# Heat of Fusion - Personal.psu.edu

```Physics Lab
Heat of Fusion
1
INTRODUCTION
If there are no phase changes, then whenever two objects with different initial temperatures are
put in contact with each other, the warmer one will cool down, and the cooler one will warm up,
until they reach the same temperature. We now know that this has to do with the motions of
molecules: what we sense as temperature is related to the average kinetic energy of the molecules of
each material: the faster they’re vibrating around, the hotter the object feels. We can sidestep this
molecular picture by dealing with objects as a whole, and treating the energy transfer as the flow of
heat, rather than kinetic energy transfer among particles.
However, some heat (energy) is required in order to cause a change in the phase (solid, liquid, or
gas) of an object. During the phase change, the temperature of the object does not change at all,
even though it is gaining or losing energy (depending on the type of change).
Experiments have shown that, in the absence of phase changes, the heat transfer Q = mcΔT,
where ΔT = Tfinal-Tinitial of the object you’re considering, m is
Specific Heat for Various Materials
(Approximate)
its mass, and c is referred to as the “specific heat” of the
Material
Specific Heat
material it’s made up of. For most materials over a wide
(J/kg C°)
range of temperatures, c is close enough to a constant value
Water
4186
that we will consider it to be exactly constant. Note that a
Aluminum
900
positive Q means that energy flowed into the object (raising
Steel
448
its temperature), while a negative Q means that energy left
Brass
386
the object (leaving it at a lower temperature than at the
Copper
380
beginning). Also note that you must be careful to associate
the mass, specific heat, initial temperature, and final temperature, for the appropriate object being
considered in any particular calculation, and not some other object.
However, during a phase change, the heat transfer Q = ±mL, where m is the mass of the object
that is going through the phase change, and L is the “heat of fusion” (for a change between liquid
and solid), or “heat of vaporization” (for a change between liquid and gas). Q is positive if heat is
being added to the object (melting or boiling), or negative if heat is being removed from the object
(freezing or condensing).
Energy is always conserved, and this is a useful fact when dealing with heat as a kind of energy
flow. If we have a perfectly insulating container, then no energy can flow into or out of that
container. So, the net heat flow for everything in the container combined Qnet must equal zero.
In this particular lab, we will take an ice cube (assumed to start at 0°C), and drop it into a
calorimeter cup partially filled with warm water. We will assume that the rest of the calorimeter is
perfectly insulating, so that:
Qnet = 0, or Qice cube + Qwarm water + Qcup = 0
If the cup were not perfectly insulating, we would also have to have a term for the heat transfer to
the surrounding air, stirrer, outer cup, etc.
However, we must be extremely careful with the Qice cube term: first, the ice cube must melt.
Then, the meltwater must itself increase its temperature, until it reaches equilibrium with the original
water, and the calorimeter cup. Therefore, a more thorough equation may be:
Qice melting + Qmeltwater + Qwarm water + Qcup = 0
Note: if the ice cube had started below 0°C, then we would have had to include a term for the heat
required to raise the temperature of the ice to 0°C.
[Insert table of heat of fusion, heat of vaporization of water, aluminum]
Physics Lab
2
Heat of Fusion
PROCEDURE
1. Gather all the necessary materials: triple-beam balance,
calorimeter cup, temperature sensor or thermometer,
styrofoam cup, and napkins. Note: the temperature sensor
that you use in your calorimeter must not have blue plastic
tubing at the end. However, never remove the blue plastic
tubing from any temperature sensor.
2. Measure the mass of the inner aluminum calorimeter cup
only (remove it from the outer cup, and remove the plastic
ring) using the triple-beam balance. Note the uncertainty in
this mass.
3. At the sink, fill the inner aluminum cup part-way with water.
You will want enough to completely melt, but not much
more. If you use too much water, the temperature change
will be too small to get reliable data. If you use too little, the
ice cube will not melt completely, and you will not be able to
get any useful data. How much water to use, and what
temperature, is something of a judgment call. If you use too
little or too cool, there will be enough time to take another set
of data.
4. Measure the mass of the inner aluminum cup (still without
the plastic ring), now partially filled with water. Note the
uncertainty in this mass. The mass of the water itself will be
this new mass, minus the mass you found in step 2.
Typical Laboratory Calorimeter Cup
(Courtesy of Welch Scientific Co.)
5. Insert the inner calorimeter cup (now containing water) into the outer calorimeter cup, with the
plastic insulating ring separating them. Place the cover over the calorimeter and insert the
second temperature sensor or thermometer through the stopper in the top cover. The stirrer
should also be inside, going through the hole near the middle of the top cover. Gently stir the
water for about a minute.
6. Take the ice cube(s) from the container of icewater at the back of the room, and place it in the
styrofoam cup. (Since the ice and water have had time to reach equilibrium, it is reasonable to
assume that it is at 0°C.) When you get back to your lab bench, dry off the ice as much as
possible with the napkin(s).
7. Once the all temperatures are stable, record the initial temperature of the cool water in the
calorimeter cup. We will assume that the aluminum inner cup is also at the same temperature.
8. Quickly remove the cover from the calorimeter. Then, drop the ice cube(s) in the inner
calorimeter cup, being careful not to splash any water out. Quickly re-cover the calorimeter.
(Remember, we want no heat to escape to the outside air.)
9
Gently stir the inner calorimeter cup, until its contents reach a final equilibrium temperature.
(You can confirm this by moving the temperature sensor around, looking for “hot spots” or “cool
spots.” Generally, as long as your temperature sensor is not near a “cool spot,” the equilibrium
Physics Lab
Heat of Fusion
3
temperature will be near your lowest reading. This is because the calorimeter is not actually a
perfect insulator, so the cooler parts will gain heat from the room, desk, etc. as time goes on.)
Record the final equilibrium temperature, with its uncertainty. (Note: much of this uncertainty
will be due to the fact that your “final” temperature is a judgment call, made when you guess that
everything has first reached equilibrium.)
10 Remove the inner calorimeter cup, and measure its mass (with the uncertainty). As long as no
water spilled or evaporated, the mass of the ice cube (and therefore of the meltwater as well) will
simply be this mass, minus the total mass you found in step 4. DO NOT FORGET TO DO THIS
STEP!
11. If time allows, you may repeat steps 3-10 for an additional ice cube(s), using a different amount
of water at a different initial temperature.
Plastic Tubing
ANALYSIS
1. Calculate Qwarm water and Qcup for each case. Note: you will need to use the accepted values for
the specific heats of water and aluminum for these calculations.
2. Using the results of the previous step and the mass and change in temperature of each ice cube,
calculate the latent heat of fusion of each ice cube.
3. Calculate the % error for each ice cube, using the value in the textbook as the accepted value.
measured accepted
 100% .
Remember: the equation for % error is: %error 
accepted
4. Using your uncertainties, calculate a worst-case maximum and minimum specific heat for at least
one ice cube.
RESULTS
Your results section should be a table, indicating each type of material, its accepted specific heat,
its experimental specific heat (with uncertainty, if applicable), and the % error.
QUESTIONS
1. List as many of the assumptions made in this experiment that you can think of. Based on your
experimental results, do you think that these assumptions were valid? Why or why not?
2. Why must the water in the inner cup be gently stirred during this experiment? Also, why stir at
all?
Physics Lab
Heat of Fusion
4
3. In step 6, if the ice cubes were not dried, and a significant amount of water were accidentally
transferred along with the ice as it is placed into the calorimeter, will this result in your
calculated heat of fusion being too large or too small? Why?
4. Do the %error results you found surprise you? Why or why not?
5. Do the accepted values fall within the experimental range of values (a “range” because of the
uncertainty)? If not, then your measurements may have been wrong, your calculations may have
been wrong, or you may have estimated too little uncertainty. Try to figure out what was the
actual cause, in your case.
EXTRA CREDIT (Optional)
For up to 3 points, design and perform a new experiment to find the specific heat of aluminum,
without using the aluminum sample (and without assuming that you already have a value for it
from any other source). Use only the equipment used here in this lab. Be sure to describe your
procedure and calculations clearly. (Note: you are allowed to use the accepted value for the
specific heat of water.)
```

25 cards

38 cards

29 cards

25 cards

38 cards