Pawat Silawattakun th 4 February, 2013 Dr Johnson
Determining the Specific Heat Capacity of Aluminium and Steel
Abstract: Two experiments were conducted in order to determine a fairly accurate value for the
specific heat capacities of aluminium and steel, which is a measurable physical quantity that is the ratio of the amount of heat energy transferred to an object to the resulting increase in temperature of the object (i.e. how quickly a particular object heats up with respect to time). A heating element was connected to a power supply which provides the object with heat – this heating element was then placed inside a block of aluminium (or steel in the second experiment); the resulting temperature change was noted as was the time taken for the temperature of the object to change. The average specific heat capacity with its uncertainties was calculated from each of the thirtysecond readings and it was found that the aluminium, with its errors, matched up quite well with the known value [1]. The values of SHC for steel, however, did not seem to match the ideal value of SHC of steel; this issue will be explained later.
Introduction: The aim of the experiment was to determine the specific heat capacities, with
uncertainties, of two different materials; for the purposes of this experiment, it was chosen to be aluminium and steel. The enthalpy was calculated from the power supply (see theory section) and the mass and temperature difference were recorded during the experiment in order to find the specific heat capacity. It is useful to know the SHC of an object because there are uses for materials with high SHCs as well as low SHCs, such as in insulating instruments, cooling towers, and cooking instruments – it is therefore important to exploit these properties of the materials as much as possible, for example in fields such as engineering and materials science.
Theory: The specific heat capacity was worked out by the equations: ΔQ = mcΔT where
Q is the enthalpy, m is the mass, ΔT is the change in temperature, and c is the
specific heat capacity. To find c (kJ/kg°C (kJ/kg°C ), ), the values of ΔQ and ΔT were T were to be deduced by the experiment, and hence the value of c of c could be worked out mathematically by the rearrangement of this equation: c = ΔQ/mΔT . To find ΔT , it was simply T final final – T initial initial .
E where E is E is energy in joules. Also, E = E = To find ΔQ, this requires another set of equations: firstly, Q = E where Pt where Pt where P is power (J/s). Finally, P = VI, VI, hence from the data, the products of voltage, current, and time therefore gives the value of the enthalpy: Q = E = VIt . To get the value in kilojoules, the answer was divided by 1000. Error calculations are discussed in the analysis.
Pawat Silawattakun th 4 February, 2013 Dr Johnson
Apparatus: Aluminium and steel blocks; power supply of 10V; multiple wires; two 328 Digital
multimeters; insulating box; thermometer; heater/heating element.
Safety: Do not touch the heating element or the blocks once the experiment has commenced, as
they will become very hot – watch thermometer and use common sense to judge when the blocks become cool enough to handle safely.
Independent Variable: Time (s) Dependent Variables: Temperature (°C), Specific Heat Capacity (kJ/kg/°C) is a constant value of a material; however, the average is being taken from every measurement, hence the value fluctuates from errors and will be plotted on the y-axis, and a line of best fit drawn through with gradient = 0.
Diagram:
Fig 1
Pawat Silawattakun th 4 February, 2013 Dr Johnson
Procedure: The experiment was setup like in the diagram (Fig 1.), with the voltmeter across the
heating element and the ammeter parallel to the main circuit. The ammeter was set to a limit of 10A, and the voltmeter to 20V. The block of metal was placed inside an insulating box, to minimize the heat lost to the surroundings. The mass of the block was taken, with an error of 0.5 g which is negligible. The dial at the power supply was set to a voltage of 10V. The initial temperature was recorded on a table using the thermometer. The heating element was placed inside the block of metal, and the switch on the power supply was turned on, and the stopwatch was started; the values of the corresponding voltages and currents were recorded at time t = 0. The voltage, current, and temperature were recorded on the table every thirty seconds for 12 minutes. The power supply was turned off and the block was allowed to cool down. The experiment was then repeated with another block of a different material.
Pawat Silawattakun th 4 February, 2013 Dr Johnson
Analysis & Conclusion:
Two methods were used to find the SHC using graphs. The graph of SHC against time was plotted. Also, if the graph of enthalpy against mΔT was plotted, the gradient is the specific heat capacity because y = mx + c, where y = Q and x = mΔT. The value of c in aluminium, from Fig 3 was found to
be 1.00 ± 0.14 kJ/kg/°C . The value of c in steel from Fig 5 is 0.65 ± 0.079 kJ/kg/°C. The value of aluminium’s SHC corresponds well with the accepted value; however, steel does not. Unfortunately,
the calculations for the heat lost to the surroundings was not accounted for, therefore, the errors may not be large enough to accommodate for the values which were collected. According to Fig 4 and Fig 6, ignoring the first few data points, a value of 0.79 ± 0.14 kJ/kg/°C and 0.49± 0.079 kJ/kg/°C were obtained for aluminium and steel, which was closer to the actual value.
The main source of error which has not been accounted for in this experiment was the loss of heat through the surroundings; this may be the reason why the value for steel did not match the actual value. It also makes sense from the first method (plotting against time) that both values of SHC that were worked out were slightly higher than the actual values; a higher SHC means that the object takes longer to heat up – this proves that the heat lost through surroundings causes the material to heat up slower due to heat lost, hence giving a higher than normal value of SHC.
The experiment could definitely be improved by heating the materials for a longer period of time, because almost half of the values collected were useless due to the large errors, but this was not known until the data was processed. The first experiment did just match the actual value thanks to the uncertainties. Another problem in the second experiment may be that the heating element was not let to cool down enough after the first experiment was conducted. Despite that, in conclusion the values from the second graph seems to give the value of c to a better accuracy, and the experiment was a successful one because 0.79 ± 0.14 kJ/kg/°C and 0.49± 0.079 kJ/kg/°C are within the range of the ideal values of 0.91 (aluminium) and 0.42 (steel).
Acknowledgements:
Lab Partners: Herman Cheng, Denis Tam Beak: Dr Johnson References: [1] http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html(SHC of steel and aluminium) [2] www.rapidonline.com [3] Advanced Physics – pp 65-66 (Specific Heat Capacity)
