Giambattista Physics Chapter 14 Heat and Phase Changes

Giambattista Physics
Chapter 14
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©McGraw-Hill Education
Chapter 14: Heat
14.1 Internal Energy
14.2 Heat
14.3 Heat Capacity and Specific Heat
14.4 Specific Heat of Ideal Gases
14.5 Phase Transitions
14.6 Thermal Conduction
14.7 Thermal Convection
14.8 Thermal Radiation

14.1 Internal Energy
Molecules move about in random directions.
This random microscopic kinetic energy is part of what we call
the internal energy of the system.
Definition of Internal Energy
The internal energy of a system is the total energy of all of the
molecules in the system except for the macroscopic kinetic
energy (kinetic energy associated with macroscopic translation
or rotation) and the external potential energy (energy due to
external interactions).

What is a System?
A system is whatever we define it to be: one object or a group of
objects.
Everything that is not part of the system is considered to be
external to the system, or in other words, in the surroundings of
the system.

Internal Energy Continued 1
Internal energy includes
• Translational and rotational kinetic energy of molecules due
to their individual random motions .
• Vibrational energy—both kinetic and potential—of
molecules and of atoms within molecules due to random
vibrations about their equilibrium points.
• Potential energy due to interactions between the atoms and
molecules of the system.
• Chemical and nuclear energy—the kinetic and potential
energy associated with the binding of atoms to form
molecules, the binding of electrons to nuclei to form atoms,
and the binding of protons and neutrons to form nuclei.

Internal Energy Continued 2
Internal energy does not include
• The kinetic energy of the molecules due to translation,
rotation, or vibration of the whole system or of a
macroscopic part of the system.
• Potential energy due to interactions of the molecules of the
system with something outside of the system (such as a
gravitational field due to something outside of the system).

Example 14.1
A block of mass 10.0 kg starts at
point A at a height of 2.0 m
above the horizontal and slides
down a frictionless incline to
point B at the bottom. It then
continues sliding along the
horizontal surface of a table that
has friction. The block comes to
rest at point C, a distance of 1.0
m along the table surface.
How much has the internal
energy of the system (block +
table) increased?

Example 14.1 Strategy
decrease in PE from A to B = increase in KE from A to B
= decrease in KE from B to C
= increase in internal energy from B
to C

Example 14.1 Solution
The initial potential energy (taking Ug = 0 at the horizontal
surface) is
The final potential energy is zero. The initial and final
translational kinetic energies of the block are both zero. Ignoring
the small transfer of energy to the air, the increase in the
internal energy of the block and table is 200 J.
A change in the internal energy of a system does not always
cause a temperature change. The internal energy of a system
can change while the temperature of the system remains
constant—for instance, when ice melts.

Example 14.2
A bowling ball at rest has a temperature of 18°C. The ball is then
rolled down a bowling alley.
Ignoring the dissipation of energy by friction and drag forces, is
the internal energy of the ball higher, lower, or the same as
when the ball was at rest?
Is the temperature of the ball higher, lower, or the same as when
the ball was at rest?

The only change is that the ball is now rolling—the ball has
macroscopic translational and rotational kinetic energy.
However, the definition of internal energy does not include the
kinetic energy of the molecules due to translation, rotation, or
vibration of the system as a whole. Therefore, the internal
energy of the ball is the same.
Temperature is associated with the average translational kinetic
energy due to the individual random motions of molecules; the
temperature is still 18°C.

14.2 Heat
Many eighteenth-century scientists thought that heat was a
fluid, which they called “caloric.”
The flow of heat into an object was thought to cause the object
to expand in volume in order to accommodate the additional
fluid; why no mass increase occurred was a mystery.
Now we know that heat is not a substance but is a flow of
energy.

Definition of Heat
Heat is energy in transit between two objects or systems due to
a temperature difference between them.
The calorie is defined as the heat required to change the
temperature of 1 g of water by 1° C (specifically from 14.5 to
15.5 °C).

Heat and Work
Heat and work are similar in that both describe a particular kind
of energy transfer.
Work is an energy transfer due to a force acting through a
displacement.
Heat is a microscopic form of energy transfer involving large
numbers of particles; the exchange of energy occurs due to the
individual interactions of the particles.
No macroscopic displacement occurs when heat flows, and no
macroscopic force is exerted by one object on the other.

Heat and Work as Transfer of Energy
A system can possess energy in various forms (including internal
energy), but it cannot possess heat or work.
Heat and work are two ways of transferring energy from one
system to another.
Direction of Heat Flow
Heat flows spontaneously from a system at higher temperature
to one at lower temperature.

Example 14.3
In an experiment similar to that done by Joule (next slide), an
object of mass 12.0 kg descends a distance of 1.25 m at constant
speed while causing the rotation of a paddle wheel in an
insulated container of water.
If the descent is repeated 20.0 times, what is the internal energy
increase of the water in joules?

Example 14.3 Continued

Each time the object descends, it converts gravitational potential
energy into kinetic energy of the paddle wheel, which in turn
agitates the water and converts kinetic energy into internal
energy.

If all of this energy goes into the water, the internal energy
increase of the water is 2.94 kJ.

The Cause of Thermal Expansion
The forces between atoms are highly asymmetrical with respect
to changes in distance between them. Two atoms separated by
less than their equilibrium distance repel one another strongly ,
while two atoms separated by more than their equilibrium
distance attract one another much less strongly.
Therefore, as vibrational energy increases, the maximum
distance between the atoms increases more than the minimum
distance decreases; the average distance between the atoms
increases.

14.3 Heat Capacity and Specific Heat
Heat Capacity
For a large number of substances, under normal conditions, the
temperature change ΔT is approximately proportional to the
heat Q. The constant of proportionality is called the heat
capacity (symbol C ):
The heat capacity depends both on the substance and on how
much of it is present.

Specific Heat
The heat capacity of the water in a drinking glass is much
smaller than the heat capacity of the water in Lake Superior.
Since the heat capacity of a system is proportional to the mass
of the system, the specific heat capacity (symbol c ) of a
substance is defined as the heat capacity per unit mass:
Specific heat capacity is often abbreviated to specific heat.

Specific Heats of Common Substances

Specific Heat Continued
C Q
Q mc T
m m T
c    


The equation applies when no phase change occurs.

Example 14.4
A saucepan containing 5.00 kg of water initially at 20.0°C is
heated over a gas burner for 10.0 min. The final temperature of
the water is 30.0°C.
(a) What is the internal energy increase of the water?
(b) What is the expected final temperature if the water were
heated for an additional 5.0 min?
(c) Is it possible to estimate the flow of heat from the burner
during the first 10.0 min?

We are interested in the internal energy and the temperature of
the water, so we define a system that consists of the water in the
saucepan.
Although the pan is also heated, it is not part of this system.
The pan, the burner, and the room are all outside the system.

Example 14.4 Solution 1
(a)

(b) We assume that the heat delivered is proportional to the
elapsed time.
The temperature change is proportional to the energy delivered,
so if the temperature changes 10.0°C in 10.0 min, it changes an
additional 5.0°C in an additional 5.0 min.
The final temperature is

(c) Not all of the heat flows into the water. Heat also flows from
the burner into the saucepan and into the room.
All we can say is that more than 209 kJ of heat flows from the
burner during the 10.0 min.

Heat Flow with More Than Two Objects 1
Suppose some water is heated in a large iron pot by dropping a
hot piece of copper into the pot. We can define the system to be
the water, the copper, and the iron pot; the environment is the
room containing the system.
Heat continues to flow among the three substances (iron pot,
water, copper) until thermal equilibrium is reached—that is, until
all three substances are at the same temperature.

Heat Flow with More Than Two Objects 2
If losses to the environment are negligible, all the heat that
flows out of the copper flows into either the iron or the water:
In this case, QCu is negative since heat flows out of the copper;
QFe and QH2O are positive since heat flows into both the iron and
the water.

Calorimetry
A calorimeter is an insulated
container that enables the careful
measurement of heat.
The calorimeter is designed to
minimize the heat flow to or from
the surroundings.
Suppose an object at one
temperature is placed in a
calorimeter with the water and
aluminum cylinder at another
temperature. Then,

Example 14.5
A sample of unknown metal of mass 0.550 kg is heated in a pan
of hot water until it is in equilibrium with the water at a
temperature of 75.0°C. The metal is then carefully removed from
the heat bath and placed into the inner cylinder of an aluminum
calorimeter that contains 0.500 kg of water at 15.5°C. The mass
of the inner cylinder is 0.100 kg.
When the contents of the calorimeter reach equilibrium, the
temperature inside is 18.8°C. Find the specific heat of the metal
sample and determine whether it could be any of the metals
listed in Table 14.1 in the text.

Heat flows from the sample to the water and to the aluminum
until thermal equilibrium is reached, at which time all three have
the same temperature.
We assume negligible heat flow to the environment—in other
words, that no heat flows into or out of the system consisting of
aluminum + water + sample.

Heat flows out of the sample (Qs < 0) and into the water and
aluminum cylinder (Qw > 0 and Qa > 0).

We summarize what we know about the substances in this
problem in the following table:

By comparing to values listed in Table 14.1 in the text, it appears
that the unknown sample could be silver.

14.4 Specific Heat of Ideal Gases
The total translational kinetic energy of a gas containing N
molecules (n moles) is
For heat transferred to a monatomic gas at constant volume
(zero work),

Equipartition of Energy
The theorem of equipartition of energy says that internal energy
is distributed equally among all the possible ways in which it can
be stored (as long as the temperature is sufficiently high).
Each independent form of energy has an average of (1/2)kT of
energy per molecule and contributes (1/2)R to the molar specific
heat at constant volume.

Diatomic Molecules
V
translations rotations
1 1 1 1 1 5 J/K
20.8
2 2 2 2 2 2 mol
C R R R R R R
      

Some Specific Heats for Gases
Each species of gas has
approximately the same
specific heat CV depending on
its type (monatomic, diatomic,
polyatomic), consistent with
the equipartition theorem.

Example 14.6
A cylinder contains 250 L of xenon gas (Xe) at 20.0°C and a
pressure of 5.0 atm.
How much heat is required to raise the temperature of this gas
to 50.0°C, holding the volume constant?
Treat the xenon as an ideal gas.
Strategy
The number of moles of xenon (n) can be found from the ideal
gas law, PV = nRT.
Xenon is a monatomic gas, so we expect CV = (3/2)R.

14.5 Phase Transitions
A phase transition occurs whenever a material is changed from
one phase, such as the solid phase, to another, such as the
liquid phase.
During the two phase transitions, heat flow continues, and the
internal energy changes, but the temperature of the mixture of
two phases does not change.

Heat Required to Turn Ice Into Steam
It takes about as much energy to
melt the ice at 0C as it takes to
heat the water from 0C to
100C.
It takes significantly more energy
to convert the water at 100C
into steam at 100C (i.e., to boil
the water).

Latent Heat
The heat required per unit mass of substance to produce a phase
change is called the latent heat ( L ). The word latent is related to
the lack of temperature change during a phase transition.
The sign of Q depends on the direction of the phase transition.
For melting or boiling, Q > 0 (heat flows into the system). For
freezing or condensation, Q < 0 (heat flows out of the system).

Latent Heats of Fusion and Vaporization
The heat per unit mass for the solid-liquid phase transition (in
either direction) is called the latent heat of fusion ( Lf ).
For the liquid-gas phase transition (in either direction), the heat
per unit mass is called the latent heat of vaporization ( Lv ).

Microscopic View of a Phase Change
When a substance is in solid form, bonds between the atoms or
molecules hold them near fixed equilibrium positions. Energy
must be supplied to break the bonds and change the solid into a
liquid.
When the substance is changed from liquid to gas, energy is used
to separate the molecules from the loose bonds holding them
together and to move the molecules apart.
Temperature does not change during these phase transitions
because the kinetic energy of the molecules is not changing.
Instead, the potential energy of the molecules changes as work
is done against the forces holding them together.

Example 14.7
A jewelry designer plans to make some specially ordered silver
charms for a commemorative bracelet.
If the melting point of silver is 960.8°C, how much heat must the
jeweler add to 0.500 kg of silver at 20.0°C to be able to pour
silver into her charm molds?
Strategy
The solid silver first needs to be heated to its melting point; then
more heat has to be added to melt the silver.

Example 14.8
Ice cube trays are filled with 0.500 kg of water at 20.0°C and
placed into the freezer compartment of a refrigerator.
How much energy must be removed from the water to turn it
into ice cubes at −5.0°C?
Strategy
First, the liquid water is cooled to 0°C. Then the phase change
occurs at constant temperature. Now the water is frozen; the ice
continues to cool to −5.0°C. The energy that must be removed
for the whole process is the sum of the energy removed in each
of the three steps.

So 214 kJ of heat flows out of the water that becomes ice cubes.

Example 14.9
Two 50-g ice cubes are placed into 0.200 kg of water in a
Styrofoam cup. The water is initially at a temperature of 25.0°C,
and the ice is initially at a temperature of −15.0°C.
What is the final temperature of the drink? The average specific
heat for ice between −15°C and 0°C is 2.05 kJ/(kg·°C).

We need to raise the temperature of the ice from −15°C to 0°C
before the ice can melt, so we first find how much heat this
requires.
Then we find how much heat is needed to melt all the ice.
Once the ice is melted, the water from the melted ice can be
raised to the final temperature of the drink.

Since heat flows out of the water and into the ice, Qw < 0 and
Qice > 0. Their sum is zero:

This result does not make sense.

What if the water initially at 25°C cools all the way to 0°C? From
cooling the water, how much heat is available to warm the ice
and melt it?
Thus, the water can supply 20.93 kJ when it cools to 0°C. But to
warm the ice requires 3.075 kJ and to melt all of the ice requires
another 33.37 kJ. The ice can be warmed to 0°C, but there is not
enough heat available to melt all of the ice.

Phase Diagrams
A useful tool in the study of phase transitions is the phase
diagram—a diagram on which pressure is plotted on the vertical
axis and temperature on the horizontal axis.
The curves on the phase
diagram are the demarcations
between the solid, liquid, and
gas phases.
At the triple point, all three
phases (solid, liquid, and gas)
can coexist in equilibrium.
Notice that the vapor
pressure curve ends at the
critical point.

The Unusual Phase Diagram of Water

14.6 Thermal Conduction
The conduction of heat can
take place within solids, liquids,
and gases.
Conduction is due to collisions
between atoms (or molecules)
in which energy is exchanged.
Conduction also occurs
between objects that are in
contact.

Fourier’s Law of Heat Conduction
where κ is the thermal conductivity of the material, A is the
cross-sectional area, d is the thickness (or length) of the
material, and Δ T is the temperature difference between one
side and the other.
The quantity ΔT / d is called the temperature gradient.

Thermal Resistance
The quantity d/( A) is called the thermal resistance R.

Conduction Through Materials in Series

Continued
For n layers,

Example 14.10
A windowpane that measures 20.0 cm by 15.0 cm is set into the
front door of a house. The glass is 0.32 cm thick. The
temperature outdoors is −15°C and inside is 22°C.
At what rate does heat leave the house through that one small
window?

Given: T = 22C – ( – 15C) = 37C;
thickness of windowpane d = 0.32  10-2 m;
area of windowpane A = 0.200 m  0.150 m = 0.0300 m2
Look up: thermal conductivity for glass = 0.63 W/(mK)
Find: rate of heat flow.

Thermal Conduction Through Windows
An accurate calculation of the
energy loss through a single-paned
window must take into account the
thin layer of stagnant air, due to
viscosity, on each side of the glass.
The temperature gradient across
the glass is considerably smaller
than the difference between indoor
and outdoor temperatures. In fact,
much of the thermal resistance of a
window is due to the stagnant air
layers rather than to the glass.

Example 14.11
The single-paned window of Example 14.10 is replaced by a
double-paned window with an air gap of 0.50 cm between the
two panes. The inner surface of the inner pane is at 22°C and the
outer surface of the outer pane is at −15°C.
What is the new rate of heat loss through the double-paned
window?

14.7 Thermal Convection
Convection involves fluid currents that carry heat from one place
to another.
In conduction, energy flows through a material but the material
itself does not move. In convection, the material itself moves
from one place to another.

Natural and Forced Convection
In natural convection, the currents
are due to gravity. Fluid with a
higher density sinks because the
buoyant force is smaller than the
weight; less dense fluid rises
because the buoyant force
exceeds the weight.
In forced convection, fluid is
pushed around by mechanical
means such as a fan or pump.

14.8 Thermal Radiation
All objects emit energy through electromagnetic radiation due to
the oscillation of electric charges in the atoms.
Thermal radiation consists of electromagnetic waves that travel
at the speed of light. Unlike conduction and convection,
radiation does not require a material medium; the Sun radiates
heat to Earth through the near vacuum of space.
An object emits thermal radiation while absorbing some of the
thermal radiation emitted by other objects.

Blackbody
An idealized body that absorbs all the radiation incident upon it
is called a blackbody .
A blackbody absorbs not only all visible light, but infrared,
ultraviolet, and all other wavelengths of electromagnetic
radiation.
It turns out that a good absorber is also a good emitter of
radiation. A blackbody emits more radiant power per unit
surface area than any real object at the same temperature.

Stefan’s Law of Radiation
(blackbody)
Since real bodies are not perfect absorbers and therefore emit
less than a blackbody, we define the emissivity ( e ) as the ratio
of the emitted power of the body to that of a blackbody at the
same temperature.

Radiation Spectrum
Blackbody radiation
At the higher temperatures,
the wavelength of maximum
radiation is shorter (Wien’s
law, next slide) and the total
power radiated, represented
by the area under the graph,
increases (Stefan’s law).

Wien’s Law
3
max 2.898 10 m·K
T
 
 
where the temperature T is the temperature in kelvins and λmax is
the wavelength of maximum radiation in meters.

Example 14.13
The maximum rate of energy emission from the Sun occurs in
the middle of the visible range—at about λ = 0.5 μm.
Estimate the temperature of the Sun’s surface.
Strategy
We assume the Sun to be a blackbody. Then the wavelength of
maximum emission and the surface temperature are related by
Wien’s law.

Simultaneous Emission and Absorption
An object simultaneously emitting and absorbing thermal
radiation has a net rate of heat flow due to thermal radiation
given by
Suppose an object with surface area A and temperature T is
bathed in thermal radiation coming from its surroundings in all
directions that are at a uniform temperature Ts. Then the net
rate of heat flow due to emission and absorption of thermal
radiation is

Simultaneous Emission and Absorption:
Emissivity
The emissivity e measures not only how much the object emits
compared to a blackbody, it also measures how much the object
absorbs compared with a blackbody.
Emissivity depends on temperature. The equation
assumes the emissivity at temperature T is the same as the
emissivity at temperature Ts. If T and Ts are very different, we
would have to modify the equation to use two different
emissivities.

Example 14.14
A person of body surface area 2.0 m2 is sitting in a doctor’s
examining room with no clothing on. The temperature of the
room is 22°C and the person’s average skin temperature is 34°C.
Skin emits about 97% as much as a blackbody at the same
temperature for wavelengths in the infrared region, where most
of the emission occurs.
At what net rate is energy radiated away from the body?

Given: surface area, A = 2.0 m2;
Troom = 22C; skin temperature, T = 34C;
fraction of energy emitted, e = 0.97
Find: net rate of energy transfer.

Example 14.15
Radiant energy from the Sun reaches Earth at a rate of 1.7 × 1017
W. An average of about 30% is reflected, and the rest is
absorbed. Energy is also radiated by the atmosphere.
Assuming equal rates of absorption and emission, and that the
atmosphere emits as a blackbody in the infrared (e = 1), calculate
the temperature of the atmosphere.
(The Sun’s radiation peaks in the visible part of the spectrum, but
Earth’s radiation peaks in the infrared due to its much lower
surface temperature.)

Earth must radiate the same power as it absorbs. We use
Stefan’s law to find the rate at which energy is radiated as a
function of temperature and then equate that to the rate of
energy absorption.

Application of Thermal Radiation: Global
Climate Change

Appendix
Two rectangular slabs of different materials are placed together
as adjacent layers. Heat flows through the layers from higher to
lower temperature. The left side of the first slab it at
temperature T1. Where the two layers touch the temperature is
T2. The opposite side of the second layer is at temperature T3.
The temperatures satisfy T1 > T2 > T3. The thickness of the first
slab is d1 and that of the second slab is d2. A graph of
temperature T as a function of position x is also shown. The
slope of the graph in either material is the temperature gradient
ΔT/d in that material. The temperature gradients are not the
same because the materials have different thermal
conductivities.

Giambattista Physics Chapter 14 Heat and Phase Changes

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