PHYS 1110 Lecture 10 Professor Stephen Thornton September 27, 2012

PHYS 1110

Lecture 10

Professor Stephen Thornton

September 27, 2012

Reading QuizReading Quiz

1 kg of water at 100°C is poured into a

bucket that contains 4 kg of water at

0°C. Find the equilibrium temperature

(neglect the influence of the bucket).

A) 0°C

B) 20°C

C) 50°C

D) 80°C

E) 100°C

Because the cold water mass is greatercold water mass is greater, it will

have a smaller temperature changesmaller temperature change!

The masses of cold/hot have a ratio of 4:1, so

the temperature change must have a ratio of

1:4 (cold/hot).

Reading Quiz Reading Quiz

1 kg of water at 100°C is poured into a

bucket that contains 4 kg of water at

0°C. Find the equilibrium temperature

(neglect the influence of the bucket).

A) 0°C

B) 20°C

C) 50°C

D) 80°C

E) 100°C

QQ11 = = QQ22

mm11ccTT11 = = mm22ccTT22

TT11 TT22 = = mm22 mm11/ /

Midterm exam next Tuesday.Chapters 1-4.

Thermodynamics will not be on the exam.

Homework, including the electric motor, is due today. I will count off 10 points a day for late homework.

Heat Exchange

Conduction – molecules touch each other and exchange energy.

Convection – hot fluids rise Radiation – electromagnetic

radiation like light, infrared,

ultraviolet radiation; all frequencies.

These are very important!!

Heat conduction

If we put a torch to a piece of metal, the molecules in the metal have increased kinetic energy. They collide with adjacent molecules, and the heat moves down the material via these collisions.

Some materials transport heat energy more easily than others. Metals are good heat conductors. Wood and plastics are poor.

Heat Conduction Through a Rod

Q is proportional to A and temperatures T2 – T1

Q is proportional to 1/L

T

Q kA tL

is heat flow

through rod

Q

where k is called the thermal conductivity W/(m K)

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The constant k is called the thermal conductivity.

Materials with large k are called conductors; those with small k are called insulators.

Note: materials that are good heat conductors are also good electrical conductors. Why?

Note in the table on thermal conductivities that air is a very poor heat conductor. In fact, we could say it is a good heat insulator.

This is why double pane windows are such good insulators both in the summer and winter. Glass panes are thin and conduct heat much better than air. The layer of air does wonders!

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Building materials are measured using R-values rather than thermal conductivity:

Here, is the thickness of the material./R k=

Heat convection

Well known phenomenon because hot fluids rise due to their lower density. We take advantage of this by putting heat ducts on the floor.

Did demo – convection chimney

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Convection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced; both these examples are natural convection.

Heat radiationHave you ever sat in front of a campfire and wondered why your face is so warm, and your behind so cold?

All objects emit electromagnetic radiation. Waves easily carry energy in the form of light, radar, microwave (cell phone), etc.

Our existence depends on heat radiation from the Sun.

Did light the match (wood) demo. Example of radiation.

Heat radiation is noted in terms of radiated power P

4

-8 2 4

unit W

is called the emissivity and is

between 0 and 1. is area.

= 5.67 10 W/(m K )

Called the Stefan-Boltzmann constant

QP e AT

t

e

A

e = 1 is a perfect emitter and absorber, and is called a blackbody.

e = 0 is an ideal reflector.

Inside of a thermos bottle is shiny and is a good reflector. The heat of the container emits radiation, but it is not absorbed by the outer wall.

The Thermos Bottle

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If you are in the sunlight, the Sun’s radiation will warm you. In general, you will not be perfectly perpendicular to the Sun’s rays, and will absorb energy at the rate:

21000 cos W/mQ

At

e qD

=D

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This cos θ effect is also responsible for the seasons.

Consider a system:Automobile engineHuman bodySimple piston and cylinder

We want to consider what happens if we add heat to our system or take heat away.

Also let the system do work or have work done on it.

What happens to internal energy? The internal energy is the sum of all the kinetic and potential energies.

The Internal Energy of a System

If we add heat Q to a system having internal energy Ei, the new internal energy of the system is Ef = Ei + Q. E = Ef – Ei = Q

Ei Ef = Ei + Q

Work and Internal Energy

If the system does work W on the outside, then the system loses internal energy.

Ei – Ef = W E = Ef – Ei = -W

E

i

Ef = Ei -W

First Law of Thermodynamics(Conservation of Energy)

Let’s combine the last two equations:

E = Ef – Ei = Q

E = Ef – Ei = -W

Because both heat flow and work can occur, the change in internal energy of a system depends on both Q and W.

E Q W First law of thermodynamics

Signs of Q and W ***

Q positive System gains heat

Q negative System loses heat

W positive Work done by system

W negative Work done on system

The convention for W is opposite of that in chemistry.( )E Q W

The internal energy E depends on the state of the system (P, V, T, m, n). They are called state functions.

Heat flow Q and work W are not state functions. They depend on how the system is changed.

A Constant-Pressure Process

System does work to push piston in cylinder at constant pressure. Volume expands.

Area of graph = work done by system

F PA

W F x PA x P V

P V W

Area of graph is W

In a general problem like this example, the area under the curve is equal to the work done by the system.

Area here is work

AreaW i i

i

W P V= Då

We add heat to a system at constant volume. What is the work done? W= PV = 0 Because volume doesn’t change, the work done W must be zero.

0W

E Q W Q

Isotherms on a PV diagram

process.

is constant.T

Isothermal

In an adiabatic process, the system is well insulated thermally, and no heat flows (Q = 0).When the piston compresses the volume, the pressure and temperature must both go up.

Adiabatic Heating

If we push down quickly, there is no time for heat to flow, and the process is adiabatic. Temperature rises quickly.

Do demo

When the piston moves up, the volume expands, and the pressure and temperature decrease.

Adiabatic process occurs often when the process is rapid, and there is no time for heat to flow.

Conceptual QuizConceptual Quiz

A) the cooler one

B) the hotter one

C) both the same

Two equal-mass liquids, initially at the

same temperature, are heated for the same

time over the same stove. You measure

the temperatures and find that one liquid

has a higher temperature than the other.

Which liquid has a higher specific heat?

Both liquids had the same increase in internal energy,

because the same heat was added. But the cooler liquidcooler liquid

had a lower temperaturelower temperature change.

Because QQ = = mcmcTT, if QQ and mm are both the same and TT is

smaller, then cc (specific heat) must be bigger.

Conceptual QuizConceptual Quiz

A) the cooler one

B) the hotter one

C) both the same

Two equal-mass liquids, initially at the

same temperature, are heated for the same

time over the same stove. You measure

the temperatures and find that one liquid

has a higher temperature than the other.

Which liquid has a higher specific heat?

Thermodynamic Processes and Their Characteristics

Constant pressure W = PV Q = Eint + PV

Constant volume W = 0 Q = Eint

Isothermal (constant temperature)

W = Q Eint = 0

Adiabatic (no heat flow)

Eint = Q – W

W = – Eint

Q = 0

Work Done by Thermal Systems

If the first law of thermodynamics is about energy conservation, then the 2nd law is about the way in which energy flows.

Examples:A bowl of water sitting in this room does not spontaneously freeze.

It is impossible to construct an engine that can extract thermal energy from a system and turn all that energy into work.

Thermal systems spontaneously change in only certain ways.

2nd Law of ThermodynamicsWe can discuss this law in a number of ways.

The law basically states the way in which heat flow occurs.

Heat flow between two objects brought together in thermal contact always goes from the hotter object to the colder object.

Lots of ways to say the same thing!

Heat Engines

An engine is a device that converts heat into mechanical work.

Engines must operate in cycles in order to be useful. A piston and cylinder must return to original position. The change in internal energy is zero.

An engine operates between two thermal reservoirs.

Schematic Diagram of Heat Engine

, , are positive.

Efficiency

1

h c

h c

h c

h h

c

h

W Q Q

W Q Q

e

Q QWe

Q Q

Qe

Q

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A steam engine is one type of heat engine.

Heat Engines

Do demos

• Heat engine

• Steam engine

cT

Our favorite heat engine.

Reversible processes.

X

hQ

cQ

Remember that thework is equal to thearea under the -curve. Total workhere is work enclosedin cycle.

P V

cT X

hQ

cQ

Carnot Cycle

• Carnot’s cycle represents the most efficient

engine possible.

• It operates between two heat reservoirs.

• All the processes are reversible – two

isothermals and two adiabatics.

• We can show for the Carnot

cycle.

c c

h h

Q T

Q T=

max

max max

1 1

For the highest efficiency, we need themaximum difference of temperatures in thermal reservoirs.

1 for Carnot cycle

Because / ,we have

1

c c

h h

c

h

h h

ch h

h

Q Te

Q T

Te

T

e W Q W eQ

TW e Q Q

T

Conceptual Quiz:A heat engine absorbs 150 J of heat from a hot reservoir and rejects 90 J of it to a cold reservoir. What is the efficiency of this engine? A)       20%B)       40%C)       60%D)       67%E)       90%

1 1c c

h h

Q Te

Q T

Answer: B

901 1 0.40

150c

h

Qe

Q

Conceptual Quiz:For the previous heat engine, you are told the temperature of the hot reservoir is 200 oC and that of the cold reservoir is 11oC. Your response is to

 A)   believe that this is possible.B)   laugh at the idea.C)   contact a patent lawyer immediately.

1 1c c

h h

Q Te

Q T

Answer: A

11 273 2841 1 1 0.4

200 273 473c

h

Te

T

It is not possible to construct an engine whose sole effect is to transform a given amount of heat completely into work!

Another statement of 2nd Law of Thermodynamics

Heat engine and refrigerator

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This figure shows more details of a typical refrigerator.

We analyze refrigerators differently. We want to remove as much heat Qc as possible for the least amount of work.

Coefficient of Performance or COP

COP =

Remember that This is the amount of heat exhausted into kitchen.For an air conditioner, this is the heat exhausted to the outside.

c

h c

Q

W

Q Q W

Air conditioner and heat pump

Maximize Qc

Maximize Qh

inside house

Heat house

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A heat pump can heat a house in the winter:

For an ideal, reversible heat pump (i.e. Carnot cycle), we have

1

1

ch c h

h

ch

h

QW Q Q Q

Q

TW Q

T

c c

hh

Q TTQ

To minimize W we want temperatures to be similar.

Various Engineshttp://www.animatedengines.com/

Look at

Four StrokeDieselTwo StrokeSteam LocomotiveNewcomen Atmospheric EngineTwo Cylinder Stirling Engine

Entropy

There are several ways to look at entropy, but eventually they are all equal.

Entropy is related to disorder in a system.

A messy bedroom has more entropy than a clean one.

The natural order of the universe is to increase entropy. Your bedroom never naturally becomes clean; it always naturally becomes messy.

Entropy is also related to probability. There is a higher probability that a block of ice will melt at room temperature than it will get colder. Thermodynamics does not prevent either action. The probability of the latter is incredibly small.

Conceptual Quiz:Humpty Dumpty falls off and breaks. Can he get back together again?

A) Yes, very easily. B) Yes, but with extremely low probability. C) No, there is no possibility.D) Are you kidding us?Humpty Dumpty sat on a wall,

Humpty Dumpty had a great fall;All the King's horses and all the King's men,Couldn't put Humpty together again.

Answer: B

From what we just learned, this is only a question of probabilities. And no, I am not kidding!

Entropy is a very fundamental property, and is a state variable. It is determined by the heat flow Q divided by the temperature T.

for constant

for nonconstant

Consider the heat flow change to bereversible. is in kelvin.Heat added to system, > 0.Heat removed from system, < 0.

QS T

TdQ

dS TT

TS

S

For a reversible heat engine, the total entropy of the engine cycle is

total

total

0 reversible

Real engines have friction and can't quite

be reversible.

0 real engine

All irreversible processes cause an increase

in entropy. ( is positive here.)

h c

h c

h c

h c

Q QS

T T

Q QS

T T

Q

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Entropy and the Second Law of Thermodynamics

The total entropy always increases when heat flows from a warmer object to a colder one in an isolated two-body system. The heat transferred is the same, and the cooler object is at a lower average temperature than the warmer one, so the entropy gained by the cooler one is always more than the entropy lost by the warmer one.

totalh c

Q QS

T T

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The fact that after every interaction the entropy of the system plus the environment increases is another way of putting the second law of thermodynamics:

The entropy of an isolated system never decreases. It either stays constant (reversible processes) or increases (irreversible processes).

The total entropy of the universe increases whenever an irreversible process occurs.

The total entropy of the universe is unchanged whenever a reversible process occurs.

This is another way to state the 2nd Law of Thermodynamics.

There is some really bad news here. Because the universe actually works through irreversible processes, the entropy is gradually increasing. There will eventually be a gradual “heat death” of the universe. The universe will be full of energy which cannot be used to perform work! We are doomed!

Order, Disorder, and EntropyAs we have stated, entropy is related to disorder.As the entropy of a system increases, its disorder increases as well.GOOD NEWS: When you go home, and your mother fusses about how messy your bedroom is, tell her it is because entropy is increasing, and it is the natural order of the universe. There is little you or your mother can do about it (without doing a lot of work!). She will be impressed by how much physics you have learned!

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Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law:

Natural processes tend to move toward a state of greater disorder.

Example: If you put milk and sugar in your coffee and stir it, you wind up with coffee that is uniformly milky and sweet. No amount of stirring will get the milk and sugar to come back out of solution.

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Another example: When a tornado hits a building, there is major damage. You never see a tornado approach a pile of rubble and leave a building behind when it passes.

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Statistical Interpretation of Entropy and the Second Law

The most probable distribution of speeds in a gas is Maxwellian:

The most probable state is the one with the greatest disorder, or the greatest entropy. With k being Boltzmann’s constant and W the number of microstates, Boltzmann showedHighly

unlikely

lnS k W=

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Statistical Interpretation of Entropy and the Second Law

In this form, the second law of thermodynamics does not forbid processes in which the total entropy decreases; it just makes them exceedingly unlikely.

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Thermal Pollution, Global Warming, and Energy Resources

Over 90% of the energy used in the U.S. is generated using heat engines to drive turbines and generators—even nuclear power plants use the energy generated from fission to heat water for a steam engine. The thermal output QL of all these heat engines contributes to warming of the atmosphere and water. This is an inevitable consequence of the second law of thermodynamics.

Conceptual QuizConceptual Quiz

In the closed thermodynamic

cycle shown in the P-V diagram,

the work done by the gas is:

A) positive

B) zero

C) negative

V

P

Conceptual QuizConceptual Quiz

In the closed thermodynamic

cycle shown in the P-V diagram,

the work done by the gas is:

A) positive

B) zero

C) negative

The gas expands at a higher pressure

and compresses at a lower pressure.

In general, clockwise = positive work;

counterclockwise = negative work.

V

P

Conceptual QuizConceptual Quiz

Given your experience of

what feels colder when you

walk on it, which of the

surfaces would have the

highest thermal

conductivity?

A) a rug

B) a steel surface

C) a concrete floor

D) has nothing to do withthermal conductivity

Conceptual QuizConceptual Quiz

Given your experience of

what feels colder when you

walk on it, which of the

surfaces would have the

highest thermal

conductivity?

A) a rug

B) a steel surface

C) a concrete floor

E) has nothing to do withthermal conductivity

The heat flow rate is k A (T1 − T2)/L. All things being

equal, bigger k leads to bigger heat loss.

From the book: Steel = 40, Concrete = 0.84,

Human tissue = 0.2, Wool = 0.04, in units of J/(s.m.C°).