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FOR SCIENTISTS AND ENGINEERS

physics

a strategic approach THIRD EDITION

randall d. knight

© 2013 Pearson Education, Inc.

Chapter 16 Lecture


Chapter 16 A Macroscopic Description of Matter

Chapter Goal: To learn the characteristics of macroscopic systems.

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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

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Chapter 16 Preview

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Chapter 16 Reading Quiz

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.

Reading Question 16.1

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



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



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

© 2013 Pearson Education, Inc. Slide 16-24

Densities of Various Materials


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 m3.

Slide 16-26


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.

QuickCheck 16.1

Slide 16-27


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.

QuickCheck 16.1

Slide 16-28

•Atomic Number: # protons

•Atomic Mass: # atomic mass units (u)

•Atomic Mass Unit: 1/12 mass of C-12 atom

• amu = u = 1.66 x 10-27 kg

•Atomic Mass of C = 12.011u (1% is C-13)

•Mass of 1 C = (12.011u) (1.66 x 10-27 kg/u)

Atomic Units

The Basics

•Mole (mol) = # atoms or molecules (particles) as

are in 12 grams of Carbon-12:

1 mole = 6.022 x 1023 particles

• Avogadro’s Number: the number of particles in

one mole: NA= 6.022 x 1023 mol-1

•# moles n contained in a sample of N particles:

n = N/ NA

• # particles in a sample is: N = n NA

Moles and Avogadro’s Number NA= 6.022 x 1023 mol-1

The mass / mol for any substance

has the same numerical value

as its atomic mass:

mass/mol C-12 = 12 g / mol

mass/mol Li = 6.941 g / mol

More on Moles

n = mass / atomic mass

n = mass / (mass/mole) = mass / atomic mass

Q: How many moles are in 1 kg of Sodium?

mass/mole = atomic mass

Na: 22.9898 g / mol

n = mass / (mass/mole)

= 1000 g / (22.9898g/mol)

= 43.5 moles

Q: How many atoms in 1 kg of Sodium?

# particles in a sample is: N = n NA

N = (43.5mol) 6.022 x 1023 mol-1

= 2.62 x 1025 atoms

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

PV = Nkt N= # particles

k =1.38 x 10-23 J/K Boltzmann’s Constant

Note: PV is units of Energy!

P V = nRT

• The only interaction between particles are

elastic collisions (no sticky - no loss of KE)

• This requires LOW DENSITY

• Excellent Approximation for O, N, Ar, CO2

@ room temperature and pressures

• “State” is described by the Ideal Gas Law

• Non “Ideal” are Van der Waals gases

Ideal Gas Problem An ideal gas with a fixed number of molecules

is maintained at a constant pressure. At 30.0

°C, the volume of the gas is 1.50 m3. What is the volume of the gas when the temperature is

increased to 75.0 °C?

1 1PV nRT

2 2PV nRT

1 1

2 2

V T

V T

22 1

1

TV V

T 3 3348

1.5 1.72303

Km m

K


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

1 u 1.66 1027 kg

The atomic mass, in u,

is close, but not exactly,

equal to the atomic

mass number.

u is the atomic mass unit:

Slide 16-29


Moles and Molar Mass

By definition, one mole of

matter, be it solid, liquid, or gas,

is the amount of substance

containing Avogadro’s number

NA of particles

NA 6.02 1023 mol1.

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


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.

QuickCheck 16.2

Slide 16-32


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.

QuickCheck 16.2

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


Which is the largest increase of temperature?

A. An increase of 1F.

B. An increase of 1C.

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.

QuickCheck 16.3

Slide 16-38


Which is the largest increase of temperature?

A. An increase of 1F.

B. An increase of 1C.

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.

QuickCheck 16.3

Slide 16-39


Absolute Zero and Absolute Temperature

Figure (a) shows a constant- volume gas thermometer.

Figure (b) shows the pressure-temperature 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 20C, 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 being added to break 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 0C and the liquid-gas boundary at 100C.

At high altitudes, where p 1 atm, water freezes at slightly above 0C and boils at a temperature below 100C.

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


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.

QuickCheck 16.4

Slide 16-44


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.

QuickCheck 16.4

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 1023 J/K.

Slide 16-47


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.

QuickCheck 16.5

Slide 16-48


If the volume of a sealed container of gas is

decreased, the gas temperature

A. Increases.

B. Stays the same.

C. Decreases.


to tell.

QuickCheck 16.5

Slide 16-49


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


to make a comparison.

QuickCheck 16.6

Slide 16-50


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


to make a comparison.

QuickCheck 16.6

Slide 16-51


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 pB

E. pA pB

QuickCheck 16.7

1 4

1 2

Slide 16-52


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 pB

E. pA pB

QuickCheck 16.7

1 4

1 2

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


The temperature of a rigid (i.e., constant-volume),

sealed container of gas increases from 100C to

200C. 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.

QuickCheck 16.8

Slide 16-56


The temperature of a rigid (i.e., constant-volume),

sealed container of gas increases from 100C to

200C. 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.

QuickCheck 16.8

Temperatures MUST be in K,

not C, to use the ideal-gas law.

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


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.

D. Adiabatic.

E. None of the above.

QuickCheck 16.9

Slide 16-66


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.

D. Adiabatic.


QuickCheck 16.9

Slide 16-67


A cylinder of gas has a frictionless but tightly sealed piston of mass M. The gas temperature is increased from an initial 27C to a final 127C. 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.

QuickCheck 16.10

Slide 16-68


A cylinder of gas has a frictionless but tightly sealed piston of mass M. The gas temperature is increased from an initial 27C to a final 127C. What is the final-to-initial volume ratio Vf /Vi?

A. 1.50

B. 1.33

C. 1.25

D. 1.00


QuickCheck 16.10

Isobaric, so

Vf Tf 400 K Vf Tf 300 K

Slide 16-69


Example 16.7 Comparing Pressure

Slide 16-70



Slide 16-71



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


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.

D. Adiabatic.


QuickCheck 16.11

Slide 16-74


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.

D. Adiabatic.


QuickCheck 16.11

Slide 16-75


What type of gas process is this?

A. Isochoric.

B. Isobaric.

C. Isothermal.

D. Adiabatic.


QuickCheck 16.12

Slide 16-76


What type of gas process is this?

A. Isochoric.

B. Isobaric.

C. Isothermal.

D. Adiabatic.


QuickCheck 16.12

Slide 16-77


A gas follows the process shown. What is

the final-to-initial temperature ratio Tf /Ti?

A. 2

B. 4

C. 8

D. 16


QuickCheck 16.13

Slide 16-78


A gas follows the process shown. What is

the final-to-initial temperature ratio Tf /Ti?

A. 2

B. 4

C. 8

D. 16


QuickCheck 16.13

Slide 16-79

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