Finding a material's specific heat capacity

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Jonathan Hobbs                                                                     -  -                                                                         09/05/2007

Physics coursework: Finding a material's specific heat capacity

Skill A

Aim:

The aim is to accurately find the specific heat capacity of a material given a certain mass of that material and other experimental equipment.  The specific heat capacity of a substance is the heat energy required to raise one kilogram of the material by one Kelvin or one degree centigrade – it is usually measured in J kg-1 K-1.  The experimental technique and results will be analysed.  The purpose is to be able to conclude the reason for certain materials having higher or lower specific heat capacities than others and to discuss these reasons scientifically.  Perhaps, during the course of the experiment, means could even be devised to reduce energy-loss when heating substances.

In addition, it should be ensured to be an entirely fair test and the results we achieve must be reliably accurate and trustworthy.  Everything will be controlled as best as it can be under the circumstances so a viable conclusion can be generated at the end, the correctness of which can be analysed.

Planning and method:

Before any experimental data was gathered, a preliminary experiment was carried out to aid the planning process, practise the procedure and to predict any difficulties that may be encountered.  The most successful methods of insulation were tried out to optimise the accuracy of the experiment by minimising heat loss.  It was decided that the specific heat capacity of copper would be found.  In addition, the apparatus that would be used could be decided after comparative tests and after assessing the sensitivities and accuracies of the instruments.  Because of the preliminary work, it was decided that the material being heated would be insulated to reduce heat loss as much as possible and then put in a measured volume of distilled water, the temperature of which would be monitored.  Hence, with the knowledge of the specific heat capacity of water at appropriate temperatures, the amount of energy wasted in order to heat the water could be calculated and factored into the results.  Finally the water container would be insulated further.

In order to measure the specific heat capacity of copper, it was decided that a given volume would be heated by an efficient electric heater.  By measuring the voltage and current of the heater and the length of time for which it was turned on, the energy transferred into the copper block could be measured by means of the following formula: energy transferred = current x voltage x time (∆E = IVt).  Then, the temperature change of the metal would be measured as well as the rate.  The block would only be heated for a short time so that its temperature did not rise by more than about 20°C.  This is because specific heat capacities change slightly as the temperature of the material changes.  By including the energy found to have been lost heating the surrounding water, values for the temperature change and corrected energy transferred can be found.  Hence, using the formula for energy transferred: change in temperature x specific heat capacity x mass (∆E = ∆Θ x c x m), the specific heat capacity can be calculated.

The following plan of action was devised:

  • A cylindrical copper block that had two small holes for temperature probes and electric heaters will be wrapped in alternating layers of cotton wool and bubblewrap held down with masking tape to provide insulation.  It will be ensured that the final layer is cotton wool as bubblewrap has a very large surface area and hence, will radiate much better losing more heat.
  • The insulated copper block will then be placed snugly in a polythene jar.
  • This jar will be stood in a larger polythene jar containing a measured volume of distilled water.  The water will be poured into the larger jar already containing the smaller flask until the level reaches the rim.  Hence, by pouring the water into a 200ml measuring cylinder and the end of the experiments, its volume and mass can be found.  The largest jar will be insulated with more layers of cotton wool and bubblewrap before being placed on top of a heat proof mat.
  • The electrical circuit used to provide heating power will be set up.  The voltmeter, ammeter, stop clock and temperature probes will be tested to ensure they work properly, are set to the correct settings and their displays will be labelled to be sure of quick and easy reading.
  • Oil will be put in the temperature probe and heater receptacles in the copper block to help transfer all the heat from the heater to the block and from the block to the temperature probe.  This is because oil is much more dense than air and hence, as the particles are more closely packed, is a far better conductor of heat.  The temperature probes will be inserted to the distilled water and copper block, as will the electric heater.
  • A lot more cotton wool will be added as insulation to the top of the apparatus to prevent heat loss out of the top.
  • All the equipment will be double checked to ensure it still works properly and no electrical devices are in danger of running out of battery power.
  • Zero readings will be taken and recorded for the temperature of the water and the temperature of the metal.  Simultaneously, the stop clock will be started and the heater turned on.  Readings for voltage and current will be noted down.
  • Readings for the temperature of the metal and the water will be taken every thirty seconds.
  • When the stop clock indicates that one hundred and fifty seconds have elapsed (02:30), the current and voltage of the heater will be noted once again and the heater will be immediately turned off.  However, it will be left inside the copper block as it will still giving out heat energy as it the heating element cools down.
  • Temperature readings will continue to be recorded for the copper block and water until both had stopping rising and started falling.
  • The whole experiment will be repeated after the copper block has cooled back down to a temperature similar to the initial starting temperature.  As many repeats as possible will be made.
  • Finally, the mass of the copper block will be recorded after measuring it with an accurate electric balance.

Once all the data has been collected, it will be tabulated.  Average percentage errors will be calculated for all measurements and figures quoted.  When two or more pieces of data are multiplied together, the resultant percentage error will be the sum of the original error of the data.  When if items of data are summed or subtracted, the resultant percentage error will be equal to the largest percentage error of the data values.

Also, graphs can be drawn.  One graph can be made showing the temperatures of the water and metal block for both experiments as time elapses and any anomalies present can be easily identified.  The temperature of the metal block is expected to begin to rise and soon rise at a constant rate in a linear fashion.  Then, some time after the heater has been switched off, the temperature will slowly fall.  The temperature of the water is expected to rise more slowly and begin to cool much later.  Also, by finding the energy transferred at any given time, the temperate can be plotted against the energy transferred for the linear section that rises linearly.  The energy at a given time can be found from the following formula:

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energy put in by heater – energy lost to heat water = running 'true' energy

= (voltage x current x time) – (change in water's temperature x mass x specific heat capacity)

The specific heat capacity assumed for water will be taken to be 4192.5 J kg-1 K-1 as this is its specific heat capacity at about 11.5°C which is the roughly the average temperature of the distilled water during the copper's period of linear temperature increase.

Thus, when the temperature of the copper is plotted against heat energy supplied for the linear section of the graph, a ...

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