Natural Sciences I lecture 7: Heat & Temperature

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The idea that substances are composed of tiny particles (atoms) can be traced back to the Greek philosophers (Democritus, ~ 500 B.C.). However, the concept of atoms did not gain widespread popularity until quite recently – ~ 200 years ago. Both Galileo and Newton were receptive to the idea, but it took the efforts of chemists in the decades just before and after 1800 to finally pull together a consistence picture of the properties and behavior of atoms and small groups of them (molecules). We'll learn more about these chemists later; for now, we need to know only that they built the foundations of what is now called the . We'll begin our discussion of heat and temperature by reviewing some key aspects and assumptions of the theory.

The kinetic molecular theory regards atoms as the smallest, fundamental units of all matter. We still accept this characterization as long as we are considering only those attributes that manifest themselves in the "bulk" properties of matter. Until the early 20th century, it was generally accepted that atoms cannot be divided, created or destroyed – and this is still believed to be true as long as the discussion is restricted to processes involving chemical and physical changes only (that is, non-nuclear process). We'll discuss atoms and subatomic particles later.

Groups of like atoms form pure substances referred to as chemical elements. Each element is composed of a particular "kind" of atom.

The chemical elements sometimes combine in specific ratios to form pure substances referred to as compounds.

A molecule is a tightly-bound group of like or different atoms. For our purposes, we consider a molecule to be the smallest particle of a compound or gaseous element that retains the properties characteristic of the substance.

Kinetic Molecular Theory

Atoms

Elements

Compounds

Molecules

The Kinetic Molecular Theory

having to do with motion

having to do with groups of atoms

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more on molecules...

Usually the word molecule refers to groups of atoms of two or more elements.

water molecule: H O (2 hydrogen atoms; 1 oxygen atom)2

salt "molecule": NaCl (1 sodium atom; 1 chlorine atom)

helium molecule: 1 atom of helium (He)nitrogen molecule: N (2 atoms of nitrogen)2

Examples...

Exceptions...

Note: Some texts use the term "phases" of matter. This usage is misleading – the word phase has a another meaning (as we'll see later in the course)...

States ("Phases") of Matter

state

solid

liquid

gas

plasma

shape

fixed

variable

variable

variable

density

high

high

low

low

volume

fixed

fixed

variable

variable

SOLIDS

crystalline

Glasses

Atoms or molecules are strongly bound together in a more-or-less rigid structure, but they vibrate around their "fixed" positions.

Most solids are , which means that their atoms or molecules are arranged in a repeating geometric pattern. are amorphous solids – their atoms occupy "fixed" positions as in crystals, but have a liquid-like randomness in distribution (no repeating geometric pattern; see next page)...

atoms vibrate around "equilibrium" positions

2-anions (e.g., Cl , O )

-

cations (e.g., Mg , Na )2+ +

3

ionic

metallic

CRYSTALS

GLASS

4

Vibrations of a WATER MOLECULE...

oxygenhydrogens

actual molecule

possible vibrations

instantaneous"shapes"

assymmetricstretch

symmetricstretch

bending

Transmission-electron microscope (TEM) image of metal atoms in titanium niobium oxide (magnified 7,800,000 times). Note the geometric arrangement of the atoms, which defines this material as crystalline.

LIQUIDS

Molecules less strongly bound together than in sol-ids and are not confined to "fixed" positions.

Molecules vibrate indi-vidually and can move with respect to one another.

A liquid has a definite volume but assumes the shape of its container.

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Digression: sizes of atoms and distances between themOn the preceding page it is stated that the distances between

atoms or molecules in a gas are "large". What does this really mean, and can we devise a comparison to familiar dimensions?

First, let's deal with the sizes of atoms. The typical diameter of an atom or ion is 0.1 nanometers (nm). To get a sense of how small this is, think about a period on a page of your textbook – the diameter is about 0.3 millimeters (mm). This means that if you strung atoms on a string to make a chain, you would need

to span the diameter of the tiny punctuation mark!Even the number 3 million is pretty difficult for mostof us to imagine – it's about the population of Chicago,or 30 large football stadiums of 100,000 fans each.

Now, what about the distance between molecules in gas? The distance depends, of course, on the pressure of the gas, but let's assume the pressure is 1 atmosphere. A cubic centimeter (cc) of gas at

19atmospheric pressure contains about 3 x 10 molecules, so there's

-20about one molecule for every 3 x 10 cc (next page...)

0.3 mm 1,000,000 nm

0.1 nm 1 mmX = 3,000,000 atoms

period

3 million atoms

across

PLASMAS

These are "gases" made up of charged (ionized) particles – usually very hot.

The most abundant form of matter in the universe

++

+

+

+

GASES

Molecules are separated by "large" distances and are weakly bound together (if at al).

Molecules are free to move in any direction.

Gases have no fixed shape or volume.

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Molecules move around...

diffusion

2KE = ½ m v

m v

the temperature and the energy of a substance are related in some way.

temperature average kinetic energy

(so they have kinetic energy!)

If you were to enter a large room and open the valve on a small bottle of pressurized gas, the gas molecules would eventually disperse throughout the entire room. Under normal circumstances, this dispersal takes place with the help of moving air currents, but it would occur even if the air were totally still, because the molecules move around randomly in a process called .

The dispersal of a gas by diffusion occurs faster at high temperatures than at low temperatures. The fact that the molecules move means that they have kinetic energy, just as do more familiar objects on much large scales. The kinetic energy of each molecule is given by a familiar equation:

where and are the mass and speed of the molecule, respectively (notice that we're using Newtonian physics, here!). The fact that the gas disperses faster at higher temperature means that, on average, the molecules have more kinetic energy at higher temperatures. This observation provides us with a key piece of information – i.e., that

The of a substance is a measure of the of the molecules that make up that substance

room

gas bottle

-20The linear dimension of a cube with a volume of 3 x 10 cc is about 3 nanometers, which should correspond roughly to the average distance between gas molecules. So the distance between gas molecules is about 30 times the size of the molecules (depending on the identity of the gas). This may be "large" by some definitions, but it's really pretty darned small...

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The kinetic energy of takes three basic forms:gas molecules

Example: Speeds of oxygen molecules in air at room temperature

TRANSLATION ROTATION VIBRATION

speed (m/s)250 500 750 1,0000

nu

mb

er

of m

ole

cule

s

Note that the range of speeds is large (~0 - 1000 m/s), but a typical oxygen molecule is moving remarkably fast:

So we're being pummeled by high-speed oxygen molecules all the time. It's a good thing the molecular mass is small.

~ 500 m/s!

What about the motion (kinetic energy) of molecules ?in liquids

Molecules in liquids can have vibrational, rotational, and some translational kinetic energy, but translational movement is inhibited by collisions with other molecules. A good analogy is being at a party in a very crowded room: you can turn around without difficulty and dance in place, but scooting across the room to catch an old friend you've spotted a the door is virtually impossible.

"Long-distance" movement still occurs, but the rate is much slower than in gases.

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What about the motion (kinetic energy) of molecules ?in solids

The kinetic energy of atoms in a solid is mainly vibrational. The atoms can oscillate about some average position in the structure. Depending on the material and the type of bonding (which we'll discuss later in the course!), there is also some rotational freedom, but "translation events" in the form of atomic jumps from one position to another are infrequent (diffusion still occurs, but it can unimaginably slow at low temperature). If you could make a digital motion picture of atom movements in a solid and trace the paths of the atom centers, the result would look something like this...

LOW TEMPERATURE HIGH TEMPERATURE

TEMPERATURE

We reached the conclusion on page 5 that temperature is a measure of the amount of kinetic energy contained in a substance. It is, however, a purely qualitative measure unless we can agree on a standard scale of some kind. Your body is an effective temperature sensor, but it evaluates temperature relative to itself: it is a heat-transfer sensor. When you come into contact with a substance (solid, liquid, or gas) you can ascertain only whether heat flows into you from the contacting substance, or vice versa.

oYour skin temperature is normally around 84 F. If you climb into a bathtub filled with water at this temperature, it will feel neither hot not cold, because little or no heat transfer occurs.

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TEMPERATURE MEASUREMENT

Today there are many different ways of measuring temperature; all have two things in common:

they take advantage of some physical property of the material they are made of

they are tied in some way to a standard

The kinds of thermometers familiar in everyday use take advantage of the fact that all materials expand on heating and shrink on cooling (the volume changes are more extreme for liquids and gases than for solids)...

iron

brass

BIMETAL

Difference in thermal expansion properties of the two metals causes the composite to bend when heated

Example: Household thermostat

BULBtype

Alcohol or mercury expands and contracts with T changes

Example:Fever thermometer

air

liquid

Question: Guess who invented the first thermometer?

Answer: Galileo, in 1597

Can you figure out how (and whether) it worked?

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Other kinds of thermometers...

voltmeter

junction of twodifferent wires

sheath

THERMOCOUPLE

Examples: householdovens; commercial &laboratory furnaces

PLATINUM RESISTANCETHERMOMETER

length of fineplatinum wire

ohmmeter

Examples: Laboratory& medical equipment

OPTICAL PYROMETER

Incandescence("glow") matchedto incandescentstandard

INFRARED RADIOMETER – now used in medical applications to measure temperature of eardrum

11TEMPERATURE SCALES

Scale

Fahrenheit

Celsius/Centigrade

Absolute/Kelvin

Symbol

F

C

K

H O freezes2

o32

o0

273

H O boils2 *

o212

o100

373

* at sea level (on Earth)

A brief and arbitrary history of temperature

The Fahrenheit scale was "invented" by a German physicist of that name in c. 1715. Interestingly, it was originally a centigrade (100-point) scale, the reference points being the temperature of an ice/salt mixture

o o(0 ) and the temperature of the human body (100 ). Problems developed because the temperature of the human body isn't all that constant, and the reference points were later redefined as the freezing and boiling points of water. Since the original 100-degree basis was retained, the Fahrenheit scale ended up with a 180-degree span between the freezing and boiling points of H O. [This is also why the 2

otemperature of the human body is roughly 100 F.]

The Celsius scale was proposed by a Swedish astronomer of that name in c. 1740. Although not used in American society, this scale is more reasonable in some ways because the freezing and boiling points

ooof H O are nice round numbers (0 , 100 ).2

The absolute scale was introduced in 1847 by physicist William Thompson, would become Lord Kelvin. Noting that the volume of a gas depends on temperature in a systematic (linear) way, he extrapolated to a volume of zero and called the temperature absolute zero...(next page)

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Both the Fahrenheit and Celsius scales are completely arbitrary, as is the absolute (Kelvin) scale in terms of the "size" of degree. The only thing that isn't arbitrary is "0 K" or "absolute zero" which is thought to be the lowest possible temperature, . Absolute zero has never actually been reached, but samples have been cooled to about a millionth of degree above 0 K.

where all molecular motions cease

volu

me

of g

as

o0 C

o100 C

o- 273 C = 0 K

o

e x t r a p o l a t i

n

measured dependenceof volume on temperature(common to all gases)

Note:

when T is expressed in K

V = const (T)gas

o (Note that the " " symbol is not used with the Kelvin scale)

A Table of Kelvin Temperatures...

lowest achieved

helium liquifies

nitrogen liquifies

CO freezes2

water freezes

room temperature

-710

4

77

196

273

293

water boils

iron demagnetizes

iron melts

surface of Sun(middle of Earth)

center of Sun

supernova center

373

1000

1800

6000

710

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