### lect_outline_16 - Colorado Mesa University

```Chapter 16 Lecture
physics
FOR SCIENTISTS AND ENGINEERS
a strategic approach
THIRD EDITION
randall d. knight
Chapter 16 A Macroscopic Description of Matter
Chapter Goal: To learn the characteristics of macroscopic systems.
Slide 16-2
Chapter 16 Preview
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Chapter 16 Preview
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Chapter 16 Preview
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Chapter 16 Preview
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Chapter 16 Preview
Slide 16-7
Slide 16-8
What is the SI unit of pressure?
A. The Nm2 (Newton-meter-squared).
B. The atmosphere.
C. The p.s.i.
D. The Pascal.
E. The Archimedes.
Slide 16-9
What is the SI unit of pressure?
A. The Nm2 (Newton-meter-squared).
B. The atmosphere.
C. The p.s.i.
D. The Pascal.
E. The Archimedes.
Slide 16-10
One “mole” of monatomic helium means
A. 0.012 kg of helium.
B. One helium atom.
C. One kg of helium.
D. 4 helium atoms.
E. 6.02  1023 helium atoms.
Slide 16-11
One “mole” of monatomic helium means
A. 0.012 kg of helium.
B. One helium atom.
C. One kg of helium.
D. 4 helium atoms.
E. 6.02  1023 helium atoms.
Slide 16-12
The SI unit for absolute temperature is
A. Celsius.
B. Fahrenheit.
C. Kelvin.
D. Newton.
E. Rankine.
Slide 16-13
The SI unit for absolute temperature is
A. Celsius.
B. Fahrenheit.
C. Kelvin.
D. Newton.
E. Rankine.
Slide 16-14
The ideal-gas model is valid if
A. The gas density and temperature are both low.
B. The gas density and temperature are both high.
C. The gas density is low and the temperature
is high.
D. The gas density is high and the temperature
is low.
Slide 16-15
The ideal-gas model is valid if
A. The gas density and temperature are both low.
B. The gas density and temperature are both high.
C. The gas density is low and the temperature
is high.
D. The gas density is high and the temperature
is low.
Slide 16-16
An ideal-gas process in which the
volume doesn’t change is called
A. Isobaric.
B. Isothermal.
C. Isochoric.
D. Isentropic.
Slide 16-17
An ideal-gas process in which the
volume doesn’t change is called
A. Isobaric.
B. Isothermal.
C. Isochoric.
D. Isentropic.
Slide 16-18
Chapter 16 Content, Examples, and
QuickCheck Questions
Slide 16-19
Solids, Liquids, and Gases
 A solid is a rigid macroscopic system consisting of
particle-like atoms connected by spring-like molecular
bonds.
 Each atom vibrates around an equilibrium position but
otherwise has a fixed position.
Slide 16-20
Solids, Liquids, and Gases
 A liquid is nearly incompressible, meaning the molecules
are about as close together as they can get.
 A liquid flows and deforms to fit the shape of its container,
which tells us that the molecules are free to move around.
Slide 16-21
Solids, Liquids, and Gases
 A gas is a system in which each molecule moves
through space as a free, noninteracting particle until,
on occasion, it collides with another molecule or with
the wall of the container.
 A gas is a fluid, and it is highly compressible.
Slide 16-22
Density
The ratio of an object’s or material’s mass to its
volume is called the mass density, or sometimes
simply “the density.”
The SI units of mass density are kg/m3. In this
chapter we’ll use an uppercase M for the system
mass and lowercase m for the mass of an atom.
Slide 16-23
Densities of Various Materials
Slide 16-24
Example 16.1 The Mass of a Lead Pipe
Slide 16-25
Number Density
 It is often useful to know the
number of atoms or molecules
per cubic meter in a system.
 We call this quantity the number
density.
 In an N-atom system that fills
volume V, the number density is:
The SI units of number density are m3.
Slide 16-26
QuickCheck 16.1
The volume of this cube is
A.
8  102 m3.
B.
8 m3.
C.
8  10–2 m3.
D.
8  10–4 m3.
E.
8  10–6 m3.
Slide 16-27
QuickCheck 16.1
The volume of this cube is
A.
8  102 m3.
B.
8 m3.
C.
8  10–2 m3.
D.
8  10–4 m3.
E.
8  10–6 m3.
Slide 16-28
Atomic Mass and Atomic Mass Number
 The mass of an atom is determined primarily by its most
massive constituents: protons and neutrons in its nucleus.
 The sum of the number of protons and neutrons is called
the atomic mass number:
  number of protons  number of neutrons
 The atomic mass, in u,
is close, but not exactly,
equal to the atomic
mass number.
 u is the atomic mass unit:
1 u  1.66  1027 kg
Slide 16-29
Moles and Molar Mass
 By definition, one mole of
matter, be it solid, liquid, or gas,
is the amount of substance
NA of particles
 NA  6.02  1023 mol1.
 The number of moles in a
substance containing N basic
particles is
One mole of helium, sulfur, copper, and
mercury.
Slide 16-30
Moles and Molar Mass
 If the atomic mass m is specified in kilograms, the
number of atoms in a system of mass M can be
found from:
 The molar mass of a substance is the mass of 1 mol
of substance.
 The molar mass, which we’ll designate Mmol, has
units kg/mol.
 The number of moles in a system of mass M consisting
of atoms or molecules with molar mass Mmol is:
Slide 16-31
QuickCheck 16.2
Which contains more molecules, a mole of
hydrogen gas (H2) or a mole of oxygen gas (O2)?
A.
The hydrogen.
B. The oxygen.
C. They each contain the same number of
molecules.
D. Can’t tell without knowing their temperatures.
Slide 16-32
QuickCheck 16.2
Which contains more molecules, a mole of
hydrogen gas (H2) or a mole of oxygen gas (O2)?
A.
The hydrogen.
B. The oxygen.
C. They each contain the same number of
molecules.
D. Can’t tell without knowing their temperatures.
Slide 16-33
Example 16.2 Moles of Oxygen
Slide 16-34
Temperature
 What is temperature?
 Temperature is related to
how much thermal energy
is in a system (more on
this in Chapter 18).
 For now, in a very practical
sense, temperature is what we
measure with a thermometer!
 In a glass-tube thermometer, such as the ones shown,
a small volume of liquid expands or contracts when
placed in contact with a “hot” or “cold” object.
 The object’s temperature is determined by the length of
the column of liquid.
Slide 16-35
Temperature
 The Celsius temperature scale is defined by setting
TC  0 for the freezing point of pure water, and TC  100
for the boiling point.
 The Kelvin temperature scale has the same unit size
as Celsius, with the zero point at absolute zero. The
conversion from the Celsius scale to the Kelvin scale is:
 The Fahrenheit scale, still widely used in the United
States, is defined by its relation to the Celsius scale,
as follows:
Slide 16-36
Temperature
Slide 16-37
QuickCheck 16.3
Which is the largest increase of temperature?
A. An increase of 1F.
B. An increase of 1C.
C. An increase of 1 K.
D. Both B and C, which are the same and larger
than A.
E. A, B, and C are all the same increase.
Slide 16-38
QuickCheck 16.3
Which is the largest increase of temperature?
A. An increase of 1F.
B. An increase of 1C.
C. An increase of 1 K.
D. Both B and C, which are the same and larger
than A.
E. A, B, and C are all the same increase.
Slide 16-39
Absolute Zero and Absolute Temperature
 Figure (a) shows a constantvolume gas thermometer.
 Figure (b) shows the pressuretemperature relationship for three
different gases.
 There is a linear relationship
between temperature and pressure.
 All gases extrapolate to zero
pressure at the same temperature:
T0  273 C.
 This is called absolute zero, and
forms the basis for the absolute
temperature scale (Kelvin).
Slide 16-40
Phase Changes
 Suppose you were to remove
an ice cube from the freezer,
initially at 20C, and then
warm it by transferring heat at
a constant rate.
 Figure (b) shows the
temperature as a function of
time.
 During the phase changes of
melting then boiling, energy is
molecular bonds, but the
temperature remains constant.
Slide 16-41
Phase Changes
 A phase diagram is used to
show how the phases and
phase changes of a substance
vary with both temperature
and pressure.
 At the normal 1 atm of pressure,
water crosses the solid-liquid
boundary at 0C and the liquid-gas boundary at 100C.
 At high altitudes, where p  1 atm, water freezes at slightly
above 0C and boils at a temperature below 100C.
 In a pressure cooker, p  1 atm and the temperature of
boiling water is higher, allowing the food to cook faster.
Slide 16-42
Phase Changes
Food takes longer to cook at high altitudes because the
boiling point of water is less than 100 C.
Slide 16-43
QuickCheck 16.4
If the pressure of liquid water is suddenly
decreased, it is possible that the water will
A. Freeze.
B. Condense.
C. Boil.
D. Either A or B.
E. Either A or C.
Slide 16-44
QuickCheck 16.4
If the pressure of liquid water is suddenly
decreased, it is possible that the water will
A. Freeze.
B. Condense.
C. Boil.
D. Either A or B.
E. Either A or C.
Slide 16-45
Ideal Gases
 The ideal-gas model is one in which we model atoms
in a gas as being hard spheres.
 Such hard spheres fly through space and occasionally
interact by bouncing off each other in perfectly elastic
collisions.
 Experiments show that the ideal-gas model is quite
good for gases if two conditions are met:
1.The density is low (i.e., the atoms occupy a volume
much smaller than that of the container), and
2.The temperature is well above the condensation
point.
Slide 16-46
The Ideal-Gas Law
The pressure p, the volume V,
the number of moles n and the
temperature T of an ideal gas
are related by the ideal-gas law
as follows:
where R is the universal gas constant, R  8.31 J/mol K.
Or:
where N is the number of molecules and kB is
Boltzman’s constant, kB  1.38  1023 J/K.
Slide 16-47
QuickCheck 16.5
If the volume of a sealed container of gas is
decreased, the gas temperature
A. Increases.
B. Stays the same.
C. Decreases.
D. Not enough information
to tell.
Slide 16-48
QuickCheck 16.5
If the volume of a sealed container of gas is
decreased, the gas temperature
A. Increases.
B. Stays the same.
C. Decreases.
D. Not enough information
to tell.
Slide 16-49
QuickCheck 16.6
Two identical cylinders, A and B, contain the same type
of gas at the same pressure. Cylinder A has twice as
much gas as cylinder B. Which is true?
A. TA  TB
B. TA  TB
C. TA  TB
D. Not enough information
to make a comparison.
Slide 16-50
QuickCheck 16.6
Two identical cylinders, A and B, contain the same type
of gas at the same pressure. Cylinder A has twice as
much gas as cylinder B. Which is true?
A. TA  TB
B. TA  TB
C. TA  TB
D. Not enough information
to make a comparison.
Slide 16-51
QuickCheck 16.7
Two cylinders, A and B, contain the same type of gas at the
same temperature. Cylinder A has twice the volume as
cylinder B and contains half as many molecules as cylinder
B. Which is true?
A. pA  4pB
B. pA  2pB
C. pA  pB
D. pA  21 pB
E. pA  41 pB
Slide 16-52
QuickCheck 16.7
Two cylinders, A and B, contain the same type of gas at the
same temperature. Cylinder A has twice the volume as
cylinder B and contains half as many molecules as cylinder
B. Which is true?
A. pA  4pB
B. pA  2pB
C. pA  pB
D. pA  21 pB
E. pA  41 pB
Slide 16-53
Example 16.3 Calculating a Gas Pressure
Slide 16-54
Ideal Gases
 All ideal-gas problems involve a gas in a sealed container.
 The number of moles (and number of molecules) will not
change during a problem.
 In that case,
 If the gas is initially in state i, characterized by the state
variables pi, Vi, and Ti, and at some later time in a final
state f, the state variables for these two states are
related by:
Slide 16-55
QuickCheck 16.8
The temperature of a rigid (i.e., constant-volume),
sealed container of gas increases from 100C to
200C. The gas pressure increases by a factor of
A. 2.
B. 1.3.
C. 1 (the pressure doesn’t change).
D. 0.8.
E. 0.5.
Slide 16-56
QuickCheck 16.8
The temperature of a rigid (i.e., constant-volume),
sealed container of gas increases from 100C to
200C. The gas pressure increases by a factor of
A. 2.
B. 1.3.
Temperatures MUST be in K,
not C, to use the ideal-gas law.
C. 1 (the pressure doesn’t change).
D. 0.8.
E. 0.5.
Slide 16-57
Example 16.4 Calculating a Gas Temperature
Slide 16-58
Ideal-Gas Processes
 An ideal-gas process can
be represented on a graph
of pressure versus volume,
called a pV diagram.
 Knowing p and V, and
assuming that n is known
for a sealed container, we
can find the temperature T
by using the ideal-gas law.
 Here is a pV diagram
showing three states of a
system consisting of 1 mol
of gas.
Slide 16-59
Ideal-Gas Processes
 There are infinitely many
ways to change the gas
from state 1 to state 3.
 Here are two different
trajectories on the pV
diagram showing how the
gas might be changed
from state 1 to state 3.
Slide 16-60
Ideal-Gas Processes
 (a) If you slowly pull a piston
out, you can reverse the
process by slowly pushing
the piston in.
 This is called a quasi-static
process.
 (b) is a sudden process,
which cannot be represented
on a pV diagram.
 This textbook will always
assume that processes
are quasi-static.
Slide 16-61
Constant-Volume Process
 A constant-volume process is called an isochoric
process.
 Consider the gas in a closed, rigid container.
 Warming the gas with a flame will raise its pressure
without changing its volume.
Slide 16-62
Example 16.6 A Constant-Volume Gas
Thermometer
Slide 16-63
Example 16.6 A Constant-Volume Gas
Thermometer
Slide 16-64
Constant-Pressure Process
 A constant-pressure process
is called an isobaric process.
 Consider a cylinder of gas
with a tight-fitting piston of
mass M that can slide up and
down but seals the container.
 In equilibrium, the gas pressure
inside the cylinder is:
Slide 16-65
QuickCheck 16.9
A cylinder of gas has a frictionless but
tightly sealed piston of mass M.
A small flame heats the cylinder,
causing the piston to slowly move
upward. For the gas inside the
cylinder, what kind of process is this?
A.
Isochoric.
B.
Isobaric.
C.
Isothermal.
E.
None of the above.
Slide 16-66
QuickCheck 16.9
A cylinder of gas has a frictionless but
tightly sealed piston of mass M.
A small flame heats the cylinder,
causing the piston to slowly move
upward. For the gas inside the
cylinder, what kind of process is this?
A.
Isochoric.
B.
Isobaric.
C.
Isothermal.
E.
None of the above.
Slide 16-67
QuickCheck 16.10
A cylinder of gas has a frictionless
but tightly sealed piston of mass M.
The gas temperature is increased
from an initial 27C to a final 127C.
What is the final-to-initial volume
ratio Vf /Vi?
A. 1.50
B. 1.33
C. 1.25
D. 1.00
E. Not enough information to tell.
Slide 16-68
QuickCheck 16.10
A cylinder of gas has a frictionless
but tightly sealed piston of mass M.
The gas temperature is increased
from an initial 27C to a final 127C.
What is the final-to-initial volume
ratio Vf /Vi?
A. 1.50
B. 1.33
C. 1.25
Isobaric, so
Vf  Tf  400 K
Vf
Tf
300 K
D. 1.00
E. Not enough information to tell.
Slide 16-69
Example 16.7 Comparing Pressure
Slide 16-70
Example 16.7 Comparing Pressure
Slide 16-71
Example 16.7 Comparing Pressure
Slide 16-72
Constant-Temperature Process
 A constant-temperature process
is called an isothermal process.
 Consider a piston being pushed
down to compress a gas.
 Heat is transferred through the
walls of the cylinder to keep T
fixed, so that:
 The graph of p versus V for an
isotherm is a hyperbola.
Slide 16-73
QuickCheck 16.11
A cylinder of gas floats in a large tank of water. It has a
frictionless but tightly sealed piston of mass M. Small
masses are slowly placed onto the top
of the piston, causing it to slowly move
downward. For the gas inside the cylinder,
what kind of process is this?
A. Isochoric.
B. Isobaric.
C. Isothermal.
E. None of the above.
Slide 16-74
QuickCheck 16.11
A cylinder of gas floats in a large tank of water. It has a
frictionless but tightly sealed piston of mass M. Small
masses are slowly placed onto the top
of the piston, causing it to slowly move
downward. For the gas inside the cylinder,
what kind of process is this?
A. Isochoric.
B. Isobaric.
C. Isothermal.
E. None of the above.
Slide 16-75
QuickCheck 16.12
What type of gas process is this?
A. Isochoric.
B. Isobaric.
C. Isothermal.
E. None of the above.
Slide 16-76
QuickCheck 16.12
What type of gas process is this?
A. Isochoric.
B. Isobaric.
C. Isothermal.
E. None of the above.
Slide 16-77
QuickCheck 16.13
A gas follows the process shown. What is
the final-to-initial temperature ratio Tf /Ti?
A. 2
B. 4
C. 8
D. 16
E. Not enough information to tell.
Slide 16-78
QuickCheck 16.13
A gas follows the process shown. What is
the final-to-initial temperature ratio Tf /Ti?
A. 2
B. 4
C. 8
D. 16
E. Not enough information to tell.
Slide 16-79
Example 16.10 A Multistep Process
Slide 16-80
Example 16.10 A Multistep Process
Slide 16-81
Example 16.10 A Multistep Process
Slide 16-82
Chapter 16 Summary Slides
Slide 16-83
General Principles
Slide 16-84
General Principles