Specific Heat
In today’s experiment, you will place hot metal into cold
water. The specific heat of water is 4.2 J·g-1·K-1. Temperature
changes are written in Kelvins. The numerical value is
exactly the same as the value measured in Celsius. That is,
a change in temperature of 10°C will be written 10K. The
water will be in a styrofoam cup with a thermometer in it.
The cup and the thermometer will also absorb some heat.
If the heat that the cup and thermometer absorb per degree
is labeled Ccup, then equation 3 becomes:
introduction1
Heat is a form of energy, often called thermal energy. Energy
can be transformed from one form to another (electric
energy to heat and light in a light bulb, for example), but it
cannot be created or destroyed; rather, energy is conserved.
The higher the temperature of a material, the more thermal
energy it possesses. In addition, at a given temperature, the
more of a given substance there is, the more total thermal
energy the material possesses.
-(Csp·m·∆T)H = (Csp·m·∆T)C + Ccup·∆T
On an atomic level, absorbed heat causes the atoms of a
solid to vibrate, much as if they were bonded to one another
through springs. As the temperature is raised, the energy of
the vibrations increases. In a metal, this is the only motion
possible. In a liquid or gas, absorbed heat causes the atoms
in the molecule to vibrate, and the molecule to both rotate
and move from place to place. Because there are more
“storage” possibilities for energy in liquids and gases, their
heat capacities are larger than in metals. Heat capacity, Cp,
is the amount of heat required to change the heat content
of 1 mole of a material by exactly 1°C. Specific heat, Csp,
is the amount of heat required to change the heat content
of exactly 1 gram of a material by exactly 1°C.
In Part 1 of this experiment, you will pour hot water into
cold water to determine the value of Ccup. In Part 2 of the
experiment, you will pour hot metal into water to determine
Csp for the metal. For Part 1, equation 4 becomes:
-(4.2 J·g-1·K-1·m·∆T)H = ((4.2 J·g-1·K-1·m + Ccup)∆T)C
You will solve the equation for Ccup. For Part 2, equation
4 becomes:
-(Csp·m·∆T)H = ((4.2 J·g-1·K-1·m + Ccup)∆T)C
You will solve the equation for Csp, the specific heat of
the metal.
Specific heat values can be determined in the following
way: When two materials, each initially at a different
temperature, are placed in contact with one another, heat
always flows from the warmer material into the colder
material until the two materials are at the same temperature.
From the law of conservation of energy, the heat gained by
the initially colder material must equal the heat lost by the
initially warmer material:
(heat lost)hot object = (heat gained)cold object
Equipment
Special supplies:
• 3 large test tubes with corks
• 1 metal sample
• 1-1000 ml beaker
• 2 styrofoam cups
From your drawer
• 1 thermometer
• 1-600 ml beaker
(1)
Since heat lost is a negative term, and heat gained is a
positive term, the equation can be written:
-qH = qC
Experiment
Read temperatures to the nearest
0.1°C. See the thermometer
use handout. Use the decigram
balances to obtain masses.
(2)
where q is used as the abbreviation for heat. The heat
quantities in this equation would be calculated as (specific
heat) x (mass of the object) x (the temperature change of
the object), because specific heat has units of energy per
(mass x degrees). Equation 2 then becomes:
-(Csp·m·∆T)H = (Csp·m·∆T)C
1 Adapted from the American Chemical Society
publication, A Materials Science Companion
(4)
(3)
1
After you obtain the equipment
from the cart, place the styrofoam
cups into the 600 ml beaker for
support. Without this support, the
weight of a thermometer could
cause the setup to tip over, which
could break the thermometer.
Part 1: Measuring Ccup
Set a 1000 ml beaker on a ring stand as shown in the
diagram below. Add about 800 ml of water. Turn on the
burner to a hot flame so that the hot water bath will be
heating while you are preparing the test tubes for the
experiment.
Pour 70 ml of deionized water into the styrofoam cups.
Weigh the cups and record the mass in the Part 1 data table.
Record the temperature of the water. Tear off a section of
paper towel and fold it until it is an inch or so wide. Make
a handle for the test tubes by placing the middle of the
length of paper at the top of the test tube and folding the
paper around the test tube:
3 large test tubes in a 1000 ml
beaker. Water level in beaker
should be higher than
contents of test tubes
Corks are
loose in test
tubes
Pour the hot water from the test tube into the cups. Stir
with the thermometer and record the highest temperature
reached. Now weigh the cups and record the mass as the
final mass of cups and water.
You will run two trials for Part 1 to see how consistent
your data is. To begin the second trial, pour the water out
of the cup, and shake out the last drops of water from the
cups. Add 70 ml of deionized water to the cups, measure
the mass as in the first trial, and record the temperature.
Add the hot water, record the temperature again. Weigh
the cups and record the mass to the nearest 0.1g. Empty
the water from the cup.
Get a large test tube with a metal sample. This test tube is
not to be used to heat the metal. Record the number of the
metal in the Part 2 data table. Pour the metal onto a paper
towel and make sure the metal is dry. If the metal is wet,
you may have to use a hot air blower to get it dry. Ask the
instructor for help.
Part 2: Measuring Csp of the Metal
You will do just one trial for Part 2. Add 100 ml of
deionized water to the cups. Weigh the cups with the water
and record the mass in Part 2 of the data table. Record the
temperature of the water in the cups. Add the metal to the
cups from the test tube in the water bath, using a paper
handle as before. Stir the cup with the thermometer and
record the highest temperature reached. Now weigh the
cups with the water and the metal in them.
Place the metal in a large clean and dry test tube and
loosely stopper it. Place it in the hot water bath. The water
level in the bath should be above the metal level. You will
need two other large test tubes and stoppers for Part 1.
Into each test tube, add 30 ml of deionized water. Loosely
stopper them, and place them into the hot water bath.
You are now finished with all of the measurements.
Carefully pour the water out of the cup without losing
any metal. Pour the metal onto a few thicknesses of paper
towel. Blot the metal dry, with more paper towel. Transfer
the metal to a dry piece of towel, spread it out, and let it sit
in the air while you do the calculations for the experiment.
Then carefully transfer the metal back into the labeled
sample test tube, stopper it, and return it to the cart, along
with the other test tubes and their stoppers, the styrofoam
cups, and the 1000 ml beaker.
When the water is boiling, turn the burner down to
maintain a gentle boil in the beaker. The test tubes should
reach the temperature in the water bath after 10 minutes of
boiling. Assume that the temperature of the boiling water
is 100.0°C.
Remove the two nestled styrofoam cups from the 600 ml
beaker and weigh them on a decigram balance. Record the
mass.
2
Part 1 Data Table
Trial 1
(masses to nearest 0.1g, temps to nearest 0.1°C)
1. Mass of two nestled cups
(assumed to be constant during experiment)
Trial 2
2. Mass after addition of 70 ml of water
g
g
g
3. Initial temperature of water in the cups
°C
°C
4. Final temperature of water in the cups after hot water is added
°C
°C
g
g
5. Final mass of cups and water
Part 1 Calculations
You will use this equation: −(4. 2
J
J
⋅ m ⋅ ∆T) Hot = ((4.2
⋅ m + C cup )∆T) Cold
g ⋅K
g⋅ K
• The mass of hot water is (data entry 5 – data entry 2) __________
__________
• ∆T for the hot water is (data entry 4 - 100.0°C).(a minus value)
__________
__________
• The mass of cold water is (data entry 2 – data entry 1) __________
__________
• ∆T for the cold water is (data entry 4 - data entry 3) __________
__________
Substitute these values in the equation, and solve for Ccup. Show your setup. Watch your algebra! Watch significant
digits.
The units will be J·K-1. It should be a small positive number, optimally from 20 to 60 in size.
Trial 1 Calculation
Trial 2 Calculation
Ccup = ___________J·K-1
Ccup = ___________J·K-1
Average value of Ccup __________
Explain what the value of Ccup describes, and why it should be a small positive number:
3
Name_________________________________________ Grade___________ Date ___________
Part 2 Calculations
Part 2 Data Table
(masses to nearest 0.1g, temps to nearest 0.1°C)
Metal # _____
1. Mass of cups and 100 ml of water
g
2. Initial temperature of water in the cups
°C
3. Final temperature of water in the cups after hot metal is added
°C
4. Mass of cups and water and added metal
You will use this equation: g
−(C sp ⋅ m ⋅ ∆T) Hot = ((4.2
J
⋅ m + C cup )∆T) Cold
g⋅ K
• The mass of cold water in the cup is (data table 2, entry 1 – data table 1, entry 1) __________
• ∆T for the water is (data entry 3 - data entry 2) __________
• The mass of metal used is (data entry 4 - data entry 1) __________
• ∆T for the hot metal is (data entry 3 - 100.0°C)
(a minus value) __________
Use the average value of Ccup from part 1. Substitute these values in the equation, and solve for Csp. Show your setup.
Watch your algebra! Watch significant digits.
The units will be J·g-1·K-1. It will be a number between 0 and 1.
Calculation:
Csp = _____________J·g-1·K-1
% Deviation =
C sp
(exp )
C sp
− C sp
(book )
(book)
Book Value _____________
Metal _____________
(Get these values from the instructor.)
x 100 = _________%
The Law of Dulong and Petit states that for a metal, Atomic Mass =
25 J / mol ⋅ K
C sp
Calculate the atomic mass of the metal from your value of the Csp of the metal.Look up the book value for the atomic
mass of the metal from the Periodic Table.
% Deviation =
AM (exp ) − AM(book )
x 100 = _________%
AM (book)
Recalculate the atomic mass, using the book value of the Csp in the Dulong/Petit relation: ________ % Deviation _____
Comment on the accuracy of the Law of Dulong and Petit:
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