Download SPECIFIC HEAT

CALORIMETRY & SPECIFIC HEAT
THEORY
Heat energy is defined as energy that flows from hot objects to cold objects. It can be measured in
calories, kilocalories, or joules of energy. One calorie is defined as the amount of heat required to
raise the temperature of 1 gram of water by 1 C. One calorie is equivalent to 4.184 joules.
Different substances of identical mass require different amount of heat to raise their temperatures
a certain degree. A specimen's heat capacity is
C
Q
,
T
where Q = amount of heat added or subtracted from the specimen, and T = temperature change
of the specimen. The specific heat capacity of the specimen's substance is
c
C
Q
,

m mT
where m = mass of the specimen. Thus, the amount of heat gained by a specimen is given by
Q = mcT.
A calorimeter can measure c for a specimen by the method of mixtures. A specimen of known
mass m is combined with water of known mass mw and specific heat capacity cw, inside a
calorimeter. Ideally, the cup is insulated such that no heat is lost or absorbed by it. The heat lost
by the specimen, Qs, is gained by the water as Qw.
Qs = Qw
mscsTs = mwcwTw.
To keep the heat flow values Qs and Qw positive, use the absolute value of the specimen's
temperature change T [express T as (Ti – Tf) to get a positive value].
Work with your lab partner to derive an expression for the specific heat capacity of the metal.
Show your instructor what you come up with. Do not plug in values until the very end.
PURPOSE
Test whether your derived expression for specific heat capacity predicts the accepted value of c
for the sample. By experimentally determining c using equation and comparing this to the
accepted value of c, the theory behind calorimetry and the method of mixtures is tested.
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SETUP
Use the Styrofoam cups, supplied beakers, and electric hot plate provided.
PROCEDURE
Heat the sample in a beaker of boiling water. Transfer to room temperature water in the
calorimeter cup. Take data using the PASCO temperature sensors during the entire time and
produce a graph of the entire process. Analyze your graph to determine the initial temperatures
of the sample and water and final temperatures of the sample and water.
SOURCES OF ERROR
Take careful care during the data gathering process to be sure your data is valid. Do not rest the
specimin and/or the thermometers on the bottom and/or against the sides of the beaker. Stir the
water in your beaker continuesly. Allow enough time for thermal equilibrium to be reached and
for the data curves to flatten out. Check your lab partners work. Have the instructor check your
work before tearing down and/or moving on to new things.
ANALYSIS
Calculate c for your unknown sample and compare to theory. Be sure to include the percent
difference of your experimental results as compared to theory in your conclusion.
The following are the accepted values of c for different elements, measured at 25 C:
caluminum = 897. JkgC, clead = 195. JkgC, ccopper = 385. JkgC,
ctin = 523. JkgC, and czinc = 388. JkgC.
STATISTICAL CONSIDERATIONS (OPTIONAL):
1.
Calculate c for each of the four runs. Tabulate c for each run n = 1 to 4.
2.
Compute c = mean of c.
3.
Compute sc = standard deviation of c.
4.
Calculate x - k, x + k = the interval that includes the parent mean  (the true mean)
with a 100(1 - ) percent confidence. Take  = .05 for a 95% confidence. Use the critical
value t formula and the t-distribution table,
 s
k  t 2
n-1
1  2 = .975
0
5.
1
12.706
c
n
2
4.303
3
3.182
4
2.776
9
2.262
Determine whether the accepted value of c falls within this 95% confidence interval. If it
does not, calculate the percent difference of the theoretical result from the given value.
REFERENCES
CRC Handbook of Chemistry and Physics, 75th edition, David R. Lide (editor), 1994,
CRC press, Incorporated, Boca Raton, Florida.
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