is for heat

QQIs For Heat

THE LAWS OF THE LAWS OF THERMODYNAMICSTHERMODYNAMICS

fundamentals that can not be fundamentals that can not be negotiatednegotiated

And the 2nd Law of Thermodynamics says…..

TheThe Fundamental Fundamental ConceptConcept

What is heat and how is it different What is heat and how is it different from temperature?from temperature?

Kinetic Theory Of Matter: All atoms Kinetic Theory Of Matter: All atoms are in motion all the time.are in motion all the time.

Heat is a measure of the energy an Heat is a measure of the energy an object has.object has.

Temperature is the average kinetic Temperature is the average kinetic energy of the particles in the object.energy of the particles in the object.

The Kinetic Theory & Ludwig The Kinetic Theory & Ludwig BoltzmanBoltzman

Particles in a container are colliding all the Particles in a container are colliding all the time.time.

These collisions create the pressure inside These collisions create the pressure inside the container.the container.

Boyles Law relates pressure to volume and Boyles Law relates pressure to volume and the Ideal Gas Law relates pressure, the Ideal Gas Law relates pressure, temperature, volume and amount of gas temperature, volume and amount of gas as: as: PV=nRTPV=nRT..

Ludwig Boltzman combined this with the Ludwig Boltzman combined this with the idea of KE to derive KE = 3kT/2 where k idea of KE to derive KE = 3kT/2 where k is Boltzman’s constant. This is how is Boltzman’s constant. This is how temperature is defined.temperature is defined.

Work – A ReviewWork – A Review

We know 2 things We know 2 things about work….about work….

Work is Force x Work is Force x distance W = F ∙ distance W = F ∙ ΔΔdd

For work to be For work to be done an object done an object must change must change position (move).position (move).


The rock experiences The rock experiences no change in position no change in position

W = F ∙ (dW = F ∙ (d22 – d – d11) = 0) = 0

Also, the energy of the Also, the energy of the rock before the rock before the event = energy after event = energy after the event.the event.

UU22 - U - U11 = 0 = 0


Here work is done on Here work is done on the box, but because the box, but because it will not return to it will not return to its starting point, no its starting point, no energy is stored in energy is stored in it.it.

W = F ∙ (dW = F ∙ (d22 – d – d11))

UU22 - U - U11 = 0 = 0

dd22dd11


Work is done against Work is done against gravity and energy gravity and energy is now stored in the is now stored in the box. The energy of box. The energy of the system has the system has increased.increased.

W = F ∙ (dW = F ∙ (d22 – d – d11) = ) = mghmgh

UU22 - U - U11 = P.E. = P.E.

d1

d2


In both cases the In both cases the work done is the work done is the area under the F area under the F vs. d curvevs. d curve

d

F

W


Work done on an elastic Work done on an elastic spring is now energy spring is now energy stored in the spring stored in the spring due to the mechanical due to the mechanical deformation of the deformation of the materialmaterial

W = F ∙ (dW = F ∙ (d22 – d – d11) = ) = 1/2kx1/2kx22

UU22 - U - U11 = E.P.E. = E.P.E.

d2

d1


Again, work done Again, work done is the area under is the area under the curve, in this the curve, in this case a direct case a direct linear relation.linear relation.

d

F

W

Work Done On A GasWork Done On A Gas

Gases tend to act like Gases tend to act like springs.springs.

If we look at an If we look at an “ideal” atomic gas “ideal” atomic gas like Argon, work like Argon, work can be done in can be done in compressing it and compressing it and like a spring, energy like a spring, energy can be stored in it.can be stored in it.

d2

d1


W = F ∙ dW = F ∙ dAlthough we can Although we can

measure force, measure force, pressure is easier to pressure is easier to deal with.deal with.

P = F/A and F = PAP = F/A and F = PAVolume of the cylinder = Volume of the cylinder =

Area x d and d = V/AArea x d and d = V/AW = PA x V/AW = PA x V/A

W = P(VW = P(V11-V-V22) ; W = P) ; W = PΔΔVV

d2

d1


The work done is the The work done is the area between 1 and area between 1 and 2.2.

Boyles Law keeps T Boyles Law keeps T constant so the curve constant so the curve is a one of constant is a one of constant temperature called temperature called an isotherm.an isotherm.

This is an isothermic This is an isothermic process and is process and is reversible.reversible.

P1

P2

V1 V2

W

1

2


If we go back to 9If we go back to 9thth grade and grade and think about Boyle’s Law….think about Boyle’s Law….

We remember that it’s an We remember that it’s an inverse relationship.inverse relationship.

Just like the rock vs. box, Just like the rock vs. box, WORK IS ONLY DONE WORK IS ONLY DONE WHEN VOLUME WHEN VOLUME CHANGES – not pressure CHANGES – not pressure (force).(force).

But wait, we have a problem.But wait, we have a problem.

P1

P2

V1 V2

1

2


With the rock, box and spring we only With the rock, box and spring we only had one pathway to travel.had one pathway to travel.

Slide the box, lift the box and stretch Slide the box, lift the box and stretch the spring.the spring.

We CAN NOT deviate from the path We CAN NOT deviate from the path defined by the defined by the mechanismmechanism involved. involved.

Gasses have no such constraints since Gasses have no such constraints since temperature can vary.temperature can vary.


Nobody said we Nobody said we had to follow the had to follow the isotherm.isotherm.

The work done via The work done via 1-3-2 is clearly 1-3-2 is clearly greater than via greater than via 1-4-2 since the 1-4-2 since the area under each area under each is different.is different.

P1

P2

V2

1

2

3

4


The path is The path is defined by defined by controlling the controlling the temp which is temp which is associated with associated with heat (Q) flow.heat (Q) flow.

P1

P2

V2

1

2

3

V1

P1

P2

V2

1

24

V1

W


But lets stick But lets stick to the to the isotherm and isotherm and add some add some heat to a gas. heat to a gas. This is an This is an OTTO cycle, OTTO cycle, which is your which is your car engine.car engine.

V2V1

a

b

c

c

Q out

Q in

W

A Car EngineA Car Engine

COE Still AppliesCOE Still AppliesThe basic law of the Universe states: The basic law of the Universe states:

Energy Can Not Be Created or Energy Can Not Be Created or Destroyed, Only Changed In From.Destroyed, Only Changed In From.

The 1The 1stst Law of Thermodynamics Law of ThermodynamicsWhen heat is transformed into any other When heat is transformed into any other

form of energy, or when other forms of form of energy, or when other forms of energy are transformed into heat, energy are transformed into heat, the total the total amount of energy (heat plus other forms) amount of energy (heat plus other forms) in the system is constantin the system is constant.. Energy is Energy is conserved.conserved.

To Say It Another WayTo Say It Another Way

The 1The 1stst Law of Thermodynamics Law of ThermodynamicsHeat added to a system transforms into Heat added to a system transforms into

other forms of energy. The total energy other forms of energy. The total energy in a system is constant. You can not get in a system is constant. You can not get more energy out than is put in.more energy out than is put in.

Ex: Heat added to water causes greater Ex: Heat added to water causes greater motion of the water molecules which is motion of the water molecules which is seen as an increase in temperature. seen as an increase in temperature. Also, ice does not freeze at room Also, ice does not freeze at room temperature, you have to remove temperature, you have to remove energy from it.energy from it.

Heat Transfer – A Basic Heat Transfer – A Basic IdeaIdea

Two objects of different temperature Two objects of different temperature will transfer heat until the pair is in will transfer heat until the pair is in thermal equilibrium.thermal equilibrium.

Hot Cold CoolingWarming

Same Temp

Time 0

Time 1

Time 2

Heat Flow

But It Gets WorseBut It Gets Worse

More of the 1More of the 1stst Law LawHeat (Energy) spontaneously flows from a Heat (Energy) spontaneously flows from a

region of high energy (SOURCE) to a region of high energy (SOURCE) to a region of lower energy (SINK). Heat will region of lower energy (SINK). Heat will not move from sink to source unless work not move from sink to source unless work is done.is done.

No process is possible where heat can be No process is possible where heat can be converted entirely into work since the converted entirely into work since the mechanism loses heat to its surroundings.mechanism loses heat to its surroundings.

Which in English IsWhich in English Is

The 1The 1stst Law of Thermodynamics Law of ThermodynamicsHeat will never by itself flow from cold to Heat will never by itself flow from cold to

hot. When heat energy flows some is lost hot. When heat energy flows some is lost to the environment and can never by to the environment and can never by recovered.recovered.

Heat flow is an Heat flow is an irreversibleirreversible process. process.No cyclic machine, process or engine can be No cyclic machine, process or engine can be

100% efficient.100% efficient.Everything in the Universe flows downhill. Everything in the Universe flows downhill.

More importantly it MUST FLOW DOWN More importantly it MUST FLOW DOWN HILL and “FRICTION” is ever present.HILL and “FRICTION” is ever present.

Heat Transfer – A Basic Heat Transfer – A Basic IdeaIdea

But what if I have three different But what if I have three different objects? What then?objects? What then?

A B

Are In Equilibrium

CB

Are In Equilibrium

CA

Must Be In Equilibrium

The 0The 0thth Law LawIf A is in equilibrium with B, and B with C then A If A is in equilibrium with B, and B with C then A must be in equilibrium with C. To change this must be in equilibrium with C. To change this condition work must be done.condition work must be done.

A B

Are In Equilibrium

CB

Are In Equilibrium

CA

Must Be In Equilibrium

Look at WaterLook at Water

Check out figure 12-Check out figure 12-14 in the book14 in the book

T

Q

Melting

Boiling

Heat of fusionHf

Heat of vaporizationHv

Look at WaterLook at Water

Check out figure 12-14 in Check out figure 12-14 in the bookthe book

T

Q

Melting

Boiling

Increasing disorderENTROPY

Entropy is a measure of disorder in a system, Entropy is a measure of disorder in a system, process or working fluid in system or process or working fluid in system or process.process.

s = Q/T (J/°K)s = Q/T (J/°K)

EntropyEntropy

With real gasses and With real gasses and processes, processes, temperature is a temperature is a function of pressure function of pressure and volume, so and volume, so entropy can be entropy can be derived in terms of derived in terms of all three gas laws.all three gas laws.

Which we won’t do Which we won’t do (save it for college).(save it for college).

P1

P2

V1 V2

Increasing disorderENTROPY

And Worse YetAnd Worse Yet

The 2The 2ndnd Law Law

All systems in the Universe will increase in All systems in the Universe will increase in entropy unless work is done on the system entropy unless work is done on the system to maintain order.to maintain order.

And The English Version And The English Version Is?Is?

The 2The 2ndnd Law of Thermodynamics Law of ThermodynamicsAll systems will tend towards increasing All systems will tend towards increasing

disorder unless work is done to keep disorder unless work is done to keep that from happening.that from happening.

Ex: Ice melts unless it’s in a freezer Ex: Ice melts unless it’s in a freezer where a machine does work to remove where a machine does work to remove energy from the ice to keep it from energy from the ice to keep it from melting. Also, a puddle of water will melting. Also, a puddle of water will evaporate to vapor even though the evaporate to vapor even though the water is well below boiling.water is well below boiling.


If we look at Charles’ If we look at Charles’ Law…..Law…..

Because we have Because we have ΔΔV V work is done on the work is done on the gas.gas.

Yet something subtle Yet something subtle is wrong with the is wrong with the diagram which will diagram which will cause great trouble cause great trouble in the real worldin the real world

V1 V2

T1

T2

W


The work done is The work done is relative to relative to absolute zero, absolute zero, which we can which we can never get to.never get to.

If we look at a real If we look at a real world process……world process……

V1 V2

T1

T2

W

T = 0


The farther apart TThe farther apart T22 and Tand T11 are the more are the more efficient the engine.efficient the engine.

But since TBut since T11 can can never of T=0, we never of T=0, we can never be 100% can never be 100% efficient.efficient.

Which is a tenant of Which is a tenant of the 1the 1stst Law. Law.

V1 V2

T1

T2

W

T = 0

a

b

c

d


In the real world TIn the real world T11 must be greater than must be greater than the environment to the environment to remove heat from remove heat from the engine to keep the engine to keep the process going.the process going.

Which is why your car Which is why your car has a radiator and has a radiator and can’t be 100% can’t be 100% efficient.efficient.

V1 V2

T1

T2

W

T = 0

a

b

c

d

TE

And Yet Even Worse StillAnd Yet Even Worse Still

The 3The 3rdrd Law Law

It is not possible to get to absolute It is not possible to get to absolute zero and as T approaches 0 entropy zero and as T approaches 0 entropy asymptoticallyasymptotically approaches a approaches a constant value.constant value.

Which MeansWhich Means

That no matter what you do, no That no matter what you do, no system can ever be perfectly ordered system can ever be perfectly ordered because you must continue to do because you must continue to do work on the system, increasing it work on the system, increasing it exponentially as you approach T=0exponentially as you approach T=0

The Nerd Joke VersionThe Nerd Joke Version

00thth Law: Everybody’s in the Law: Everybody’s in the same game.same game.

11stst Law: You Can’t Win. Law: You Can’t Win.

22ndnd Law: You Can’t Break Even. Law: You Can’t Break Even.

33rdrd Law: You Can’t Get Out Of Law: You Can’t Get Out Of The Game.The Game.

Water As A Working Water As A Working FluidFluid

The 3 gas laws limit The 3 gas laws limit one variable at a one variable at a time to explain time to explain behavior. In the real behavior. In the real world this is not world this is not possible, P, V & T all possible, P, V & T all change over time.change over time.

The implication is that The implication is that thermo is 3 thermo is 3 dimensional dimensional exercise.exercise.

Process VocabularyProcess Vocabulary

Isochoric – constant volumeIsochoric – constant volume

Isothermal – constant temperatureIsothermal – constant temperature

Isentropic – constant entropyIsentropic – constant entropy

Isobaric – constant pressureIsobaric – constant pressure

Adiabatic – no heat is lostAdiabatic – no heat is lost

Enthalpy – heat contentEnthalpy – heat content

The Carnot CycleThe Carnot Cycle

Here’s an Here’s an example of the example of the “most “most efficient” efficient” engine engine possible.possible.

Volume changes Volume changes isothermically isothermically and pressure and pressure changes changes adiabatically adiabatically

Carnot Cycle

Scared? Don’t Be. It’s Scared? Don’t Be. It’s EasyEasy

Thermo is like accounting and Thermo is like accounting and geometry mixed together. When a geometry mixed together. When a process is graphed as Pressure vs. process is graphed as Pressure vs. Volume (PV), PT, Ts, VT the area of Volume (PV), PT, Ts, VT the area of the curve is the amount of work the curve is the amount of work done by or on the process. The area done by or on the process. The area under curve is the work or energy under curve is the work or energy added to or removed by the process.added to or removed by the process.

It’s that easy.It’s that easy.

The FrigThe Frig

Specific HeatSpecific Heat

All materials have intensive properties such All materials have intensive properties such as conductivity, density, malleability, etc.as conductivity, density, malleability, etc.

Like density, materials have a property of Like density, materials have a property of heat conductivity or lack of it called the R heat conductivity or lack of it called the R value.value.

They also have a property called SPECIFIC They also have a property called SPECIFIC HEAT which can be thought of as the heat HEAT which can be thought of as the heat storage capacity.storage capacity.

Q = mcQ = mcΔΔTT

At The Collegiate LevelAt The Collegiate Level

In a collegiate THERMO class each In a collegiate THERMO class each process, associated math, and process process, associated math, and process graphs will be laid out for you in detail.graphs will be laid out for you in detail.

In the real world no such perfect “ISO” In the real world no such perfect “ISO” processes exist. But as a learning tool processes exist. But as a learning tool it helps to vary only one process it helps to vary only one process parameter at a time. Just like the gas parameter at a time. Just like the gas laws.laws.

But there are some basic ideas that have But there are some basic ideas that have far reaching applications.far reaching applications.

A Basic Premise Of Heat A Basic Premise Of Heat EnginesEngines

The larger the temperature difference The larger the temperature difference the greater the amount of work the the greater the amount of work the engine can do.engine can do.

The closer the low temperature of the The closer the low temperature of the SINK is to ambient the more SINK is to ambient the more efficient the engine is.efficient the engine is.

The greater the specific heat of the The greater the specific heat of the WORKING FLUID the smaller the WORKING FLUID the smaller the engine can be.engine can be.

Here’s What You’re In Here’s What You’re In ForFor

Adiabatic Process:Adiabatic Process:

PVPVγγ = Constant and VT = Constant and VTαα = Constant where = Constant where γγ is is ratio of specific heats of pressure and ratio of specific heats of pressure and volume.volume.

And after about two pages of derivation we And after about two pages of derivation we getget

(lnP – lnP(lnP – lnP00)/ (lnV – lnV)/ (lnV – lnV00) = () = (αα + 1)/ + 1)/αα

Which obviously reduces to:Which obviously reduces to:

PVPV((αα + 1)/ + 1)/αα = P = P00VV00 ((αα + 1)/ + 1)/αα = PV = PVγγ

GOT IT?!?!?!GOT IT?!?!?!

is for heat

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