Class
notes by RE-SEED Leader - Alex
Vanderburgh
RESEED Notes - Class 11 - 25 Sep 01 - Framingham - Temp/Heat - 11-1
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We all know what it is! It's just a measure of how hot or how
cold it is! This is very hard to do, and it is therefore hard to
tell what we mean by "temperature". And, it has been very hard
to
find a numerical measure! We know that Fahrenheit, Celsius, Roemer,
and Kelvin were leaders in the effort, and there were many others.
In 1967 it was agreed that the official Kelvin degree was
fundamental and "K" without the degree sign should be used.
The
triple point of water is called 273.16 Kelvins - not 273.16 degrees
Kelvin, and the Kelvin is by definition 1/273.16 of this "triple
point". [Note that the size is the same as the Celsius degree. The
Kelvin definition is based on a lot of history, and is arbitrary.]
Our measurement is OK when our thermometer is small, and the
`object' is a liquid in a well insulated container. BUT large
objects, for example a human body, can have different temperatures
in different places. And, as usual, the human range (0-100 C) seems
reasonable. But the farther you get from human senses, the more
difficult the idea is. The surface of the Sun and an Atomic
explosion involve temperature in millions of Kelvins. Does an
electron HAVE a temperature? (My guess is that `temperature' is not
applicable.) (Radar Engineers talk about the "temperature" of
their
antenna pickup device. Does that make any sense in middle school?)
Ordinary mortals still use Fahrenheit and Celsius (or
Centigrade if you are old enough). [And we still have to say
`degrees'.] Both F and C scales have two fixed points - the
freezing point and boiling point of water. It has long been known
that many gases and liquids expand as the temperature rises. A gas
thermometer using air can be made from a bottle with a stopper and a
glass tube. A drop or two of colored water in the tube will move as
you heat or cool the bottle. You can mark the two known points,
pick a number of divisions and just extend the scale above and
below. Whereas we frown on our intuition as non-scientific, we
should not dismiss it entirely. If you plot pressure vs.
temperature, and fit a straight line to the points, you find that
pressure goes to zero at about -273 C. If you call that point
"zero", you get the Kelvin scale. This seems to be pure intuition
to me, but I'm told there is good reason to go along. It's an act
of faith, and there are more to come. For example, it turns out
that the pressure in an ideal gas is proportional to absolute
temperature (Kelvin), but not to Celsius or Fahrenheit. [Just for
fun, see the Enclyclopaedia Brittanica under "Heat" (30 pages),
and
under "Thermometry" (14 pages).]
Fahrenheit picked 32 for freezing, and 212 for boiling. [These
peculiar choices were based on the Roemer scale and influenced by
mercury thermometers. [The zero was the coldest temperature they
could make in the lab.] Celsius picked 0 for freezing and 100 for
boiling. The 100 steps in between are identical. [By definition.]
[It is curious that "normal" body temperature - 98.6 F comes
out
to an even 37 C. My theory is that it was chosen in Europe.]
Celsius did indeed create a real thermometer, but it was upside-
down! In its rightside-up form it existed as "Centigrade" until
1948!
11-2
One design of an air thermometer has the sensing bulb at the
top, and the bottom sits in a colored liquid. The liquid goes up
and down as the air contracts and expands. This would seem to be
upside down to us. (After all, the liquid in the tube goes down as
the air heats up.) Fahrenheit's success has been attributed to the
fact that he was a manufacturer of thermoscopes. They were based on
mercury in glass and were very well made and reliable. The peculiar
choice of 32 and 212 for freezing and boiling came from his degree
size - about 1/4 the Roemer degree - and from the fact that his
lowest laboratory temperature was a little lower than Roemer's.
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Heat:
We know that a mixture of hot and cold changes the
temperature to "warm". We say that "Energy" has flowed
from the hot
to the cold. We have heard "Energy" before. "Potential
Energy",
"Kinetic Energy", "Chemical Energy" , "Electrical
Energy" - to name
a few. "Heat Energy" is the same stuff. The twelve dollar word
is
"Thermodynamics". [Looks like heat and motion. It used to be
mostly steam engine design! The first steam engines made use of the
same source of force that collapsed our soda cans in class #6. They
were about 1 or 2 percent efficient!] Note that "heat" and
"Temperature" are different. Heat refers to energy flow.
Temperature refers to a state of being.
Heat is measured in "Calories". A "calorie" is the
amount of
heat needed to raise a cubic centimeter of water one Kelvin. [The
English system uses the BTU (British Thermal Unit). A BTU is the
amount of heat needed to raise a pound of water one degree
Fahrenheit. (About a quarter of a KiloCalorie. BUT there's a hitch.
A KiloCalorie is sometimes called a Calorie - (Cap. C) - especially
by dieticians. The BTU is 1054.5 J.]
`Temperature' does refer to how hot/cold it is, but not how
hot/cold it feels! Our fingers react to the heat they absorb, or
the heat they give up. When we touch anything, we change the
temperature at the point of contact. The amount of change depends
on the material we touch! We are not especially good at being
thermometers! This is easy to demonstate. Have a student put his
left hand in ice water, and his right hand in hot water. If you
now ask the student to put both hands in a bowl of water that is at
room temperature, the left hand (from ice water) will feel warm, and
the right hand will say "cold".
The early thermometers were based on the expansion of mercury
in glass tubes. [They tried alcohol and water too, but mercury
works better. It freezes much lower and boils much higher.] The
simplest callibration uses the boiling point and the freezing point
of water. We can do this as a demonstration, but alas the
uncalibrated thermometers in our kits do not go as high as
boiling water. Ice water is OK, but what do we use for another
reference? Body temperature is a possibility, but varies about 2%.
We could try adding an equal amount of boiling water to our ice
water. Would it come out half-way between boiling and freezing?
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First and Second Laws of Thermodynamics: 11-3
First Law: The energy of a "system" changes only by adding or
removing heat or by applying some "work".
It wasn't clear at first, but, thanks to Joule, we know that heat
and work are equivalent. W = JQ . Where J = 4.185 Joules per
calorie. [See errata] Joule did this by stirring an insulated
container of water using a falling weight and by measuring the rise
in temperature caused by the energy transfer. [Since this was done
in 1840 or so in Merry Olde England, he did it in Brittish units.
Note that the unit for work and energy in the current SI system is
named after him. [There are often little gems in the encyclopaedia.
For example, Joule was the owner of a big brewery and used the
profits to finance his research.]
Second Law: You can't get it all when you try to convert heat
to work.
There must be some temperature difference to make heat flow, and we
need flowing energy to get work out. If the lower temperature is at
zero Kelvins all of it could go into work, but we don't have any
zero Kelvin reservoirs. The best we have is the ocean, or the
atmosphere. We therefore are forced to give away some heat. Early
Steam engines were 1 or 2 % efficient. Watt improved that to about
4%. The best we can do today is around 50%.
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Materials and Heat - Specific Heat, and Conductivity
What does "hot" mean? Why do the carrots in the soup seem to
be hotter than the potatoes? Why does a silver spoon in the soup
feel hotter than a wooden one? Why do metallic objects in your
kitchen seem to be colder than an empty plastic foam cup? [The
basic answer is "Because they ARE!"] It truly IS so (at the
time,
and the place). The handle of a silver spoon in your soup is not
the same as a similar wooden spoon. It feels hotter! It IS
complicated. We've got soup, spoon, and fingers to consider.
We can describe the situation better by using the words -
"Specific Heat", and "Conductivity". Specific heat
is a measure of
how much "heat" a given gram of any material will hold.
Conductivity is a measure of how fast the material will transfer
heat. Both of these are involved in the soup. Silver and other
metals conduct heat very well. Wood is an insulator. The silver
spoon very quickly picks up enough heat to have about the same
temperature as the soup, and "conducts" it to your finger. The
wooden spoon is hot at the end that is in the soup, but wood is a
poor conductor. It will be hot at the soup end, but it will take a
long time for the handle end to heat up.
11-4
When both are at room temperature, your silver fork feels
colder than your plastic foam cup. But, at the point where you are
touching them, the temperatures are different! Since silver is a
good conductor, you have to warm up the whole fork with your finger.
With the plastic cup, you need to warm up only a small area - your
finger print! Anything that conducts well stays at room temperature
longer and feels cold. Things that conduct poorly warm up fast and
feel warm because they ARE warm in that small area. In the soup
bowl, carrots and potatoes are at the same temperature. In your
mouth, potatoes cool off quicker! [Crackers are even quicker!] In
this case, we are interested in the final temperature. (Or we get a
burned tongue!) It turns out that the average cooked carrot will
hold more heat per gram than the average chunk of potato. "Specific
Heat" is the ratio of this heat capacity to that of water.
Therefore, the specific heat of water is 1. (At sea level,zero
C,etc.) Nearly everything has a specific heat less than water.
Vegetables like carrots and onions, which have a large water
content, will feel hotter in the soup!
So now that we know that metals conduct heat better than wood,
and now that we have defined heat conductivity and specific heat,
and now that we can measure these things, we know WHY a silver spoon
will feel hotter or sometimes colder than a plastic spoon! It is
because the specific heat of silver and the conductivity of silver
are higher than they are for plastic! Isn't it nice to know WHY ?
[Well not really. It is nice to know MORE about the world, but I
can't say we know WHY it is as it is.]
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Errata:
Page 121 Line 30 Change `Experiment 1' to `Experiment 2'.
Page 124 Line 5 Change `to each can' to `to each test
tube'.
Page 124 Lines 13 to 16. Keep the first sentence in this
paragraph. Change the rest to:
He found that the amount of work W needed for a
one Kelvin increase in the temperature of a substance, is
JQ where Q is the amount of heat needed, and J is a
constant. [J = 4.185 Joules per calorie.]
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