Introduction to Thermal Physics

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15 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Introduction to Thermal Physics

Heat, energy and temperature pervade our lives. Just think about it. We give attention to hot and cold in deciding what
we wear during the day, at night and when we go to bed. We think about the topic when deciding how many covers, if
any at all, we will w
rap in or sleep under at night in order to maintain
the right temperature
. Many of us have heating
and cooling systems in our homes, schools and work places that control the temperature during the day and night to
keep us as comfortable as possible without

spending too much money. We install fans or use portable fans in our homes
to keep us comfortable. Most of us have cars equipped with heating and air conditioning systems; some may even have
meters in their cars that register the indoor and outdoor temper
atures. Many of us watch and listen to weather reports,
especially the forecasted temperatures, with great interest so that we can make decisions about what to wear and what
to do on the following day.

Our bodies are highly sensitive to hot and cold. We l
e
arn very early in life
that we shouldn't touch a hot pot on the stove
or a hot light bulb in a lamp. It is a remarkable lesson that makes an impression for a lifetime.
W
e

also

learn that we
shou
ld be careful about
tasting hot foods. We learn how to use our

hands to feel the heat that emanates from such
foods and we learn how to blow gently on the food to help cool it down. Those of us with either poor gen
es or poor
dental care

know the pain of cold ice cream hitting a nerve in a tooth cavity. And we all hav
e vivid memories of Mom
and Dad sticking a thermome
ter under our tongue

to get our body temperature to see if we had a fever. We all know
the experience of perspiring
-

our bodies built
-
in mechanism of cooling us down when temperatures begin to rise. Our
b
odies have a narrow range of temperatures that they can maintain. Any departure from this range can result in major
consequences, including death.

Energy topics have become topics of national and global interests. Politicians and scholars debate topics as
sociated with
energy supplies, energy alternatives and the impact of our energy dependencies upon the environment. Global
warming

is a
hot topic

in both national and global circles. As the price of octane gasoline rises at the pump, our interest in energy
efficient transportation becomes heightened. Scientists search passionately for alternative fuels which will be cost
effective and environmentally friendly. We often hear of an energy crisis or even an energy shortage. Meanwhile,
scientists preach about th
e law of
conservation of energy
, leaving the public confused about how there can be a
shortage of something that is
conserved
.

What is heat and where does it come from? How does heating and cooling work? When something cools down, what is
it losing or gai
ning? What is hot and cold? Is heat the same thing as temperature? What is temperature? How does a
thermometer measure temperature? What is energy and where does it come from? What is meant by energy
conservation? Why do we need this thing we call energy?
How do we measure heat and energy? What happens to
energy after it is used?

These are among the questions that we hope to
shed light upon during this uni
. Like the laws of gravity, the unwritten
laws of heat and energy seem to govern the thermal behavior o
f our bodies and those objects around us. We wish to
understand these behaviors and the laws that seem to govern them. Our understanding needs to be both
macroscopic

and
particulate
. The patterns that are observed with regard to temperature, heat and energ
y can be explained if we
think about matter at the particle level. We will learn that the behavior of atoms and molecules
-

the building blocks of
matter
-

are the basis for understanding heat and energy. To put it simply, matter consists of little
bangers

and
wigglers
.
These particles
-

bangers and wigglers
-

are in constant motion. They bang against each other and against the walls of
the container. And they also wiggle about a fixed position. The behaviors we observe
-

the macroscopic level
-

are
explain
ed by the behaviors we can't observe
-

the behavior of the
bangers

and
wigglers

at the particle level. Our
effort
throughout this chapter
is to understand the observed patterns of thermal behavior and to explain such patterns in
terms of the particles that

such matter is made of.

Temperature and Thermometers

We all have
a feel

for what temperature is. We even have a shared language th
at we use to

describe temperature. The
water in the shower or bathtub feels hot or cold or warm. The weather outside is
chill
y

or
steamy
. We certainly have a
good feel for how
one temperature is

different than another temperature. We may not always agree on whether the
room temperature is too hot or too cold or just right. But we will likely all agree that we possess built
-
in th
ermometers
for making qualitative judgments about relative temperatures.

What is Temperature?


Despite our built
-
in feel for temperature, it remains one of those concepts in science that is difficult to define. It seems
that a tutorial page exploring the t
opic of temperature and thermometers should begin with a simple definition of
temperature
:



The degree of hotness or coldness of a body or environment.



A measure of the warmth or coldness of an object or substance with reference to some standard value.



A me
asure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or
degrees designated on a standard scale.



A measure of the ability of a substance, or more generally of any physical system, to transfer heat energy to

another physical system.



Any of various standardized numerical measures of this ability, such as the Kelvin, Fahrenheit, and Celsius scale.

For certain, we are comfortable with the first two definitions
-

the degree or measure of how hot or cold and objec
t is.
But our understanding of temperature is not furthered by such definitions. The third and the fourth definitions that
reference the kinetic energy of particles and the ability of a substance to transfer heat are scientifically accurate.
However, these

definitions are far too sophisticated to serve as good starting points for a discussion of temperature. So
we will resign to a definition similar to the fifth one that is listed
-

temperature can be defined as the reading on a
thermometer
. Admittedly, thi
s definition lacks the power that is needed for eliciting the much
-
desired
Aha! Now I
Understand!
moment. Nonetheless it serves as a great st
arting point for this lesson on

heat and temperature.
Temperature

is what the thermometer reads. Whatever it is that temperature is a measure of, it is reflected by the
reading on a thermometer. So exactly how does a thermometer work? How does it reliably
meter

whatever it is that
temperature is a measure of?

How a Therm
ometer Works


Today, there are a variety of types of thermometers.
The type that most of us are familiar with from science class is the
type that consists of a liquid encased in a narrow glass column.

Older thermometers of this type used liquid mercury. In

response to our understanding of the health concerns associated with mercury exposure, these types of thermometers
usually use some type of liquid alcohol. These liquid thermometers are based on the principal of thermal expansion.
When a substance gets ho
tter, it expands to a greater volume.

Nearly all substances exhibit this behavior of thermal
expansion. It is the basis of the design and operation of thermometers.

As the temperature of the liquid in a thermometer increases, its volume increases
. The liqu
id is enclosed in a tall,
narrow glass (or plastic) column with a constant cross
-
sectional area.
The increase in volume is thus due to a change in
height of the liquid within the column. The increase in volume, and thus in the height of the liquid column,
is
proportional to the increase in temperature
. Suppose that a 10
-
degree increase in temperature causes a 1
-
cm increase
in the column's height. Then a 20
-
degree increase in temperature will
cause a 2
-
cm increase in the column's height. And a 30
-
degree inc
rease in
temperature will cause s 3
-
cm increase in the column's height. The
relationship between the temperature and the column's height is linear
over the small temperature range for which the thermometer is used. This
linear relationship makes the calibr
ation of a thermometer a relatively
easy task.

The calibration of any measuring tool involves the placement of divisions
or marks upon the tool to measure a quantity accurately in comparison to
known standards. Any measuring tool
-

even a meter stick
-

mus
t be calibrated. The tool needs divisions or markings; for
instance, a meter stick typically has markings every 1
-
cm apart or every 1
-
mm apart. These markings must be accurately
placed and the accuracy of their placement can only be judged when comparing i
t to another object known to have an
accurate length.

A thermometer is calibrated by using two objects
of known temperatures. The typical process
involves using the freezing point and the boiling
point of water.

Water is known to freeze at 0°C and
to boil

at 100°C at an atmospheric pressure of 1
atm. By placing a thermometer in mixture of ice
water and allowing the thermometer liquid to reach
a stable height, the 0
-
degree mark can be placed
upon the thermometer. Similarly, by placing the
thermometer in boi
ling water (at 1 atm of pressure)
and allowing the liquid level to reach a stable
height, the 100
-
degree mark can be placed upon
the thermometer. With these two markings placed upon the thermometer, 100 equally spaced divisions can be placed
between them t
o represent the 1
-
degree marks. Since there is a linear relationship between the temperature and the
height of the liquid, the divisions between 0 degree and 100 degree can be equally spaced. With a calibrated
thermometer, accurate measurements can be made

of the temperature of any object within the temperature range for
which it has been calibrated.

Temperature Scales


The thermometer calibration process described above results in what is known as a
centigrade thermometer
.

A
centigrade thermometer has 100 divisions or intervals between the normal freezing point and the normal boiling
point of water. Today, the centigrade scale is known as the
Celsius scale
, named after the Swedish astronomer Anders
Celsius who is credited w
ith its development.
The Celsius scale is the most widely accepted temperature scale used
throughout the world. It is the standard unit of temperature measurement in nearly all countries, the most notable
exception being the United States. Using this scale
, a temperature of 28 degrees Celsius is abbreviated as 28°C.

Traditionally slow to adopt the metric system and other accepted units of measurements, the United States more
commonly uses the Fahrenheit temperature scale. A thermometer can be calibrated usi
ng the Fahrenheit scale in a
similar manner as was described above.
The difference is that the normal freezing point of water is designated as 32
degrees and the normal boiling point of water is designated as 212 degrees in the Fahrenheit scale.

As such, t
here are
180 divisions or intervals between these two temperatures when using the Fahrenheit scale.
The Fahrenheit scale is
named in honor of German physicist Daniel Fahrenheit.
A temperature of 76 degree Fahrenheit is abbreviated as 76°F.
In most countrie
s throughout the world, the Fahrenheit scale has been replaced by the use of the Celsius scale.

Temperatures expressed by the Fahrenheit scale can be converted to the Celsius scale equivalent using the equation
below:

°C = (°F
-

32°)/1.8

Similarly,
temperatures expressed by the Celsius scale can be converted to the Fahrenheit scale equivalent using the
equation below:

°F= 1.8•°C + 32°


The Kelvin Temperature Scale


While the Celsius and Fahrenheit scales are the most widely used temperature scales, t
here are several other scales
that have been used throughout history. For example, there is the Rankine scale, the Newton scale and the Romer
scale, all of which are rarely used
. Finally,
there is the
Kelvin temperature scale
, which is the standard metric
system
of temperature measurement and perhaps the most widely used temperature scale used among scientists.

The Kelvin
temperature scale is similar to the Celsius temperature scale in the sense that there are 100 equal degree increments
between the normal
freezing point and the normal boiling point of water. However, the zero
-
degree mark on the Kelvin
temperature scale is 273.15 units cooler than it is on the Celsius scale.
So a temperature of 0 Kelvin is equivalent to a
temperature of
-
273.15 °C
.
Observe t
hat the degree symbol is not used with this system.

So a temperature of 300 units
above 0 Kelvin is referred to as 300 Kelvin and not
300 degree Kelvin; such a temperature is
abbreviated as 300 K. Conversions between Celsius
temperatures and Kelvin temper
atures (and vice
versa) can be performed using one of the two
equations below.

°C = K
-

273.15°

K = °C + 273.15



The zero point on the Kelvin scale is known as
absolute zero
.

It is the lowest temperature that can be achieved.

The
concept of an absolute t
emperature minimum was promoted by
Scottish physicist William Thomson (a.k.a. Lord Kelvin)
in 1848.
Thomson theorized based on thermodynamic principles that the lowest temperature which could be achieved
was
-
273°C. Prior to Thomson, experimentalists such
as Robert Boyle (late 17th century) were well aware of the
observation that the volume (and even the pressure) of a sample of gas was dependent upon its temperature.
Measurements of the variations of pressure
and volume with changes in the
temperature coul
d be made and plotted.
Plots of volume vs. temperature (at
constant pressure) and pressure vs.
temperature (at constant volume) reflected
the same conclusion
-

the volume and the
pressure of a gas reduces to zero at a
temperature of
-
273°C. Since these are

the
lowest values of volume and pressure that
are possible, it is reasonable to conclude
that
-
273°C was the lowest temperature
that was possible.

Thomson referred to this minimum lowest temperature as
absolute zero

and argued that a temperature scale be

adopted that had absolute zero as the lowest value on the scale. Today, that temperature scale bears his name.
Scientists and engineers have been able to cool matter down to temperatures close to
-
273.15°C, but never below it. In
the process of cooling ma
tter to temperatures close to absolute zero, a variety of unusual properties have been
observed. These properties include super
-
conductivity, super
-
fluidity and a state of matter known as a Bose
-
Einstein
condensate.


Temperature is what the thermometer rea
ds. But what exactly is temperature a reflection of? The concept of an
absolute zero temperature is quite interesting and the observation of remarkable physical properties for samples of
matter approaching absolute zero makes one ponder the topic more deep
ly. Is there something happening at the
particle level which is related to the observations made at the macroscopic level? Is there something deeper to
temperature than simply the reading on a thermometer? As the temperature of a sample of matter increases

or
decreases, what is happening at the level of atoms and molecules?



TUESDAY



Due on Friday!

Check Your Understanding

Name ________________________________________ Date _________________

1. In the discussion on the calibration of a thermometer, it was

mentioned that there was a linear relationship between
temperature and the height of the liquid in the column. What if the relationship was not linear? Could a thermometer
still be calibrated if temperature and the column height of the liquid were not rel
ated by a linear relationship?



2. Which is the smaller temperature increment
-

a degree Celsius or a degree Fahrenheit? Explain.



3. Perform the appropriate temperature conversions in order to fill in the blanks in the table below.



Celsius (°)

Fahrenheit (°F)

Kelvin (K)

a.

0



b.


212


c.



0

d.


78


e.


12