Transcript lect_outline_17 - Colorado Mesa University

Chapter 17 Lecture
physics
FOR SCIENTISTS AND ENGINEERS
a strategic approach
THIRD EDITION
randall d. knight
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Chapter 17 Work, Heat, and the First Law of
Thermodynamics
Chapter Goal: To develop and apply the first law of
thermodynamics.
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Chapter 17 Preview
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Chapter 17 Preview
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Chapter 17 Preview
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Chapter 17 Preview
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Chapter 17 Preview
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Chapter 17 Reading Quiz
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Slide 17-8
Reading Question 17.1
What quantities appear in the first law of
thermodynamics?
A.
B.
C.
D.
E.
Force, mass, acceleration.
Inertia, torque, angular momentum.
Work, heat, thermal energy.
Work, heat, entropy.
Enthalpy, entropy, heat.
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Slide 17-9
Reading Question 17.1
What quantities appear in the first law of
thermodynamics?
A.
B.
C.
D.
E.
Force, mass, acceleration.
Inertia, torque, angular momentum.
Work, heat, thermal energy.
Work, heat, entropy.
Enthalpy, entropy, heat.
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Slide 17-10
Reading Question 17.2
What was the original unit for measuring heat?
A.
B.
C.
D.
E.
BTU.
Watt.
Joule.
Pascal.
Calorie.
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Reading Question 17.2
What was the original unit for measuring heat?
A.
B.
C.
D.
E.
BTU.
Watt.
Joule.
Pascal.
Calorie.
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Reading Question 17.3
What is the name of an ideal-gas process in
which no heat is transferred?
A.
B.
C.
D.
E.
Isochoric.
Isentropic.
Isothermal.
Isobaric.
Adiabatic.
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Reading Question 17.3
What is the name of an ideal-gas process in
which no heat is transferred?
A.
B.
C.
D.
E.
Isochoric.
Isentropic.
Isothermal.
Isobaric.
Adiabatic.
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Reading Question 17.4
Heat is
A. The amount of thermal energy in an
object.
B. The energy that moves from a
hotter object to a colder object.
C. A fluid-like substance that flows from
a hotter object to a colder object.
D. Both A and B.
E. Both B and C.
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Reading Question 17.4
Heat is
A. The amount of thermal energy in an
object.
B. The energy that moves from a
hotter object to a colder object.
C. A fluid-like substance that flows from
a hotter object to a colder object.
D. Both A and B.
E. Both B and C.
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Reading Question 17.5
The thermal behavior of water is characterized by
the value of its
A.
B.
C.
D.
Heat density.
Heat constant.
Specific heat.
Thermal index.
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Reading Question 17.5
The thermal behavior of water is characterized by
the value of its
A.
B.
C.
D.
Heat density.
Heat constant.
Specific heat.
Thermal index.
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Chapter 17 Content, Examples, and
QuickCheck Questions
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Energy Review
 The total energy of a
system consists of the
macroscopic energy plus
the microscopic thermal
energy.
 The final energy
statement of Chapter 11
was:
The total energy of an isolated system, for which
Wext = 0, is constant.
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Energy Transfer by Work
 Doing work on a system
increases its energy.
 Consider lifting a block
with a rope at a steady
speed.
 The rope’s tension is an
external force doing
work Wext.
 Energy transferred into
the system goes entirely
into the macroscopic
potential energy Ugrav.
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Energy Transfer by Work
 Doing work on a system
increases its energy.
 Consider dragging a
block with a rope at a
steady speed.
 The rope’s tension is an
external force doing work
Wext.
 Energy transferred into
the system goes entirely
into the thermal energy of
the object + surface
system Eth.
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Energy Transfer by Heat
 Work is energy transferred in a mechanical interaction.
 Energy can also be transferred between the system and
the environment if they have a thermal interaction.
 The energy transferred in a thermal interaction is called
heat.
 The symbol for heat is Q.
 The complete energy equation is now:
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QuickCheck 17.1
A steady force pushes in the
piston of a well-insulated cylinder.
In this process, the temperature
of the gas
A.
B.
C.
D.
Increases.
Stays the same.
Decreases.
There’s not enough information to tell.
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QuickCheck 17.1
A steady force pushes in the
piston of a well-insulated cylinder.
In this process, the temperature
of the gas
A.
B.
C.
D.
Increases.
Stays the same.
Decreases.
There’s not enough information to tell.
No heat flows (well insulated) ...
... but work is done on the gas.
First law: Q + W = ΔEth
Work increases the gas’s thermal
energy and with it the temperature.
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Work in Ideal-Gas Processes
 Consider a gas cylinder
sealed at one end by a
movable piston.
 The external force does
work on the gas as the
piston moves.
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The Sign of Work
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Work in Ideal-Gas Processes
 On a pV diagram, the
work done on a gas W
has a nice geometric
interpretation.
 W = the negative of the
area under the pV curve
between Vi and Vf.
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QuickCheck 17.2
The work done on the
gas in this process is
A.
B.
C.
D.
E.
8000 J.
4000 J.
0 J.
–4000 J.
–8000 J.
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QuickCheck 17.2
The work done on the
gas in this process is
A.
B.
C.
D.
E.
8000 J.
4000 J.
0 J.
–4000 J.
–8000 J.
W = –(area under pV curve)
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QuickCheck 17.3
Three possible processes
A, B, and C take a gas from
state i to state f. For which
process is the magnitude of
the work the largest?
A.
B.
C.
D.
Process A.
Process B.
Process C.
The work is the same for all three.
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QuickCheck 17.3
Three possible processes
A, B, and C take a gas from
state i to state f. For which
process is the magnitude of
the work the largest?
A.
B.
C.
D.
Largest area
under the curve.
Process A.
Process B.
Process C.
The work is the same for all three.
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Problem-Solving Strategy: Work in a Ideal-Gas
Process
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Example 17.1 The Work Done on an
Expanding Gas
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Example 17.1 The Work Done on an
Expanding Gas
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Example 17.1 The Work Done on an
Expanding Gas
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Work Done on an Ideal Gas
In an isochoric process, when the volume does not
change, no work is done.
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Work Done on an Ideal Gas
In an isobaric process, when pressure is a constant
and the volume changes by V = Vf − Vi, the work done
during the process is:
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Work Done on an Ideal Gas
In an isothermal process, when temperature is a
constant, the work done during the process is:
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Example 17.2 The Work of an Isothermal
Compression
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QuickCheck 17.4
Dragging an object across a rough surface makes
it warm, or even hot. The temperature increase
occurs because of
A.
B.
C.
D.
E.
Work.
Heat.
Thermal energy.
Both work and heat.
None of these.
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QuickCheck 17.4
Dragging an object across a rough surface makes
it warm, or even hot. The temperature increase
occurs because of
A.
B.
C.
D.
E.
Work.
Heat.
Thermal energy.
Both work and heat.
None of these.
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Work in Ideal-Gas Processes
 Figure (a) shows two
different processes that take
a gas from an initial state i
to a final state f.
 The work done during an
ideal-gas process
depends on the path
followed through the pV
diagram.
 During the multistep
process of figure (b), the
work done is not the same
as a process that goes
directly from 1 to 3.
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Heat
In the 1840s James Joule showed that heat and work,
previously regarded as completely different phenomena,
are simply two different ways of transferring energy to or
from a system.
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Heat, Temperature, and Thermal Energy
 Thermal energy Eth is an
energy of the system due to
the motion of its atoms and
molecules.
 Heat Q is energy transferred
between the system and
the environment as they
interact.
 Temperature T is a state
variable that quantifies the
“hotness” or “coldness” of a
system.
A temperature difference is required in order for heat to
be transferred between the system and the environment.
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The Sign of Heat
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Understanding Work and Heat
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Units of Heat
 The SI unit of heat is the Joule.
 Historically, a unit for measuring heat, the calorie, had
been defined as:
1 calorie = 1 cal = the quantity of heat needed to
change the temperature of 1 g of
water by 1°C
 In today’s SI units, the conversion is:
1 cal = 4.186 J
 The calorie you know in relation to food is not the
same as the heat calorie.
1 food calorie = 1 Cal = 1000 cal = 1 kcal = 4186 J
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The First Law of Thermodynamics
Work and heat are two
ways of transferring
energy between a
system and the
environment, causing
the system’s energy to
change.
If the system as a whole is at rest, so that the bulk
mechanical energy due to translational or rotational
motion is zero, then the conservation of energy
equation is:
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QuickCheck 17.5
A cylinder of gas has a frictionless but tightly
sealed piston of mass M. Small masses are
placed onto the top of the piston, causing it to
slowly move downward. A water bath keeps
the temperature constant. In this process:
A. Q > 0.
B. Q = 0.
C. Q < 0.
D. There’s not enough information to say anything about the
heat.
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QuickCheck 17.5
A cylinder of gas has a frictionless but tightly
sealed piston of mass M. Small masses are
placed onto the top of the piston, causing it to
slowly move downward. A water bath keeps
the temperature constant. In this process:
A. Q > 0.
B. Q = 0.
C. Q < 0.
D. There’s not enough information to say anything about the
heat.
0
+ –
Eth = W + Q
No temperature
change
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Energy flows out to the water to
keep the temperature from changing
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Three Special Ideal-Gas Processes
 For an isochoric
process, insert the
locking pin so the volume
cannot change.
 For an isothermal
process, keep the thin
bottom in thermal contact
with the flame or the ice.
 For an adiabatic
process, add insulation
beneath the cylinder, so
no heat is transferred in
or out.
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Three Special Ideal-Gas Processes
 Shown is the first-law
bar chart for an
isochoric cooling
process.
 The gas is cooled by
allowing heat energy to
transfer out of the
system to a cooler
environment.
 The volume of the gas
does not change, so no
work is done (W = 0).
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QuickCheck 17.6
Which first-law bar chart
describes the process
shown in the pV diagram?
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QuickCheck 17.6
Which first-law bar chart
describes the process
shown in the pV diagram?
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Three Special Ideal-Gas Processes
 Shown is the first-law bar
chart for an isothermal
expansion.
 The gas is heated by
allowing heat energy to
transfer into the system from
a warmer environment.
 The volume of the gas
expands as the pressure
drops.
 Negative work is done on the
gas, and the thermal energy
is constant (Eth = 0).
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Slide 17-56
Three Special Ideal-Gas Processes
 Shown is the first-law bar
chart for an adiabatic
compression.
 The gas is compressed by
shrinking the volume.
 Insulation prevents heat
energy from entering or
leaving the gas (Q = 0).
 Positive work is done on
the gas, which increases
the temperature.
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Slide 17-57
QuickCheck 17.7
Three possible processes A, B,
and C take a gas from state i to
state f. For which process is the
heat transfer the largest?
A.
B.
C.
D.
Process A.
Process B.
Process C.
The heat is the same for all three.
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QuickCheck 17.7
Three possible processes A, B,
and C take a gas from state i to
state f. For which process is the
heat transfer the largest?
A.
B.
C.
D.
Process A.
Process B.
Process C.
The heat is the same for all three.
Same for all three
Eth = W + Q
Most negative for A ... ... so Q must be most positive.
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Slide 17-59
Temperature Change and Specific Heat
 The amount of energy that raises the temperature of
1 kg of a substance by 1 K is called the specific heat
c of that substance.
 If W = 0, so no work is done by or on the system, then
the heat needed to bring about a temperature change
T is:
The molar specific heat C is the amount of energy that
raises the temperature of 1 mol of a substance by 1 K.
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QuickCheck 17.8
Two liquids, A and B, have equal masses and equal
initial temperatures. Each is heated for the same
length of time over identical burners. Afterward, liquid
A is hotter than liquid B. Which has the larger specific
heat?
A. Liquid A.
B. Liquid B.
C. There’s not enough information to tell.
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Slide 17-61
QuickCheck 17.8
Two liquids, A and B, have equal masses and equal
initial temperatures. Each is heated for the same
length of time over identical burners. Afterward, liquid
A is hotter than liquid B. Which has the larger specific
heat?
A. Liquid A.
Q
T
=
B. Liquid B.
mc so larger c gives smaller T.
C. There’s not enough information to tell.
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Slide 17-62
Specific Heats of Various Materials
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Slide 17-63
Example 17.3 Running a Fever
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QuickCheck 17.9
1 kg of silver (c = 234 J/kg K) is heated to 100C. It is
then dropped into 1 kg of water (c = 4190 J/kg K) at 0C
in an insulated beaker. After a short while, the common
temperature of the water and silver is
A.
B.
C.
D.
E.
0C.
between 0C and 50C.
50C.
between 50C and 100C.
100C.
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QuickCheck 17.9
1 kg of silver (c = 234 J/kg K) is heated to 100C. It is
then dropped into 1 kg of water (c = 4190 J/kg K) at 0C
in an insulated beaker. After a short while, the common
temperature of the water and silver is
A.
B.
C.
D.
E.
0C.
between 0C and 50C.
50C.
between 50C and 100C.
100C.
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Phase Change and Heat of Transformation
A phase change is characterized by a change in
thermal energy without a change in temperature.
 The amount of heat
energy that causes 1 kg
of substance to undergo
a phase change is the
heat of transformation
L of that substance.
 The heat required for
a system of mass M to
Lava—molten rock—undergoes a phase change when it
undergo a phase
contacts the much colder water. This is one way in which
new islands are formed.
change is:
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QuickCheck 17.10
If you heat a substance in an insulated container,
is it possible that the temperature of the substance
remains unchanged?
A. Yes.
B. No.
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QuickCheck 17.10
If you heat a substance in an insulated container,
is it possible that the temperature of the substance
remains unchanged?
A. Yes. If there’s a phase change.
B. No.
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Slide 17-69
Phase Change and Heat of Transformation
Suppose you start with a system in its solid phase and heat
it at a steady rate.
 The specific heat c can be
measured from the slope of
the linear increases.
 The heat needed for the
phase changes is:
where Lf is the heat of
fusion and Lv is the heat
of vaporization.
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Melting/Boiling Temperatures and Heats of
Transformation
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Calorimetry
 Consider two systems with
different temperatures T1 and
T2 that can interact thermally
with each other but are isolated
from everything else.
 Heat will naturally flow from the
hotter to the colder system until
they reach a common final
temperature Tf.
 If Qi is the heat transferred to
system i, then:
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QuickCheck 17.11
50 g of ice at 0C is added to 50 g of liquid water at
0C in a well-insulated container, also at 0C. After a
while, the container will hold
A.
B.
C.
D.
E.
All ice.
> 50 g of ice, < 50 g of liquid water.
50 g of ice, 50 g of liquid water.
< 50 g of ice, > 50 g of liquid water.
All liquid water.
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QuickCheck 17.11
50 g of ice at 0C is added to 50 g of liquid water at
0C in a well-insulated container, also at 0C. After a
while, the container will hold
A.
B.
C.
D.
E.
All ice.
> 50 g of ice, < 50 g of liquid water.
50 g of ice, 50 g of liquid water.
< 50 g of ice, > 50 g of liquid water.
All liquid water.
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Problem-Solving Strategy: Calorimetry Problems
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Example 17.6 Three Interacting Systems
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Example 17.6 Three Interacting Systems
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The Specific Heats of Gases
 Processes A and B have
the same T and the
same Eth, but they
require different amounts
of heat.
 The reason is that work is
done in process B but not
in process A.
 The total change in
thermal energy for any
process, due to work and
heat, is:
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Slide 17-78
The Specific Heats of Gases
 It is useful to define two different versions of the specific
heat of gases, one for constant-volume processes and
one for constant-pressure processes.
 We will define these as molar specific heats because
we usually do gas calculations using moles instead of
mass.
 The quantity of heat needed to change the temperature
of n moles of gas by T is:
where CV is the molar specific heat at constant
volume and CP is the molar specific heat at constant
pressure.
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Slide 17-79
CP and CV
Note that for all ideal
gases:
where
R = 8.31 J/mol K is
the universal gas
constant.
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Slide 17-80
QuickCheck 17.12
1 mol of air has an initial temperature of 20C. 200 J of heat
energy are transferred to the air in an isochoric process, then
200 J are removed in an isobaric process. Afterward, the air
temperature is
A.
B.
C.
D.
< 20C.
= 20C.
> 20C.
Not enough information is given to answer the question.
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Slide 17-81
QuickCheck 17.12
1 mol of air has an initial temperature of 20C. 200 J of heat
energy are transferred to the air in an isochoric process, then
200 J are removed in an isobaric process. Afterward, the air
temperature is
A.
B.
C.
D.
< 20C.
= 20C.
Q
> 20C. T = nC so a smaller T in isobaric with larger C.
Not enough information is given to answer the question.
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Example 17.7 Heating and Cooling a Gas
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Example 17.7 Heating and Cooling a Gas
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Example 17.7 Heating and Cooling a Gas
The figure shows the process on a pV diagram. The gas expands
(moves horizontally on the diagram) as heat is added, then cools
at constant volume (moves vertically on the diagram) as heat is
removed.
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Slide 17-85
Heat Depends on the Path
 Consider the two idealgas processes shown.
 There’s more area under
the process B curve, so
the work |WB| > |WA|.
 Both values of W are
negative as the gas
expands.
 Thermal energy is a state variable, therefore Eth is the
same for both processes, so WA + QA = WB + QB.
 This can only be true if QB > QA.
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Slide 17-86
The First Law of Thermodynamics
 An isothermal process is one for which the
temperature of a specific amount of gas is held
constant (no change in total thermal energy).
 An isochoric process is one for which the volume of the
gas is held constant.
 An adiabatic process is one in which no heat energy is
transferred.
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Slide 17-87
Adiabatic Processes
 An adiabatic process is one for which:
where:
 Adiabats are steeper than
hyperbolic isotherms, so
the temperature falls
during an adiabatic
expansion, and rises
during an adiabatic
compression.
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Slide 17-88
QuickCheck 17.13
A gas in a container expands
rapidly, pushing the piston out.
The temperature of the gas
A.
B.
C.
D.
Rises.
Is unchanged.
Falls.
Can’t say without knowing more.
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Slide 17-89
QuickCheck 17.13
A gas in a container expands
rapidly, pushing the piston out.
The temperature of the gas
A.
B.
C.
D.
Rises.
Is unchanged.
Falls.
Can’t say without knowing more.
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Example 17.9 An Adiabatic Compression
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Example 17.9 An Adiabatic Compression
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Example 17.9 An Adiabatic Compression
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Slide 17-93
Example 17.9 An Adiabatic Compression
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QuickCheck 17.14
A gas in a container expands
rapidly, pushing the piston out.
The temperature of the gas falls.
This is because
A.
B.
C.
D.
E.
The gas pressure falls.
The gas density falls.
Heat energy is removed.
Work is done.
Both C and D.
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QuickCheck 17.14
A gas in a container expands
rapidly, pushing the piston out.
The temperature of the gas falls.
This is because
A.
B.
C.
D.
E.
The gas pressure falls.
The gas density falls.
Heat energy is removed.
Work is done.
Both C and D.
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Slide 17-96
Heat-Transfer Mechanisms
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Conduction
Convection
Radiation
Evaporation
Slide 17-97
Conduction
For a material of crosssection area A and
length L, spanning a
temperature difference
T = TH – TC, the rate of
heat transfer is:
where k is the thermal conductivity, which
characterizes whether the material is a good
conductor of heat or a poor conductor.
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Slide 17-98
Conduction
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Example 17.10 Keeping a Freezer Cold
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Example 17.10 Keeping a Freezer Cold
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Example 17.10 Keeping a Freezer Cold
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Convection
 Thermal energy is easily
transferred through air, water,
and other fluids because the
air and water can flow.
 When the fluid is heated it
generally expands and
becomes less dense.
 Buoyancy then causes the
warmer fluid to flow upward,
while the cooler fluid sinks to
take its place.
 This transfer of thermal energy
by the motion of a fluid is
called convection.
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Warm water (colored) moves by convection.
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Radiation
 All objects emit energy in the form of radiation,
electromagnetic waves generated by oscillating
electric charges in the atoms that form the object.
 This satellite image
shows radiation emitted
by the ocean waters off
the east coast of the
United States.
 You can clearly see the
warm waters of the Gulf
Stream, a large-scale
convection that
transfers heat to
northern latitudes.
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Radiation
 If heat energy Q is radiated in a time interval t by an
object with surface area A and absolute temperature T,
the rate of heat transfer is:
 The parameter e is the emissivity of the surface, a
measure of how effectively it radiates.
 The value of e ranges from 0 to 1.
  = 5.67  10–8 W/m2K4 is the Stefan-Boltzmann
constant.
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QuickCheck 17.15
Suppose the temperature of the sun suddenly dropped
to half its present value. The sun’s power output would
decrease by a factor of
A.
B.
C.
D.
E.
1.
1/2.
1/4.
1/8.
1/16.
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QuickCheck 17.15
Suppose the temperature of the sun suddenly dropped
to half its present value. The sun’s power output would
decrease by a factor of
A.
B.
C.
D.
E.
1.
1/2.
1/4.
1/8.
1/16.
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P is proportional to T 4.
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Example 17.11 Taking the Sun’s Temperature
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Example 17.11 Taking the Sun’s Temperature
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Chapter 17 Summary Slides
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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Important Concepts
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Important Concepts
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