Heat and Temperature, Part IV
Specific Heat and the Importance of Water
The weather patterns around Puget Sound, in the region west of the Cascade Mountains,
is very different from the weather patterns around Yakima, east of the Cascades.
In a normal year, where would you expect to see the highest temperatures: east or
west of the Cascades?
In a normal year, where would you expect to see the lowest temperatures: east or
west of the Cascades?
On a typical autumn day, where would you expect to see the biggest difference
between the daytime temperatures and the nighttime temperatures, east or west of
the Cascades?
There are lots of factors that combine to produce the differences noted above, but
the biggest one has to do with something that seems to be all around us when we
are west of the Cascades. It isn't completely absent east of the Cascades but there
is a lot less of it. Take a guess. It's...
Your answer above may or may not be correct, but try to think of a reason or a
few reasons (this is a prediction, so it may also be completely incorrect) why the
presence of this stuff would have this influence on temperatures around here.
Discuss your ideas with your classmates.
Did your explanation have anything to do with the tremendous sizes of some bodies of
water around here? If so, good job! Imagine a week in Chicago (next to Lake Michigan)
where it has been –10 oC for the entire week . Even in these conditions Lake Michigan
doesn’t freeze. But here’s the interesting thing. If you took a thermometer and measured
the temperature of both the lake and the surrounding ground (mostly sand), you would
find that the ground was colder than the lake. The ground temperature might be as low as
–5 oC or even lower! Now here's the strange part: There is more ground in the Chicago
area than there is water in Lake Michigan, so the size of the lake alone does not explain
this observation. The same thing happens in the summer. It can get to be 38 oC (100 oF)
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in Chicago in the summer, and even then Lake Michigan will never get warmer than 27
o
C (80 oF). Yet the sand, sidewalks, and roads are all roasting hot.
Even a small amount of water can stabilize temperatures more than you might think.
Farmers will often store a barrel or two of water in the same shed where they store their
fruit in winter. In sheds without water barrels the fruit freezes solid (and is often ruined).
In sheds with water barrels the fruit stays nice and cold but generally above freezing.
Think about what you know about heat and its relationship to temperature in water.
For water: "heat (cal) = mass (g) x ∆T (deg C)"
The soil (rocks, sand, humus, etc.) around Lake Michigan changes temperature more
than the water does when receiving the same amount of heat from the sun.
What does that tell you about heat and its relationship to temperature in materials
other than water? Will the equation above still hold true, say, for sand? If not,
which side of (what used to be) the equation will be bigger?
To really answer this question we need to do an experiment about a concept called
specific heat.
In this experiment we’ll be looking at the factors that affect heat transfer between the
rock (a piece of metal for our experiment) and “Lake Michigan” (some water in a foam
cup). First, think back to a previous experiment where you mixed different amounts of
water at different temperatures and measured the final temperature.
Refresher Question: If 50 g. of water at 0 oC is mixed with 50 g of water at 60 oC,
what do you expect will be the final temperature of the water?
If 50 g. of water at 0 oC is mixed with 100 g of water at 60 oC, what do you expect
will be the final temperature of the water? (an estimate is okay)
Hopefully you recall that the amount of heat transferred between two objects depends on
two things: the temperature of the objects and the mass of the objects. There’s a third
factor as well, one that has to do with the material(s) that the objects are made of. In your
experiments with the water you didn’t observe this effect because you only experimented
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with one substance (water). Today’s experiments introduce this third variable by looking
at heat transfer between different substances.
Now it’s time to get started on the experiment. Here’s what you’ll need. Before starting,
assemble the following items at your desk.
A partner or group (you'll need more than two hands)
A piece of zinc or copper (not aluminum, and make sure it doesn't attract a magnet)
A Styrofoam cup with a cover.
Enough room temperature water to cover the zinc or copper in the foam cup.
A scale for measuring the mass of your water and your metal
A source of hot water to be used for heating the zinc or copper.
A thermometer
A piece of string
Experiments often begin with questions, so here’s a question:
Which substance will have the greater ability to change the temperature of the
other object: water or metal? (Guess and discuss with your classmates)
In order to look at heat transfer, the metal and the water will need to be at different
temperatures. We can add cold metal to hot water, or hot metal to cold water. We will use
hot metal because it is easier.
Get an idea for how much room temperature water is needed to cover your piece
of metal in your foam cup. You want to be able to cover the metal and gently
swirl the water without exposing the metal to too much air, but not much more
than that. Once you have the right amount of water, carefully record the mass of
the water and set it aside.
Now record the mass of your metal (and the type of metal you are using).
Next we need to heat the metal to a known temperature. The easiest way to do
that is to immerse it in hot water (of a known temperature) for a long enough
period of time that we can be confident that the hot water and the metal are at the
same temperature. Tie a string around the middle of your metal rod and then hang
the metal in some hot water. Let it stay there for a couple of minutes. Record the
temperature of the hot water. This will be the initial temperature of your metal.
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Record the temperature of the room temperature water. (It should be about 20-ish
degrees Celsius). This will be the initial temperature of your water.
When you are ready, quickly remove the metal from the hot water, tap it to
remove drops of hot water, and quickly immerse it in the room temperature water
in the foam cup. Cover the foam cup and gently swirl the room temp water around
the metal until the water and metal no longer change temperatures. Record the
final temparature. This will be the final temperature of both your metal and your
water.
Repeat the experiment two more times recording your data below.
Data Table:
Trial 1
Type of metal
Mass of metal (g)
Mass of Water (g)
(room temp water)
Trial 2
Trial 3
(this shouldn't change)
(this shouldn't change)
(this shouldn't change)
(this shouldn't change)
Initial Temperature
of Water (oC)
Initial Temperature
of metal (oC)
Final Temperature
of both (oC)
In this experiment, the hot metal gave up heat (in calories) to the cooler water.
Which was greater, the heat lost by the metal or the heat absorbed by the water?
(Yes, this is a trick question. Explain why.)
Which was greater, the change in temperature of the metal or the change in
temperature of the water? (This is not a trick question.)
Let’s calculate the heat and changes in temperature to really see the difference.
Recall that we use the symbol
change in temperature.”
to mean “change in”. For example, T means “the
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Since we sort of understand water, let's focus on the water first.
Trial 1
Trial 2
Trial 3
Initial temp, water:
Final temp, water
T water
Mass, water (g)
Heat absorbed
by the water:
If this heat was absorbed by the water where did it come from?
By concentrating on the water we have learned the amount of heat that changed hands. It
is now time to focus on the metal.
Trial 1
1
2
3
4
5
6
8
Trial 2
Trial 3
Heat lost
by the metal:
Mass, metal (g)
Heat lost by each
gram of metal:
The amount that the
temperature of
water would have
changed if each
gram had lost the
heat shown above:
Initial temp, metal
Final temp, metal
T metal
The amount of heat
lost per gram of
water that would
produce this same
change in temp.
► Compare the temperature changes in line 4 and line 7 in the previous table. Which is
greater: the temperature change of the metal or the amount that the temperature would
have changed had the metal been made of water?
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► Compare the amounts of heat in lines 3 and 8 of the previous table. Which is greater:
the heat required to get a certain temperature change in water or the heat required to get
the same temperature change in your metal?
Copy rows three and seven from your previous table into this table, and then calculate the
new quantity: The amount of heat per gram per degree of temperature change. What
would the units be?
Trial 1
Trial 2
Trial 3
Heat lost by each gram
3
of metal:
T metal
New!
The amount of heat lost
per gram
per degree of change
in temp.
(divide row 3 by row 7)
Copy rows three and eight from your original table into this table, and then calculate the
new quantity: The amount of heat per required to change the temperature of your metal
compared to the amount of heat required to change the temp of water. What would the
units be?
Trial 1
Trial 2
Trial 3
Heat lost by each gram
3
of metal:
The amount of heat lost
per gram of water that
would produce this
8
same change in temp.
The amount of heat
needed to change the
temp of this metal
New!
compared to the heat
needed for water
(divide row 3 by row 8)
You should see that the numbers for the previous two "new" quantities are the same. The
units and the interpretations are somewhat different but they tell us the same thing so they
are essentially the same quantity. This quantity is called specific heat.
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Specific Heat:
The amount of heat required to raise (or lower) the temperature of 1 gram of a
substance by 1 oC.
All substances have different specific heats. The specific heat of water, for example, is
1.0 cal/goC. This means that it takes one calorie to raise the temperature of 1 gram of
water by 1 oC. (Remember that the calorie is a unit for heat or energy). Test your
understanding of this concept by answering the questions below. Include units with your
answers.
Was the specific heat of your metal greater than or less than the specific heat of
water?
Your metal probably changed temperature by more than one degree. Would the
amount of heat required to change the temperature of your metal by one degree be
greater than or less than it would have been for water?
We mentioned that this equation: "heat (cal) = mass (g) x ∆T (deg C)"
only works for water. You may have noticed that even for water the units in the
equation do not work out right. In order to make the units work out right, and in
order to make the equation apply to things other than water, we need to insert
specific heat (abbreviated s), but where? Try to fix the equation below:
[ heat (cal) ]
[ mass (g) ] x [ ∆T (oC) ]
=
This is hard. Check your answer with an instructor before continuing.
The reason that the numbers for the "new" quantities turned out to be the same is that
the specific heat of water in these units is just one (cal/goC). So the specific heat tells
us both how much heat is required to change the temperature of a gram of material
AND how hard it is to change the temperature of that material compared to water. For
this reason, specific heat is sometimes also called the "water equivalent for heat."
Almost every substance we encounter has a specific heat which is LESS than the specific
heat of water. This one reason why water changes temperature so little compared to the
things around it.
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► Rearrange your equation on page 8 to solve for s, the specific heat of the substance.
Check your work with an instructor before continuing.
► Go back to your table and based on your three experiments, try to estimate the specific
heat for your metal.
► There were lots of sources of error in our experiment. There were lots of places for
heat to go besides just the metal and the water. Nonetheless, see how you did. Look up
the specific heat of your metal and see how close your measurement was.
► Now that you now an accurate value for the actual specific heat for your metal, try to
answer this question: How much heat would be required to raise the temperature of 125
grams of your metal from a temperature of 21o C to a temperature of 25o C? Check your
work with an instructor.
END OF MODULE QUESTIONS: Answer these questions on another sheet of paper.
1. A cup with 40 grams of 90 C water is mixed with a cup with 70 grams of water at
10 C.
a. Predict the final temperature of the water. Explain your reasoning.
b. Calculate the expected final temperature of the water. (Assume that no heat is
lost to the surroundings).
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2. 10 calories of heat were added to both a sample of water and a sample of copper.
a) The 10 calories of heat increased the temperature of a sample of water by 5 C.
What was the mass of the water?
b) The 10 calories of heat increased the temperature of 22 g of copper by 5 C. Find
the specific heat of copper.
3. In a lab experiment, an 80 g sample of water at 20 oC is mixed with 80 g of aluminum
at 50 oC. The specific heat of aluminum is 0.20 cal/goC. In other words, it takes only
0.2 calories to raise the temperature of 1 g of aluminum by 1 oC.
a. What is your estimation of what the final temperature of the mixture will be? (Do
not do any calculations yet). Explain your reasoning.
b. How many calories are required to change the temperature of 1 gram of aluminum
by 5 oC? Show your work.
c. How many calories are required to change the temperature of 80 grams of
aluminum by 5 oC? Show your work.
d. Complete the following table by filling in the number of calories needed to
change the temperature of the aluminum by 5 oC, and the resulting temperature
change of the cold water. Continue until you have determined the final
temperature of the mixture. (Note: if you have trouble doing this in 5 oC
increments, you can do it in 1 oC increments, but it will take many more steps)
Total Calories
Transferred
0
Temperature of
80 g of Al
50 oC
45 oC
Temperature of
80 g of cold water
20 oC
e. What is the final temperature of the mixture?
f. How many total calories are transferred?
g. What is the temperature change of the water in this experiment?
h. What is the temperature change of the metal in this experiment?
g. Compare the heat lost by the metal to the heat gained by the water. Explain your
reasoning.
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