Abstract
The purpose of this experiment was to determine the specific heat capacity of unknown substance and use the quantity to identify the substance. The specific heat capacities of the metals were determined to be 0.890 Jg-1K-1 and 0.361 Jg-1K-1. The metals were identified as aluminum and copper respectively. The percentage uncertainty in the determination of specific heat capacities of aluminum and copper were found to be 0.78% and 6.23% respectively. These errors were attributed to loss of heat in the atmosphere.
Introduction and Theory
The amount of heat absorbed or released by a substance is proportional to its mass and temperature differences (Arfken 297). That is Q∝ m∆T. This equation can be rewritten as Q=c m ∆T. The constant of proportionality (c) is called the specific heat capacity of the substance. It is the quantity of heat needed to change the temperature of 1 gram of substance by 1ºC (Myers 86). The specific heat capacity depends on the material. Consequently it is an intensive characteristic of a substance.
Usually, a calorimeter is used to measure the specific heat capacity of a substance. Calorimeter works using the principle of conservation of energy. The heat released by the substance is absorbed by the surrounding which is usually water. Calorimeter consists of Styrofoam cup with lid and two openings. The first opening is for the stirrer while the other opening is meant for immersing the thermometer into the calorimeter. It is properly insulated to minimize heat loss to the surrounding.
The specific heat capacity of a metal can be determined by measuring the mass of the metal and then heating it. The hot metal with known mass and temperature is immersed in a Styrofoam cup having cold water with known volume and initial temperature. Heat would flow the hot metal to the water until such a time when both have the same temperature. The first Law of Thermodynamics predicts that the sum of heat supplied by the hot metal and that absorbed by water would be zero. That is Q m + Q w = 0. This is the equation used to compute specific heat capacity of the substance under investigation.
The steam generator was filled with water and aluminum piece placed in it. The water was heat until it boiled. A Styrofoam cup was half filled with cold water. The temperature of the cold was measured. The aluminum piece was transferred to the water when its temperature reached that of boiling water. The same procedure was repeated for copper piece
Data and Tables
The following table shows the masses and temperatures of water and metals as measured during the experiment
The following table contains the calculated values of product of masses of the metal or water and change in temperatures
Calculations and Results
Specific Heat capacity of aluminum
Heat given out by the aluminum = Heat absorbed by water
Qa=Qw
cama∆Ta=cwmw∆Tw
Where ca and cw are the specific heat capacities of aluminium and water respectuvely
The ma and mw are the masses of aluminium and water respectively
∆Ta and ∆Tw are changes in temperatures of aluminium and water respectively
Trial 1
∆Ta=371.5-292.3=79.2K
∆Tw=292.3-288.1=4.2K
ca X 79.2 X 87.9=360.7 X 4.2 X 4.18
0.910
Trial 2
∆Ta=366.4-289.8=76.6K
∆Tw=289.8-285.3=4.5K
ca X 76.6 X 87.9=346.6 X 4.5 X 4.18
0.968
Trial 3
∆Ta=389.0-291.3=97.7K
∆Tw=291.3-287.4=3.9K
ca X 97.7 X 87.9=417.5 X 3.9 X 4.18
0.793
Average of specific heat capacities
0.910+0.968+0.7933
0.890
Uncertainty
0.897-0.8900.897
0.78%
Specific Heat Capacity of Copper
Heat given out by copper = Heat absorbed by water
Qc=Qw
ccmc∆Tc=cwmw∆Tw
Where cc and cw are the specific heat capacities of copper and water respectuvely
The mc and mw are the masses of copper and water respectively
∆Tc and ∆Tw are changes in temperatures of copper and water respectively
Trial 1
∆Tc=373.0-288.1=84.9K
∆Tw=288.1-282.4=5.7K
cc X 84.9 X 268.6=360.7 X 5.7 X 4.18
0.377
Trial 2
∆Tc=363.3-290.4=72.9K
∆Tw=290.4-284.5=5.9K
cc X 72.9 X 268.6=346.6 X 5.9 X 4.18
0.271
Trial 3
∆Tc=357.8-287.8=70.0K
∆Tw=287.8-283.1=4.7K
cc X 70.0 X 268.6=417.5 X 4.7 X 4.18
0.436
Average of specific heat capacities
0.377+0.271+0.4363
0.361
Uncertainty
0.385-0.3610.385
6.23%
Graphs
The following is a graph of the product of the mass of aluminum and change in temperature versus product of mass of water and change in temperature
The following is a graph of the product of the mass of copper and change in temperature versus product of mass of water and change in temperature
Discussion of questions
The slopes of the two graphs give the ratio of the specific heat capacities of the metals and specific heat capacities of water. The experimental values of the specific heat capacities were very close to the theoretical values. The small deviation between the experimental and theoretical values is an indication that the metals were correctly identified. The deviations were caused by errors associated with loss of heat into the surrounding when the metals were being transferred to the Styrofoam cup. Some of the heat might have been lost through the openings in the lid of Styrofoam cup. Future recommendations for reducing the errors include minimizing the time taken to transfer the metal to the Styrofoam cup and using a properly insulated calorimeter.
Conclusion
The specific heat capacities of the metals were determined and the metals identified. The small value uncertainty in the determination of the specific capacities of the metals is a proof that the experiment was very successful.
Works Cited
Arfken, George B. University Physics. Orlando: Academic Press, 1984. Print.
Myers, Richard L. The Basics of Physics. Westport, Conn: Greenwood Press, 2006. Print.
