Transcript Physics 201 - University of Virginia

PHYS 1110
Lecture 10
Professor Stephen Thornton
September 27, 2012
Reading Quiz
A) 0°C
1 kg of water at 100°C is poured into a
B) 20°C
bucket that contains 4 kg of water at
C) 50°C
0°C. Find the equilibrium temperature
D) 80°C
(neglect the influence of the bucket).
E) 100°C
Reading Quiz
A) 0°C
1 kg of water at 100°C is poured into a
B) 20°C
bucket that contains 4 kg of water at
C) 50°C
0°C. Find the equilibrium temperature
D) 80°C
(neglect the influence of the bucket).
E) 100°C
Because the cold water mass is greater, it will
have a smaller 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).
Q1 = Q2
m1cDT1 = m2cDT2
DT1 / DT2 = m2 / m1
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 heat flow
through rod
Q is proportional to A and temperatures T2 – T1
Q is proportional to 1/L
 DT
Q  kA 
 L

t

where k is called the thermal
conductivity W/(m K)
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?
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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!
Building materials are measured using Rvalues rather than thermal conductivity:
R=
Here,
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/k
is the thickness of the material.
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
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.
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Heat radiation
Have 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
DQ
P
 e AT 4
unit W
Dt
e is called the emissivity and is
between 0 and 1. A is area.
 = 5.67 10 W/(m  K )
-8
2
4
Called the Stefan-Boltzmann constant
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
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:
DQ
= 1000 e A cos q W/m 2
Dt
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This cos θ effect is also
responsible for the seasons.
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Consider a system:
Automobile engine
Human body
Simple 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
Ei
Ef = Ei + Q
If we add heat Q to a system having internal
energy Ei, the new internal energy of the
system is Ef = Ei + Q.
DE = Ef – Ei = Q
Work and Internal Energy
Ef = Ei -W
E
i
If the system does work W on the outside, then
the system loses internal energy.
E i – Ef = W
DE = Ef – Ei = -W
First Law of Thermodynamics
(Conservation of Energy)
Let’s combine the last two equations:
DE = Ef – Ei = Q
DE = 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.
DE  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. (DE  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
Area of graph is W
F  PA
W  F Dx  PADx  PDV
System does work
to push piston in
cylinder at constant
pressure. Volume
expands.
Area of graph = PDV  W work done by system
In a general problem like this example,
the area under the curve is equal to the
work done by the system.
W  Area
W = å Pi D Vi
i
Area
here is
work
We add heat to a system at constant volume.
What is the work done?
W= PDV = 0
Because volume doesn’t change, the work
done W must be zero.
W 0
DE  Q  W  Q
Isotherms on a PV diagram
Isothermal process.
T is constant.
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.
Do demo
Adiabatic
Heating
If we push down
quickly, there is
no time for heat to
flow, and the
process is
adiabatic.
Temperature rises
quickly.
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 Quiz
Two equal-mass liquids, initially at the
same temperature, are heated for the same
A) the cooler one
time over the same stove. You measure
B) the hotter one
the temperatures and find that one liquid
has a higher temperature than the other.
Which liquid has a higher specific heat?
C) both the same
Conceptual Quiz
Two equal-mass liquids, initially at the
same temperature, are heated for the same
A) the cooler one
time over the same stove. You measure
B) the hotter one
the temperatures and find that one liquid
has a higher temperature than the other.
C) both the same
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 liquid
had a lower temperature change.
Because Q = mcDT, if Q and m are both the same and DT is
smaller, then c (specific heat) must be bigger.
Thermodynamic Processes
and Their Characteristics
Constant pressure
W = PDV Q = DEint + PDV
Constant volume
W=0
Q = DEint
Isothermal (constant W = Q
temperature)
Adiabatic (no heat
W=–
flow)
DEint
DEint = Q – W
DEint = 0
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 Thermodynamics
We 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
W  Qh  Qc
W , Qh , Qc are positive.
Efficiency e
W Qh  Qc
e

Qh
Qh
Qc
e  1
Qh
Heat Engines
A steam engine is one type of heat engine.
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Do demos
• Heat engine
• Steam engine
Our favorite
heat engine.
Q
h
Reversible
processes.
Qc
X Tc
Remember that the
work is equal to the
area under the P - V
curve. Total work
here is work enclosed
in cycle.
Q
h
Qc
X Tc
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 Qc = Tc for the Carnot
Qh Th
cycle.
Qc
Tc
e  1
 1
Qh
Th
For the highest efficiency, we need the
maximum difference of temperatures in
thermal reservoirs.
Tc
emax  1 
for Carnot cycle
Th
Because e  W / Qh , we have W  eQh
Wmax
 Tc 
 emax Qh  1   Qh
 Th 
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?
Qc
Tc
e  1
 1
Qh
Th
A)
20%
B)
40%
C)
60%
D)
67%
E)
90%
Answer: B
Qc
90
e  1
 1
 0.40
Qh
150
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
Qc
Tc
e  1
 1
Qh
Th
A) believe that this is possible.
B) laugh at the idea.
C) contact a patent lawyer immediately.
Answer: A
Tc
11  273
284
e  1  1
 1
 0.4
Th
200  273
473
Another statement
of 2nd Law of
Thermodynamics
It is not possible to construct an engine
whose sole effect is to transform a given
amount of heat completely into work!
Heat engine and refrigerator
This figure shows more details
of a typical refrigerator.
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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
Qc
COP =
W
Remember that Qh  Qc  W
This is the amount of heat exhausted
into kitchen.
For an air conditioner, this is the heat
exhausted to the outside.
Air conditioner and heat pump
inside house
Maximize Qh
Maximize Qc
Heat
house
A heat pump can heat a house in the winter:
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For an ideal, reversible heat pump (i.e.
Carnot cycle), we have Qc  Tc
Q
h
T
h
 Qc 
W  Qh  Qc  Qh 1  
 Qh 
 Tc 
W  Qh 1  
 Th 
To minimize W we
want temperatures to
be similar.
Various Engines
http://www.animatedengines.com/
Look at
Four Stroke
Diesel
Two Stroke
Steam Locomotive
Newcomen Atmospheric Engine
Two 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.
Q
DS 
T
dQ
dS 
T
for constant T
for nonconstant T
Consider the heat flow change to be
reversible. T is in kelvin.
Heat added to system, DS > 0.
Heat removed from system, DS < 0.
DS total
For a reversible heat engine, the
total entropy of the engine cycle is
Qh Qc
 
0
reversible
Th Tc
Real engines have friction and can't quite
be reversible.
DS total
Qh Qc
 
0
Th Tc
real engine
All irreversible processes cause an increase
in entropy. (Q is positive here.)
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
Q Q
by the warmer one.
DStotal  
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Th

Tc
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).
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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 Entropy
As 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!
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:
Highly
unlikely
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
showed
S = k ln 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.
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Conceptual Quiz
A) positive
In the closed thermodynamic
cycle shown in the P-V diagram,
B) zero
C) negative
the work done by the gas is:
P
V
Conceptual Quiz
In the closed thermodynamic
A) positive
cycle shown in the P-V diagram,
B) zero
the work done by the gas is:
C) negative
The gas expands at a higher pressure
and compresses at a lower pressure.
In general, clockwise = positive work;
P
counterclockwise = negative work.
V
Conceptual 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 with
thermal conductivity
Conceptual Quiz
Given your experience of
what feels colder when you
walk on it, which of the
A) a rug
B) a steel surface
surfaces would have the
C) a concrete floor
highest thermal conductivity?
E) has nothing to do with
thermal 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°).