

It is a measure of disorder (randomness) of energy (and matter) in asystem. The change of entropy ( S) is defined by the integration of thechange in the transferred heat (dQ) divided by temperature (T):

For an infinitesimal change, we write

1. For an irreversible process, this relation is not directly applicable(but only applicable using a trick, which is replacing the irreversible process by a series of isothermal reversible processes. This isacceptable since entropy depends only on the initial and finalstates), for the irreversible process, entropy is ever increasing: S > 0When mixing equal masses of hot and cold water, entropy increase ofcold water is greater than the entropy decrease of hot water), so the

overall irreversible process leads to a net increase of entropy(S >0).

2. For non-cyclic single reaction, that is infinitesimal and reversibleprocess, underisothermal conditions

i.e., d

Q = T d

S

To calculate total entropy change under isothermal conditions (e.g.ice melting):

i.e.

3. When considering several reversible processes in a cycle process(like Carnot cycle, and thawing-freezing), we get:

This means that the reversible cyclic process is a special case of theirreversible process (with entropy increase in part of the system

balancedby entropy decrease in the other part.

This is the criterion for thermodynamic equilibrium.

In fact, here S = 0, since cycles (like Carnot cycle) have noirreversible process.

Remember, entropy can never decrease in a whole system

undergoing a natural irreversible process.

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4.For an adiabatic reversibleprocess (reversible adiabatic expansion or

adiabatic compression), there is no heat transfer(dQ = 0) so, there isno change in entropy(dS= 0).

This is known as an isentropic process.

But for an irreversible adiabaticprocess (like free expansion of a gaswithout doing work on a piston), there should be a given amount ofentropy change that can only be calculated using a trick (replacingthe irreversible adiabatic process by a series ofisothermal reversibleexpansion - for the case of free expansion - for example, that can besolved using equations applicable to the reversible process).

For the natural irreversible process which takes place when thermalimbalance exists between two systems (like heat flow from a hot bodyto a cold on in contact or by mixing), before doing the process there

existed an opportunity for developing mechanical work. Thisopportunity becomes irrevocably (= irreversibly orirretrievably) lost if the systems were allowed to come intothermal equilibrium in an uncontrolled way. (the simpleinterpretation is: Even if you do get something, you won't get as much as you

thought you might!).

Note:Combining the 1st law

U=Q - Win its isobaric infinitismal form (where V.dP = 0)

dU=dQ - dW

with the 2nd law for a reversible reaction

dQ=T dS

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Note

The second law of thermodynamics gives a definition of a property called

entropy

Entropy can be thought ofas a measure of how close asystem is to equilibrium (it is at maximum at equilibrium ,whereas internal energy is at minimum ) .

Entropy can also be thought of as a measure of the disorder inthe system.

The second law states that the entropy of an isolated systemcan never decrease.

Thus, when an isolated system achieves a configuration of maximumentropy, it can no longer undergo change: It has reached equilibrium(e.g. thermal equilibrium to which hot and cold water reachwhen they are put into contact, or mixed).

We can say that Nature seems to prefer disorder, or chaos.

It can be shown that the second law stipulates (= imposes a condition) that, inthe absence of a particular work(introduced through a givenhuman arrangement like in refrigerators and air-conditioning),heat cannot be transferred from a region at a lowertemperature to one at a higher temperature.

It is not enough to conserve energy (according to the first law), but a direction

of the natural process must be also respected.

An imaginary machine that would deliver work while violating the secondlaw (by continually draw energy from a cold environment to do work in a hot

environment at no cost) is called a perpetual-motion machine of thesecond kind The second law says that this machine can never be invented.

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The Third Law of Thermodynamics

The second law suggests the existence of an absolute temperature scale thatincludes an absolute zero of temperature (on a plot of the relationship between

pressure on the vertical axis and temperature on the horizontal axis in anisobaric process, the temperature of -273.16 Celsius is obtained at pressure zero). Thethird law of thermodynamics states that:

The Absolute zero cannot be attained by any procedure in a finitenumber of steps. The absolute zero can be approached arbitrarilyclosely, but it can never be reached.

If all the thermal motion of molecules (kinetic energy) could be removed, a

state called absolute zero would result and all energy would be randomlydistributed.

Absolute Zero = 0 degrees Kelvin = -273.15 degrees Celsius.

For all materials, entropy is zero at absolute zero.

At any other temperature (T), we can calculate the value of entropy for the

material in an reversible reaction from the relation defining the heat capacity:

d

Q = m C dT i.e. C = d

Q / m d

T

In addition, for a reversible process , we already know that

dS That is to say dQ=TdSBy substitution: C = TdS / m dT

dS = m CdT= m C

Consequently, the value of entropy, S, can be obtained by integration ofthis equation (and the term under the integral in the right-hand side is normallyformulated as a polynomial, for which the solution is known.) The example of mixingof mass, m, of hot water with a mass, m, of cold water is showing this integration forany of the two bodies: Shot or cold = = m . C . = m . C .

with m mass (of hot or cold water), kg.C specific heat of water (4190, J/Kg . K)

assumed constant for the applied temperature range.T temperature, in degrees KelvinS J / K

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The absolute zero is the temperature at which Carnot ideal calculation of

efficiency (ec) leads to ec = one (i.e. 100%), for a vapor machine (blueline in the following diagram) or an explosion motor (red line in the diagram);something which is completely impossible.

Theoretically, at 20 C (= 20 + 273.15 = 293.16 K) the efficiency ec is 0.38 for thevapor machine, and 0.77 for the explosion motor. However, the real efficiency ismuch less for both for several industrial/technologic reasons.

Note that the x-axis on left-hand side diagram is on Celsius temperature scale,the right-hand side diagram is on the Kelvin temperature scale.

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OPTIONAL READINGThermodynamic Cycles

All the important thermodynamic relations used in engineering are derivedfrom the first and second laws of thermodynamics. One useful way of discussingthermodynamic processes is in terms of cycles (processes that return a system to itsoriginal state after a number of stages, thus restoring the original values for all therelevant thermodynamic variables).

In a complete cycle, the internal energy of a system depends solely on thesevariables and cannot change. Thus, the total net heat transferred to the systemmust equal the total net work delivered from the system (i.e. respecting the

first law of thermodynamics).

An imaginary ideal cycle would be performed by a perfectly efficient heatenginethat is, all the heat would be converted to mechanical work.

In the 19th-century the French scientist Nicolas Lonard Sadi Carnot, whoconceived a thermodynamic cycle that is the basic cycle of all efficient heat engines,

showed that such an imaginary engine (perpetual machine of the secondkind) cannot exist. Any heat engine must expend some fraction of

its heat input as exhaust (due to the increase of entropy).

The second law of thermodynamics places an upper limit on the efficiencyof engines; that upper limit is much less than 100 percent.

The limiting case is now known as a Carnot cycle.

Carnot Engine

The idealized Carnot engine was envisioned by the French physicist NicolasLonard Sadi Carnot, who lived during the early 19th century. The Carnot engine is

theoretically perfect, that is, it converts the maximum amount ofenergy into mechanical work.

Carnot showed that the efficiency of any engine depends on thedifference between the highest and lowest temperatures reachedduring one cycle.

The greater the difference, the greater the efficiency.

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An automobile engine, for example, would be more efficient if the fuelburned hotter (T2), and the exhaust gas came out of thecylinder at a lower temperature (T1). Note that (T1) and (T2)must be in Kelvin.

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The Microscopic Basis of Thermodynamics

The recognition that all matter is made up of molecules provided a microscopicfoundation for thermodynamics. A thermodynamic system consisting of a puresubstance can be described as a collection of like molecules, each with its individual

motion describable in terms of such mechanical variables as velocity and momentum.

At least in principle, it should therefore be possible toderive the collective properties of the system by solvingequations of motion for the molecules. In this sense,thermodynamics could be regarded as a mere application ofthe laws of mechanics to the microscopic system.

Objects of ordinary sizethat is, ordinary on the human scalecontainimmense numbers (in the order of 1024) of molecules. Assuming spherical molecules,each would need three variables to describe its position and three more to describe itsvelocity.

Describing a macroscopic system in this way would be atask that even the largest modern computer could not manage.

A complete solution of these equations, furthermore,

would tell us where each molecule is and what it is doing atevery moment. Such a vast quantity of information would betoo detailed to be useful and too transient to be important.

Statistical methods were devised therefore to obtain averages of the mechanicalvariables of the molecules in a system and to provide the gross features of the system.

These gross features turn out to be the macroscopic thermodynamic variables.

The statistical treatment of molecular mechanics is called statistical mechanics,and it anchors thermodynamics to mechanics.

Viewed from the statistical perspective, temperature can be definedas a measure of the average kinetic energy of the molecules ofa system.

Increases in temperature reflect increases in the vigor of molecular motion.

When two systems are in contact, energy is transferred between molecules because ofcollisions. The transfer will continue until uniformity is achieved, in astatistical sense, which corresponds to thermal equilibrium.

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Heat can be defined as the kinetic energy of the molecules since itcorresponds to heat and (together with the potential energyarising from interaction between molecules) makes-up the

internal energy of a system.

The conservation of energy, a well-known law of mechanics, translatesreadily to the first law of thermodynamics,

The concept ofentropy translates into the extent of disorder on themolecular scale. By assuming that all combinations of molecular motion are

equally likely, thermodynamics shows that the more disordered the state

of an isolated system, the more combinations can be foundthat could give rise to that state, and hence the morefrequently it will occur. The probability of the moredisordered state occurring overwhelms the probability of the

occurrence of all other states. This probability provides astatistical basis for definitions of both equilibrium state andentropy.

Finally, temperature can be reduced by taking energy out of a system, that is,by reducing the vigor of molecular motion. Absolute zero corresponds to the state ofa system in which all its constituents are at rest. This is, however, a notion fromclassical physics.

In terms of quantum mechanics, residual molecularmotion will exist even at absolute zero.

An analysis of the statistical basis of the third law goes beyond the scope of thepresent discussion.

The Second Law and Equilibrium

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For all materials, the entropy is zero at the absolute zero. At anytemperature (T), we can calculate the change of entropy for a material in areversible process from the relation defining the specific heat capacity:

dQ = m C dT i.e. C = dQ / m dT

In addition, for a reversible process , we already know that

dS That is to say dQ=TdSBy substitution: C = TdS / m dT

dS = m CdT S = m CNote: If we deal one mole of material we do not use the mass

mConsequently, the value of entropy, S, can be obtained by integration of

this equation (and the term under the integral in the right-hand side is normallyformulated as a polynomial, for which the solution is known.) The example of mixingof mass, m, of hot water with a mass, m, of cold water is showing this integration forany of the two bodies:Shot or cold = = m . C . = m . C .

with m mass (of hot or cold water), kg.C specific heat of water (4190, J/Kg . K)

assumed constant for the applied temperature range.T temperature, in degrees KelvinS J / K

In the chemical application of thermodynamics, we are interested in a state

function known as Gibbs free energy(G) and its change(dG).In fact, Gibbs free energyis a measure that determines the free enthalpy

(the energy that is free for carrying out the reaction). i.e., a measure that determinesthe chemical work(a type of work that differs from the usual gas work that dependson the change of volume and pressure).

In fact, we are always interested in knowing the change of Gibbs free

energy (G) to compare the free energy of materials (i.e. to know the amount ofheat available, between two materials, to carry out a reaction), instead of looking

for the absolute value of Gibbs free energy). In other words, (G) is the motiveforce that drive the reaction.

G = H - T.S

G = H - T.SWhere

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G Gibbs free energy change, in J/kg, or, in kJ/mole.H enthalpy (= U+ PV), in J/kg, or, in kJ/mole.S entropy (disorder or randomness), in J/mole.K.

The term (H - T.S) means: the chemical workdone in order to tackle thenatural tendency of disorder (entropy) increase.

This means also that:a fraction of the energy, in any system, can NEVER appear in the form of work.

The reason: this hidden and lost fraction of energy is already consumed inthe increase of entropy. This is a natural role in the universe; it cannot beavoided.

Reactions will be initiated, and go on spontaneously, as longas the Gibbs free energy difference (the change, G) betweentwo suggested reacting materials is a negative value (G < 0).At G= zero, equilibrium is achieved.

If(S) and (H) are both positive, and T S > H, a melting reaction mayoccur.

If(S) is positive, and (H) is negative, an ignition reaction can occur.If(S) and (H) are both negative, and T S > H, a crystallization (or asolidification) reaction can occur.

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In any other case of sign, reaction cannotoccur (e.g. when both S and H are either positive or negative, andT S < H). In addition, when S is negative and H positive.

In fact, to know if a certain chemical reaction or a certain physical process

can or cannot occur, calculate G for thereaction(by addition of the G of formation for the components phases -,including the reactants and products and their stoichiometric coefficients).If theobtained G is negative the reaction can occur.If it is zero, the reaction is at equilibrium.

We usually use an equality that says that the (Gr)ofreaction is the sumof(Gr), at the standard state, and the term (RT ln Keq)Gr = Gr + RT ln KeqRT ln Keq = Gr - Grl

n Keq = (Gr - Gr)/RT68


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Keq = e(G

r - G

r)/RT

Now, as we know that at equilibrium, G r = zero, consequently,Keq = e

-

G

r/RT

Hence, we use this formula to calculate the equilibriumconstantKeq using Gr obtained from the thermodynamic tables (knowingthe Gf of reactants and products). In addition, we can obtain a calculated Kvalue (the ionic activity product) and compare it with theoretical Keq, in orderto know if a system is at equilibrium, K= Keq), far behind (under-saturated, K

Keq).

In reactions that take place in aqueous solutions, we obtain the intensive

property known as the chemical potential by dividing G by the numberof moles. We write a relation (similar to what is given above) for the

chemical potential, i, of each aqueous species (ions and complexes):i = i + RT ln aiRT l

n a

i = i - iln a i = (i- i)/RTai = e(

i-

i)/RT

Where

ai the activity of the aqueous species (activity is the product ofmolality andactivity coefficient; and the later is the fraction of the total concentration that iscontributes in the reaction).

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OPTIONAL READING

Thermodynamics and Chemical Reactions

In a chemical reaction like:

aA + bB = c C + dDWhere

A, B, C, D concentrations (or activities or pressures) of reactants and product.a, b, c, d their stoichiometric coefficients.

thermodynamics can be used to understand the equilibrium constant K (or the

solubility product, Ksp in the dissolution-precipitation reactions, or the standard half-cell potential in the redox reactions) which describes the tendency of thereactants to form products.

ln K= cln[C] + dln[D] -aln[A] -bl n[B]In a chemical reaction, a change in composition takes place since the

reactants are transformed into products. This is associated with certain changein internal energy (U) that results in difference of the internal energy ofproducts and reactants that reflects the difference in mechanical stability of both(since any amount of macroscopic chemical substance is an agglomeration ofnumerous simple mechanical systems). U can be obtained be four methods:

1. Carrying out the reaction in a constant volume (i.e. under isochoric

conditions) and measuring the emitted (or the absorbed) heat (Qv) which willbe equal to (U). From the first law, U = Q - W, and since W= 0, we get:U = Qv

2. Carrying out the reaction under constant pressure (isobaric conditions) - asusual under atmospheric pressure - and measuring the emitted (or the

absorbed) heat (Qp) which will be equal to the change in enthalpy (H).Enthalpy (which is U under isobaric conditions, is greater under isobaric

conditions than U under isochoric conditions by the work done, i.e. Qp is greater

than Qvby the work done). Enthalpy is a state function that is defined (onlyunderisobaric conditions) as following:

H = U + WH = U + P. V70


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H = Qp- W + P. VH = Qp(In both methods, 1 and 2, when an exothermic reaction takes place, Q will benegative, i.e. energy of products will be lower than energy of reactants, whereas

when an endothermic reaction takes place, Q will be positive, i.e. energy ofproducts will be greater than energy of reactants).

3. when H cannot be measured, Hess Law for constant heat sum is used tocalculate H, but this could be as difficult as the above-mentioned methods.

4. calculating (H R ) for the reaction from formation enthalpy ( H f ) ofreactants and products in their standard states (stoichiometric coefficientsare for sure included). HR=(when the range of temperatures under which the reaction takes place is small,

we suggest that enthalpy of reaction, HR, does not depend on temperaturesince Cp will be small to ignore the integral in the formula for one mole:H2= H1 +under isochoric conditions: i.e. dU = Cv . dTand under isobaric conditions: i.e. dH = Cp . dT

From the second law of thermodynamics, chemically we can predict the

extent to which the spontaneous reaction can develop. Also, the second law givesan interpretation for the direction of the spontaneous reaction (for example, a gas

flows out from a hole - not for decreasing its energy as can be suggested from thefirst law - note that this interpretation based on the first law is not right since gasenergy does not depend on its volume but on its temperature - ; the rightinterpretation is given by the second law: during a spontaneous reaction a materialhas a natural tendency to arrive to a higher disorder - and entropy increase - bythe irreversible reaction which results in producing products which accommodatewith the higher probability of the microscopic states associated with one macroscopicstate, and since the microscopic states can never by described by equations due totheir extremely huge number, the only way we have is to express the macroscopicstate in terms of its entropy).

In the irreversible reaction, the process takes place at a given rate (whichis usually slow; like dissolution, evaporation and solution mixing). If this reactioninvolved a change in temperature or pressure, there should be a substantialdifference between temperature and pressure of the system and its

surroundings, so this reaction cannot be stopped or reversed in direction bymaking a very small change in the external conditions of the surroundings sincethis small change will not be able to supersede the great difference intemperature and pressure (or other thermodynamic functions) between the systemand its surroundings (difference which is originally behind the occurrence of the

irreversible reaction).

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Also, in the irreversible reaction, the work done by the system is smaller(than if the reaction were reversible), and the amount of heat needed by theirreversible reaction is smaller (than that needed if the reaction were reversible).

An irreversible reaction is conveniently replaced by a series of reversiblereactions in order to apply the quantitative estimate of entropy valid only for the

reversible reactions.Contrary to the irreversible process, the reversible process (which is aconceptual simplification that has no real existence) is a process that takes placesuch that state functions does infinitesimally change (so it is sometimes called thesemi-static process) also the state functions of the system are very slightlydifferent from the surroundings. The reversible process (for example, equilibrium,and to some extent precipitation of solid-phases and condensation of water fromvapor) is very fast, and we can control its direction by doing a very small changein surroundings conditions.

Also, in the reversible reaction, the work done by the system is greater

(than if the reaction were irreversible), and the amount of heat needed by theirreversible reaction is greater (than that needed if the reaction were irreversible).We previously said that in a reversible process, entropy is constant (entropychange for the system and its surroundings together is zero; S = 0).

For the reversible process, Gibbs free energy (more precisely Gibbs freeenthalpy for reactions done under constant pressure) is zero (dG = 0).

If the calculated dG was negative (dG


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For liquids evaporation: S =S =And if evaporation is considered as a reversible process (instead of itsreality as irreversible process) taking place under isobaric conditions, theamount of heat Q, added to the system, will be equal to enthalpy of

formation:

Q = HfHence, S = =

For all liquids, S associated with evaporation = approximately 87.9 J K-1.When SR is a smallpositive value, the reaction is irreversible and

the structures of reactants and products are similar (like in evaporation), whereas

if SR was a great positive value, the reaction is irreversible with theatomic structure of the products and reactants being greatly different.

Note that using S for judging if the process is reversible orirreversible requires the recognition of the characteristics of the systemand the surroundings (not only the system), so we need an easier way, or a

simpler criteria, that depends only on system characteristics; this criteriais known as Gibbs free energy G (it is a state function, just like volume,internal energy, entropy and equilibrium, i.e. its change G, does notdepend on the pathway, but only on the initial and the final situations).

End of Optional Reading

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7.1 temperature scales

7.1.1 Celsius (Swedish scientist)Before 1954 two points were selected- upper: water boiling assigned 100 oC (temperature of water and vapor

mixture in equilibrium under 1 a tm).- lower: ice point assigned 0 o C (temperature of water and ice in

equilibrium with saturated air under 1 atm).

After 1954 one point was selected on the ideal gas temperature scalethis point is the tertiary (triple) water point (ice-water-vapor inequilibrium), it is 0.01 oC(and practically, water boiling point = 100 o C).

i.e. there is agreement before and after 1954.

The Absolute Temperature Scale:results from the second law of thermodynamics. Its advantage: on this

scale, temperature does not depend on any thermometry material.Disadvantage: its use is very complicated. So, practically we use the:

Practical International Scale:

based on assignment of different temperatures to some points which canbe easily repeated.

The link between the Absolute Temperature Scale and the Celsius Scale

is the Kalvin Scale.

7.1.2 Fahrenheit7.1.3 Reaumr7.1.4 Kelvin (Lord William Thomson)

OPTIONAL READING74


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7.2 thermometers

7.2.1 Based on solid-phase expansion(bi-metallic thermometer)

- Two metal bands that obviously differ in their thermalexpansion coefficients. The deviation of their free ends are usedto move a pointer (or producing the closure of an electriccircuit).

7.2.2 Based on the expansion of a liquid- Well known! Mercury and colored alcohol filled capillary

connected to a liquid reservoir.

7.2.3 Based on the expansion of gas- Constant volume gas bulb reservoir (kept constant by a

connected U-shape Mercury manometer and to read gaspressure deviation h from atmospheric).

- fitness to ice point- fitness to water boiling point

- fitness to temperature t to be measured=P h atm0 0 + =P h atm100 100 + =P h atmt t +

P P

P P

tt

0

100 0100=

h h

h h

tt

0

100 0 100=

7.2.4 Based on temperature-inducedelectromotive force (e. m. f.)

- temperature difference between the ends of two welded metal

wires produces an e.m.f.

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- fitness to ice, boiling water and temperature t to be measured- thermocouple- Platinum resistance thermometer

- a Wheat

stone bridge is used to measure the electric resistance R.

R R

R R

tt

0

100 0 100=


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7.3 internal energy and thermal energy7.3.1 Internal energy

- Internal energy =

Sum ofKinetic + Potential + Pressure + Chemical + Electric + Nuclear(where Kinetic= transitional + rotational + vibrational)

7.3.2 Thermal energy- defined as energy flow upon contact of two bodies having

different temperatures; as said before.

7.4 heat capacity andspecific heat capacity- Amount of heat to change temperature of a body by 1 degree.- Amount of heat to change temperature of mass unit by 1 degree.

7.5 latent heat7.5.1 Latent heat

- Amount of heat to change state of matters unit mass withoutchanging its temperature. (Melting, vaporization,solidification). (Contrary to sensible heat that can be measured)

7.5.2 Heat of evaporation- Amount of heat to transform liquids mass unit into vapor.

Heat of condensation- Amount of heat to transform vapors mass unit into liquid.

7.6 specific heat measurement (calorimtrie)7.6.1 Based on temperature differences

1- Mixing methodamount of gained heat = amount of lost heatamount of heat = mass * specific heat * temperature difference

= m * S * ( 1 2)

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2- Newton Cooling Law

It is an excellent example on a first order law of kinetics related to heatdissipation from a higher to a lower temperature body (one directional processaccording to the second law of thermodynamics) accompanied by a certainunavailability of energy through entropy increase, but it is also related to the

zeroth law (due to the approach to equality of temperatures of two systems with athird) as long as we are measuring temperatures using a thermometer during thcooling-down process.

From a kinetic point of view, while temperature of the cooling-down body isalways decaying, the rate of cooling (dT/dt) is ever decreasing with the decreaseof the temperature difference (T-C) between the body temperature (T) and roomtemperature (C). This law can be derived as follows:

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Derivation of the Newtons Cooling Lawd T

d t T C

( )

d T

d tk= T C

( )d T k d t = T C .

Divide both sides by (T - C) and

multiply by (-1) to prepare for integration

( )

=1

T C

d T k d t .

By integration of (T-C) at time, t=0 zero

t=t

( )( )

( )

=

1

00

T Cd T k d t

T C

T C tt

. ( ) ( )[ ] = ln lnT C T C k d t tt

0

0

( )

( )

=ln

T C

T Ck tt

0

( )

( )

=ln /T C

T Ck timet

0

( )

( )

T Ct

T Ce

k t

=

0

( )T T C ek t

Ct =

+0

. With kh A

m S

c

p

=.

.

ktemperature decay constant, (in time-1)Room temperature (C) which is assumed constant and >T

h

cthermal convection coefficientA the cross-section aream massSpspecific heat

- Note that the type of this law is frequently used in otherapplications such as radio-active decay, and Beer-Lambert Law,in optics.

- If we know the value of the decay constant, k, Newtons lawcan be used to know time, t

- knowing the values ofk, Sp,A and m, the last formula can beused to determine the value ofhc, but usually we get its valueby dimensional analysis or by experimental work.

Note that specific heatS p can also be obtained using equalcooling rates oftwo different liquids knowing the specific

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heat of one of them (e.g. water) when we heat both to sametemperature then we left them to cool-down in the same room.

Consequently, they cool down during different times, t1 and t2,but the two cooling rates (amount of heat divided by time for

each liquid) are equal (note that the masses of two calorimeters

are mcal 1 and mcal 2 and they are made-up of the samematerial, so their specific heat,Sp cal, is the same). Hence, wecan calculate the unknown specific heat of the liquid,Sp liquid:

( ) ( )m S m S

t

m S m S

t

cal cal water water cal cal liquid liquid 1

1

2

2

+=

+

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Newton's Cooling Law

0

20

40

60

80

100

0 10 20 30 40 50

time, minute

T and T-C oC

T model

data

room temp.

T-C model

data

always temperature differs

27.9

28.1

28.3

28.5

28.7

28.9

50 52 54 56 58 60

time, minute

T,oC

model

room temp.

In the bottom diagram that we use ln of the inverse fraction, hence thenegative sign disappeared.

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OPTIONAL READING

7.6.2 Specific heat measurementbased on latent heat

1- Bunzen ice calorimeter

- Mixing a known heated mass of the body with an ice mass, afraction of ice melts.s

- Using the mass of the melted ice and the latent melting heat (L),the amount ofheat gained by ice is defined, it is equal to heatlost by the body, so bodys specific heat can be determined.

- Preparation of the apparatus for experimental work (page 143).- Mass of molten ice is calculated from the observation of the

recession of Mercury in capillary tube.

mV

V

r l= =

2

10908 10001. .

m * L = m * S *(2 1)

2- Condensation method- hot water vapor at 100oC is inflow is conducted into a

chamber where a body (of mass m1) is suspended at the plate ofa balance, body temperature increases from to 100 o C,

whereas a fraction of vapor condenses (its lost heat is controlledby its latent heat, L, and the condensed mass, m).

m * L = m1 * S * (100 )

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7.7 thermal expansion7.7.1 solid-phase expansion

- longitudinal expansion coefficient (

o

C

-1

).=

L L

T

/or

d L

d T L

1 (T = temperature)- volume expansion coefficient (oC-1).=

V V

T

/or

dV

d T V

1

Suppose the body is homogenous in three dimensions, so:

( )dV L d l =3 2

divide by dT( )d V

d T

L d l

dT=

32

divide by V =L3

( )1 3 123V

d V

d T

L d l

dT L=

( )=

3 1d l

dT L

= 3

7.7.2 liquid-phase expansion

- liquid volume expansion coefficient (oC-1).

real apparent container= +

7.7.3 gaseous-phase expansion- previously dealt with under Charles law.

V Vt

t o= +

1273

7.8 heat transfer

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7.8.1 by convection- Heat flow mode with the movement of fluid particles due to

decrease of density with temperature increase (convectioncurrents).

- Water column stratification in deep lakes.- Flow of air during air-conditioning.- Flow of air from sea-side inland and vice versa during the day.

application:domestic water heating

- hot-water flows upward in the heated reservoir, whereas colderwatersinks down (higher density).

7.8.2 by conduction- Heat Q flow mode (without translocation of particles) due to

heat gradient effect on increasing kinetic energy.

- it depends on heat gradientR, area A and time t :

R d=

1 2Q R

(d= distance)

- exposed cross-section area,A. Q A

- duration, t. Q t

Q A t R

Q k A t

d

=

1 2

Thermal conduction coefficient, k:

( )k

Q d

A t=

1 2

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Determination of heatconductivity coefficient

- By Searles cylinder method- steady state flow of heat is accomplished in the apparatus

(shown in the book page 150), this state is verified by constantreading of four thermometers during enough long time (two inthe metal cylinder and two others in cooling water-tube coil).

- the gradient is created by fixation ofone end of the metalcylinder in a vapor chamber.

- heat transferred by conduction = heat gained by flowing water( )Q k A t

dm S=

=

1 24 3.

( )( )

km S d

A t=

. .

4 3

1 2

- By Lees disk method- The unknown metal disk is inserted between two brass disks.- heating the upper surface of the unknown disk by boiling

water vapor, for long time to accomplish steady state, this stateis verified by constant temperature readings of twothermometers inserted in the upper and lower brass disks.

- Heat transferred by conduction = heat lost by radiation to air

Q k A t d

m S=

=

1 2 .

7.8.3 By radiation- no need for any material medium for heat transfer by radiation.

- Stefan law:( ) R e T T net = . 14 24

e = constant.

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= emission coefficient (fraction in the range from 0T1 = body temperature, k.T2 = surroundings temperature, k.Rnet = net emission by radiation, watt/ m

-2 i.e. Joul-1.s-1.m-2.

- Heat radiation measurementby a thermopile

- The thermopile is a set of thermocouples connected in series.The extreme ends are connected to a galvanometer.

- The welded points are exposed to radiation increases, whereas

the non-exposed welded points are exposed.

- Temperature gradient generates an electric current that canbe read by the galvanometer.

7.9 other applications of heat theories

(thermostats)

- Thermostats are used to control constant temperature in oven,refrigerators and incubators.

7.9.1 Gas release regulator

- When temperature increases, mercury level rises and blocks gasrelease.

7.9.2 Heat electric-regulator

- When temperature increases, mercury rises and contact isensured with a wire closing an electric circuit, this activates a

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magnet, which in turn isolates another electric circuit (includingresistance) that controls temperature in the device to be heated(an oven, for example). This situation is activated as long astemperature is in the defined range.

- When temperature drops, mercury surface drops, the wire becomes isolated, the magnet is inactivated, and the heatingresistance circuit is closed to re-start heating the concerneddevice.

7.9.3 Thermocouple regulator

- Two ends of a thermocouple are welded and connected to theheating circuit inserted into the device to be heated (an oven, forexample), whereas the other ends of the thermocouple areconnected to a galvanometer.

- When temperature increases to the required level, an electriccurrent is generated in the thermocouple and the galvanometerputs off the heating circuit.

- When temperature drops, no electric current is produced in the

thermocouple, so the galvanometers returns back to a positionthat connects the heating circuit, and oven heating restartsagain.


Documents

5_a Thermodynamics and Heat