Experiment 11
Specific Heat and Heat of Fusion
Preparation
Study for this week's quiz by reviewing harmonic motion and by reading the sections of your
book that cover heat, heat of fusion, and specific heat capacity. Look up the definition of a mole
(the chemical kind, not the small tunneling rodent.)
Principles
Thermal energy is the energy associated with the random motion of all the molecules of any
substance. Two substances with the same amount of thermal energy can have different
temperatures. A large block of ice and a small cup of hot tea will have very different
temperatures but might have the same total amount of thermal energy.
Temperature is a measure of the average kinetic energy of the individual molecules of a
substance. A cup of lake water and the water in the lake may be at the same temperature but the
total energy of all the water in the lake will be enormously greater than the thermal energy of the
water in the cup.
Heat is thermal energy which "flows" from a hotter object to a cooler one because of the
temperature difference between them. Heat flows through conduction, convection, radiation, or
some combination of these processes. In mechanical or electrical measurements energy is
usually measured in Joules, but in thermal measurements the "calorie" is usually used as the
energy unit. One calorie is equal to 4.186 Joules. Heat is usually represented as Q.
If two objects at different temperatures are brought together heat will flow from the warmer to
the cooler object until the temperatures are equal. This process is called heat exchange. The
heat lost by the warmer object must equal the heat gained by the cooler one
Qlost = Qgained .
This can be used to find another property of a substance called specific heat. Specific heat, c, is
defined as the amount of heat required to change the temperature of one kilogram of a substance
1 °C,
Q
.
c=
m∆T
The unit for specific heat is J/kg°C, Joule per kilogram - degree. The equation for heat can then
be rewritten
Q = mc∆T .
In this experiment you will use the known specific heat of water to find the specific heat of
copper.
The calorie (cal) is defined as the amount of thermal energy required to raise the temperature of
one gram of pure water from 14.5 °C to 15.5°C. Thus the specific heat of water in this
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temperature range is 1.00 cal/g°C. The "dietary calorie" or "Calorie" (spelled with a capital "C")
which is used to define the energy equivalent of foods, is equal to a kilocalorie. Thus
1 kcal = 1 Cal = 10 3 cal = 4186 J .
When a substance is undergoing a phase transition, that is, changing from one physical state to
another, it will gain or lose heat without a change in temperature until the phase transition is
complete. The amount of heat necessary to melt a substance is called the latent heat of fusion,
L f , and has units of J/kg. The amount of heat necessary to completely change a substance from
solid to liquid, without changing its temperature is given by
Q = mL f .
In this part of the experiment you will find the latent heat of fusion of ice. When ice at 0 °C is
mixed with warm water at some initial temperature, Ti , the water will cool to a final temperature,
T f . In the process it will lose heat equal to mwater cwater (Ti - T f ) . Some of the lost heat will be
used to melt the ice, mice L f , and the rest will raise the temperature of the melted ice to the final
temperature of the water. Therefore
mwater cwater (Ti - T f )= mice L f + mice cwater (T f - 0 °C) .
The amount of heat required to raise the temperature of one mole (abbreviated mol) of a
substance 1 °C is called its molar specific heat. A mole of any substance contains 6.022 x 1023
particles and has a mass equal to the gram molecular mass of the substance. Thus one mole of
diatomic oxygen has a mass of 32.0 g.
In the middle of the nineteenth century, Dulong and Petit found that the molar specific heats of
almost all solids have the same value when measured at around room temperature. That value is
approximately 25 J/mol °C. In 1905, Einstein developed a crude theoretical model, based on
quantum ideas, which predicted this result and also explained why these values change when
measurements are made at lower temperatures. In fact, for all substances, the molar specific heat
approaches zero as the temperature approaches absolute zero.
In this experiment you will use a calorimeter which is a device that thermally isolates enclosed
substances from their surroundings so that no heat flows in or out. A thermos bottle is a fairly
good example of a calorimeter.
Equipment
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digital thermometer
calorimeter
graduated cylinder
pan balance
hot copper shot
ice
paper towels
Procedure
Use SI units. Measure temperature to 0.1 °C; measure mass to 1 g. The digital thermometers
require a few seconds to register temperatures accurately. Be sure the reading is no longer
changing before you record a measurement.
1.
Mass the empty calorimeter. Be sure you include the liner and the cover.
2.
Get about 100 ml of ice water from the pitcher.
3.
Record the mass of the calorimeter and the cold water together. Measure and record the
temperature of the cold water.
4.
Your instructor will have a pot of hot shot at the front table. Collect a cup of shot and
record its temperature. Do this quickly as the shot will cool rapidly one it is removed from
the heat.
5.
Dump the shot into the cold water in the calorimeter. Be sure you don't spill any of the
water. Put the lid back on the calorimeter. Mass the calorimeter with the water and the
shot.
6.
Use the thermometer to stir the shot and water. Within a few minutes the shot and water
will reach their final temperature. Record this. Be sure that the temperature has stopped
changing before you record your temperature.
7.
Use the strainer to drain the shot and put the wet shot into the beaker on the cart. Do not
mix wet shot with the dry shot.
8.
Fill the calorimeter cup about half full of water that is at least 15° above room temperature.
Place the cup in the calorimeter and find the mass. Stir the water and record its
temperature.
9.
Get some ice cubes. Dry each piece with a paper towel and carefully slide the ice into the
water, one piece at time, until the water temperature drops about 15 or 20 degrees. Stop
adding ice at this point. Be sure that no water splashes out of the cup.
10.
When all the ice has melted, stir the water. Record its final temperature and again find the
mass of the cup and calorimeter.
11. Put all your equipment away and be sure your instructor signs your notebook.
Data
Data for first part of the experiment consists of masses of empty calorimeter, calorimeter with
water in it, and calorimeter with water and shot, and temperatures of cold water, hot shot, and
final temperature. Data for the second part consists of the masses of the calorimeter and warm
water before and after ice was added and the temperature of the water before and after the ice is
added.
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Analysis
Pay attention to units.
1.
Calculate the experimental specific heat of copper. Find your percent error from the
accepted value of 93 cal/kg °C.
2.
Calculate the experimental latent heat of fusion for water. Find your percent error from the
accepted value of 333 kJ/kg.
3.
One mole of copper has a mass of 63.5 g. Use your data to calculate the molar specific
heat of copper, that is, the number of calories it takes to raise the temperature of one mole
of copper by 1° C. Convert your answer to J/mol °C and compare it to the accepted value
of 24.5 J/mol °C.
4.
Pick two other elements and calculate their molar specific heats. (Use the tables for
specific heat and atomic mass in your textbook.) What do you notice about the results?
Questions
Be sure to answer questions in detail.
1.
Suppose you have equal masses of two substances that have different specific heat
capacities that are initially at different temperatures. You mix them together and wait for
them to reach thermal equilibrium. Which substance will show the larger change in
temperature, the one with the higher specific heat or the one with the lower specific heat?
Explain how you arrived at your conclusion.
2.
Why is it better to put ice rather than an equal mass of cold water into a drink you want to
chill?
3.
It was important to dry the ice cubes before you put them into the water when you did the
latent heat of fusion experiment. How would the value you calculated for L f have changed
if you had used wet ice cubes instead?
4.
Suppose you had done the latent heat of fusion experiment with ice that was considerably
colder than 0 °C. What additional value would you have needed to know in order to
calculate the latent heat of fusion for the ice? Write out the new equation you would need
to determine L f .
5.
You can cook vegetables by dropping them into boiling water or by placing them in a
basket over boiling water, putting the lid on the pot and steaming them. Which method do
you think would be faster? Explain your reasoning clearly.
If it applies to you, write "I have not cheated on this lab report" and sign your name.
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Grading
4 pts
Data and Analysis.
2 pts
Each for questions 1, 2, and 3.
5 pts
Each for questions 4 and 5.
Your instructor will give you the final due date for your notebook. If you haven’t turned it in by
then, your work will not be graded.
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