Specific Heat of Solids Salvacion, Jozel John. P. Physics Department, De La Salle University, 2401 Taft Avenue, Manila
[email protected]
Abstract - This experiment was done to determine the Specific Heat Capacity, or Specific Heat, of Aluminum, Copper, and Lead with the use of a Calorimeter, Thermometer, and an Electric Steam Generator. Using the method of mixtures, the metal samples should undergo change in temperature and attain thermal equilibrium with the water. After the experiment, it was shown that Aluminum had the highest specific heat and Lead had the lowest specific heat out of all the three (3) metals tested. Even though Aluminum had the highest percentage error out of the experiments, the calculated value is still within the threshold set by the facilitator making the value acceptable. Furthermore, if this experiment were done in a well-controlled environment and with more accurate equipments, the resulting figures would have had less percentage error. This experiment was proved to be a reliable way to calculate for the specific heat of a material because it yields results with errors well under 15% if done correctly. Keywords - Specific Heat Capacity; Thermal Equilibrium; Change in Temperature; Method of Mixtures I. INTRODUCTION The Specific Heat Capacity, or Specific Heat, of a substance is the amount of heat required to raise the temperature of the substance by one (1) degree Celsius. Specific Heat is often denoted by the variable c. The unit used for the Specific Heat of a substance is in calories per gram degree Celsius (cal/g-Cº). Thermal Equilibrium is when two contacting bodies are no longer transferring or absorbing heat from one another. Related to that, the temperature of both bodies is no longer changing and is in an equilibrium or state of stability.
The Method of Mixtures makes use of the concept of the Law of Heat Exchange. It states that when a cold substance is mixed with a hot substance, the system undergoes change in temperature where the cold substance absorbs heat from the hot substance until thermal equilibrium is attained. In this case, the cold substance is the water and the hot substance is the heated metal. The resulting masses (m) and changes in temperature (ΔT) of the metal and water in the experiment is needed to calculate for the specific heat of the metal used and is denoted as
C sample
. The data gathered
will be substituted in Equation (1).
C sample =( M water Cwater ) Δ T water M sample Δ T sample (1)
M water
and
M sample
is the mass of the
water and mass of the metal sample respectively. While
ΔT water
Δ T sample
and
is the change in
temperature of the water and the metal sample respectively. Lastly,
C water
is already at a fix value of
1 cal/g-Cº II. METHODOLOGY We first prepared the materials needed which are the Calorimeters, Water, Thermometer, Weighing Scale, Thread, Cold Water, Electric Steam Generator, and samples of Aluminum, Copper, and Lead. After the preparation of the materials, the Electric Steam Generator is filled halfway with tap water
to boil it. Next, the mass of a dry and empty calorimeter and the mass of a metal sample is then measured and represented by the variables
mcal
msample
and
respectively. After measuring the mass of the metal sample, a string is then tied to it and it is suspended in the boiling water for a couple of minutes for the heat to be transferred fully.
ΔT sample =100 ºC−T final The process is then repeated for the other 2 metal samples. The data obtained is substituted back to Equation (1) and then compared to the standard value by calculating for the percentage error. The threshold for error was established at 15%.
A calorimeter is then filled with enough cold water to submerge the metal sample. The temperature of the cold water is then recorded as
T cold
. Immediately
after taking down the temperature of the cold water, we then pulled out the metal sample out of the boiling water, wiped it briefly yet thoroughly, and then submerged it in the cold water. The cold water with the submerged metal sample is then stirred with the thermometer until it reaches the maximum possible temperature it can achieve and this temperature is known as the system's thermal equilibrium. The temperature at the equilibrium is then recorded as
T final
III. RESULTS AND DISCUSSION Table 1: Data Sheet Material of Metal Sample Mass of Calorimeter,
.
Immediately after recording the final temperature, the mass of the water is then computed by subtracting the total mass of the calorimeter, metal sample, and the water, with the mass of the calorimeter and the metal sample. This process can be represented by Equation (2).
M water= M total −( M cal + M sample )
mcal
Mass of Metal Sample,
msample
change of temperature of the water (
Δ T water ¿
after
Mass of Calorimeter, Water, and Metal
mtotal
coming into contact with the heated metal sample using Equation (3).
Δ T water =T final−T cold (3) Using Equation (4), we then computed for the change of temperature of the metal sample.
mwater
14
14
18
205
200
238
456
495
468
251
281
212
13.8
9.3
9.1
25.3
14.8
11.8
11.5
5.5
2.7
(g)
(g)
Temperature of Water,
T cold
Lead
(g)
Mass of Water,
The next thing we did was to compute for the
Copper
(g)
Sample,
(2)
Aluminum
(ºC)
Equilibrium Temperature of Water and Metal Sample,
ΔT final
(ºC)
Temperature Change of Water,
ΔT water
(ºC)
Temperature Change of Metal Sample ,
Δ T sample
(ºC)
71
81.5
84.5
Specific Heat of Water,
c water
(cal/g-Cº)
1
1
1
Calculated Specific Heat (cal/g-Cº)
0.198
0.095
0.028
Standard Value of Specific Heat
0.220
0.093
0.031
Percentage Error
15%
2%
8%
Table 1 shows the data obtained from the experiment and the resulting values for the Specific Heat of the Aluminum, Copper, and Lead metal samples. It was shown in the table that the highest change of temperature of the water was caused by the Aluminum while the lowest change was caused by Lead. Furthermore, the metal that had the highest temperature change was Lead and the lowest was Aluminum. Lastly, it was evident that Aluminum had the highest specific heat while Lead had the lowest. I believe that if a metal sample's temperature can be easily increased and it does not heat water effectively, then that said metal has a low specific heat capacity and vice versa. Since the specific heat capacity of a metal is the amount of heat required to increase the temperature of the metal by 1 degree Celsius, then the pattern shown in the data is not an anomaly but rather an expected outcome in the experiment.
The resulting error could have been because of the temperature of the room, accuracy of the instruments, human error in reading the values shown by the instruments, or the duration of the wiping of the metal sample after being pulled out from the hot water. Nonetheless, the values acquired were either under or equal to the threshold (15%) given by our instructor. IV. CONCLUSION The experiment was proved to be a reliable way to calculate for the specific heat of a material. The values obtained were 0.198, 0.095, and 0.028 for Aluminum, Copper, and Lead respectively. The resulting values were equal or below 15%. REFERENCES [1] Specific Heat of Solids PDF available at : http://www.dlsu.edu.ph/academics/colleges/cos/physics/_p df/cos-specific-heat-of-solids.pdf
