# LAB 3 Uniformly Accelerated Motion by shitingting

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```									                                LABORATORY 11

Specific Heat

Purpose

In this experiment we will measure the        experimentally measured values with
specific heat capacities of some metal        accepted values for these metals.
specimens. We will compare our

Equipment

   Calorimeter                                   Support rod
   Steam generator                               String
   Metal cubes (2)                               Ice
   Digital thermometer                           Paper towels
   Glass beaker
   Table stand

Principles
in, “Ouch! That’s hot!”). There is
Heat and Temperature                          energy associated with this motion; the
temperature of an object is a measure of
It is an empirical fact that two objects in   the average energy of its constituent
physical contact will eventually come to      particles. The particles of an object at a
the same temperature. We now                  higher temperature have more energy, on
understand this process as a net flow of      average, than those of an object at a
energy from the hotter object to the          lower temperature.
cooler object. This flow of energy
occurs on sub-microscopic scales, on the      When the two objects are placed in
level of molecules and atoms, and is          physical (or thermal) contact, collisions
called heat.                                  will occur between their constituent
particles. In these collisions, slower
The constituent particles (atoms or           particles will tend to be sped up; faster
molecules) of matter are constantly           particles will tend to be slowed down.
vibrating or otherwise in motion. This        The average energy of the particles in
motion is not evident to our sight, but it    the cooler object will increase, raising its
is often evident to our sense of touch (as

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temperature, while the average energy of
the particles in the hotter object will       The specific heat capacity, c, of a
decrease, lowering its temperature.           substance (usually called just “specific
Eventually, the temperature of the two        heat”) is the heat capacity per unit mass:
objects will equalize, and there will be
no more net flow of energy from one to                            C   Q
(1)            c     
the other. This situation is called                               m mT
thermal equilibrium.
where m is the mass of the substance.
Since heat, usually abbreviated Q, is a       Specific heat is thus the amount of heat
flow of energy, it is measured in energy      Q necessary to raise a unit mass of a
units: joules in the SI system. An            substance one degree of temperature. It
alternate unit often used is the calorie.     is a property of the substance itself and
This usage dates from the early 19th          can be used to identify different
century, when it was thought that heat        materials.
was the flow of a hypothetical substance
called the caloric fluid. In 1843 Robert      The SI units of specific heat are
Joule showed experimentally that one          jouleskg-1C-1 (joules per kilogram per
calorie of heat is equivalent to 4.186        degree Celsius). The specific heats of
joules of energy, establishing that heat is   various metals and of water are listed in
a form of energy flow.                        Table 1 in units of calories per gram per
degree (calg-1C-1). It is left as an
Since thermal properties are often listed     exercise for the reader to convert these
in calorie units, we should remember the      values into SI units.
conversion factor:

1 calorie = 4.186 joules               Determining Specific Heat

In this lab, we will measure temperature
In this experiment, you will be given two
on the Celsius temperature scale. The
metal specimens. Your job is to measure
unit of temperature is the degree Celsius,
the specific heat of each metal. The
abbreviated C.                               procedure we will use is this:

First, heat the metal to a high
Heat Capacity and Specific Heat
temperature. Then suspend the
specimen in a cup of water at a low
We define the heat capacity, C, of an         temperature. The metal will cool down
object or of a quantity of a substance as     as it gives up heat energy to the water.
the amount of heat necessary to raise its     The water will warm up as it gains heat
temperature one degree:                       energy from the metal. After a few
minutes, the water plus metal system
Q
C                            will come to its final (equilibrium)
T                       temperature. From the masses of the
water and the metal, the known specific
where Q is the amount of heat and T is       heat of water, and the initial and final
the change in temperature.

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temperatures, we can calculate the           small metal cup that sits inside a larger
specific heat of the metal.                  container, with a plastic lid that fits over
all.
For our calculation, we rearrange the
definition of specific heat (1) to get an    When placed in the calorimeter, the
expression for the amount of heat energy     small cup is surrounded by an air pocket.
that must flow into a substance for a        Air is an excellent heat insulator
given change in temperature:                 (conversely, it is a poor conductor of
heat), so that little heat flows from the
(2)            Q  mcT                      cup to the room or from the room to the
cup.
Now energy is conserved. If we take
steps to prevent any heat energy being       On the other hand, the cup itself will be
gained or lost to the environment, then      in thermal contact with the water. When
the same heat energy that flows out of       we place the hot metal into the water,
the metal must flow into the water. Let      some heat will flow into the cup itself.
Q represent the amount of energy that        We must take this into account, so we
flows in to a substance and –Q be the        revise our above expression to
amount of energy that flows out of it.
Then:                                                 Qmetal  Qwater  Qcup

 Qmetal  Qwater               or

which means that                             (3)  mc T  m0 c0 T0  mcup ccup T0

 mc T  m0 c0 T0                  where the final term represents the heat
energy that flows into the calorimeter
where the parameters without subscripts      cup. Since the cup is in thermal contact
refer to the metal and the parameters        with the water at all times, the
with the subscript “0” refer to the water.   temperature change for the cup should
be the same as that for the water, T0.
However, the above leaves out of
account heat energy that flows into the      We can solve equation (3) for the
container that holds the water – the         specific heat of the metal, c.
calorimeter.                                 Calorimeter cups are usually made of
aluminum. The specific heat of
aluminum, ccup, and the specific heat of
The Calorimeter                              water, c0, are listed in Table 1. We can
measure the masses and the different
As the name implies, the calorimeter is a    temperatures in equation (3) to calculate
device used to measure heat flow. Its        the unknown specific heat. (Note:
main purpose is to insulate a system         remember that T = Tfinal – Tinitial.)
from the environment (i.e., the air in the
room) so that heat gains or losses to and    In the above, we have assumed that the
from the system are minimized. The           temperature is uniform at any time
calorimeter we will use consists of a        throughout the materials (the water, the

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metal or the cup). In practice, some          occur. Experience shows that the final
temperature gradients are inevitable, and     temperature in this experiment will be
these will be one source of error in this     about 4-6 C above room temperature.
experiment. We can minimize these by          We will “split the difference” of the
gently stirring the water with our            unwanted heat flow by starting with
temperature probe before taking               water about 5 C below room
temperature measurements – gently, so         temperature. Then heat that flows out of
that the stirring itself does not raise the   the calorimeter when the water is hotter
temperature of the water.                     than room temperature will be
approximately offset by heat that flows
Another source of error is that our           into the calorimeter when the water is
calorimeters are not perfect, and heat        cooler than room temperature.
flow into or out of the calorimeter will

Procedures
here is to have the lid ready to be
1. Heat the metal.                                   placed on the calorimeter, with
the string running through it.)
   Fill the steam generator about ¾             Suspend the metal in the water in
full with water. Turn on the                  the generator so that the top of
power and turn the knob to full.              the specimen is slightly above the
(Of course, we want to be careful             surface of the water. Try to keep
of the steam and the hot water                the top dry so that you do not
when the water boils. Arrange                 pull out hot water when you
things so that the generator will             transfer the specimen to the
be out of your way when you                   calorimeter. The specimen
transfer the cube into the                    should be fully submerged and
calorimeter.)                                 should not touch the sides or
   Weigh the specimen to be                      bottom of the generator.
measured and record the mass in              Let the water come to a boil.
the data table. Also record the               Meanwhile, perform steps 2, 3
metal and/or a description of the             and 4.
metal for identification purposes.
   Attach a support rod to a table        2. Weigh the calorimeter cup.
stand. Get a piece of string about
30 cm long. Tie the metal                    Take the small cup out of the
specimen to one end, then run the             calorimeter and weight it.
other end through the hole in the             Record its mass.
calorimeter lid. Finally, wrap the
free end of the string around the      3. Mix up some cool water.
support rod. Perch the
calorimeter lid on the end of the            Using a beaker, get a supply of
support rod to keep it out of the             cold water from the ice water
way temporarily. (The purpose

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supply provided. Make sure                   initial temperature of the water,
there is no ice in your cold water.          T1.
   Fill the calorimeter cup about ½            Measure the temperature of the
full with tap water. Then add                boiling water. Stir the water with
cold water (with no ice) and stir,           the thermometer’s probe first,
until the calorimeter water is               then read temperature to the
about 5 degrees below room                   nearest 1/10 degree C. Record
temperature. (Use the digital                this as the initial temperature of
thermometer to measure room                  the metal, T2. (Since the metal is
temperature. Note: don’t                     in thermal equilibrium with the
assume room temperature will                 boiling water, it should have the
remain the same throughout the               same temperature.)
lab session. It won’t.)
6. Transfer the metal to the
4. Weigh the calorimeter cup with               calorimeter.
the water in it.
   The best way to do this is to lift
   Weigh the cup with the cool                  the metal out of the generator by
water in it. The difference                  the string, swivel the support rod
between this mass and the mass               or move the table stand, then
of the cup alone is the mass of              lower the cube into the
the water, which you will use in             calorimeter. Then put the
the calculation. Record the mass             calorimeter lid in place.
of the water in the data table.
   Place the calorimeter cup in the             Note: While transferring, shake
calorimeter. Use a cloth or paper            or brush off any hot water
towel as a temporary lid for the             droplets that adhere to the
calorimeter to keep the water                specimen. You do not want to
cool. (You can always readjust               transfer any hot water. Make
the temperature of the water by              sure the metal is fully submerged
adding more cold water. But                  and is not touching the sides or
then you must weigh the water                bottom of the calorimeter.
again.)
7. Measure the final (equilibrium)
5. Take the initial temperature                 temperature
   After the temperature in the
   After the water in the steam                 calorimeter stops changing,
generator boils, but before                  gently stir the water with the
transferring the metal, measure              thermometer probe.
the temperature of the cool water           Measure the temperature to the
in the calorimeter. Gently stir              nearest 1/10 degree C and record
the water with the probe of the              this as the final temperature of
digital thermometer, then take               the system, Tf.
the reading to the nearest 1/10
degree C. Record this as the

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8. Solve equation 3 for the specific              List the accepted value in SI
heat of the metal.                              units. To do this you will have to
convert from units of calg-1C-1
9. Using your data, determine the                  to jouleskg-1C-1. Determine a
specific heat of the metal.                     conversion factor for doing this
and write it in the space
   Record your results in the               provided.
calculations table below.
with those in the table (which are
listed in units of calg-1C-1.)

Table 1: Specific Heats

Substance             Specific Heat
(calg-1C-1)

Aluminum              0.215

Antimony              0.0495

Brass/Copper          0.0924

Iron                  0.108

Magnesium             0.243

Silver                0.0562

Tin                   0.0543

Tungsten              .0322

Water                 1.00

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Lab 12: Specific Heat                                          Name:

Date:

Class:

Data & Analysis

Experimental data

Group number _______                                 Mass of calorimeter cup __________

Metal        Mass of       Mass of          Initial             Initial              Final
Speci                    metal         water         Temperature         Temperature          Temperature
men      (Description)                                 of Water            of Metal
(T1)               (T2)                  (Tf)

1

2

3

4

Solve equation (3) algebraically for the specific heat of the metal:

Note: Use the symbols T1, T2 and Tf for the initial water temperature, the initial metal
temperature, and the common final temperature, respectively.

157
Lab 12: Specific Heat                               Name:

Date:

Class:

Data & Analysis

Calculations

Speci         Metal           Calculated     Accepted value      Percent
men                          specific heat   for specific heat    error
(Description)     (joulekg-     (joulekg-1C-1)
1
C-1)

1

2

3

4

Conversion factor:           __________
(for converting calg C to joulekg-1C-1)
-1  -1

158
Lab 12: Specific Heat                                Name:

Date:

Class:

Data & Analysis

Questions

1. One source of error in this experiment is that the metal specimen gives up heat to the
room during the transfer process. Which of the metals you measured would be most
affected by this? Do the percent errors in your results reflect this?

2. What experimental problem would result if the mass of the water were very much
larger – 1000 times, say – than the mass of the metal?

3. Use your data and the accepted value for the specific heat of aluminum to calculate
what the final temperature should be for an error-free experiment. Consider the metal
and the water only and ignore the calorimeter cup in the calculation.

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