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Finding a Material's Specific Heat Capacity

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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:
====================

[IMAGE]

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:

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 straight line
of best fit can be drawn for each repeat of the experiment. By
comparing the lines, it is possibly to check that the two experiments
give consistent data. The gradient of the line of best fit will give
the reciprocal of the specific heat capacity multiplied by the mass.
This is because ∆E = ∆Θ x c x m

Hence, as the graph plots ∆Θ against ∆E the gradient will give ∆Θ/∆E
which equals 1/c x m. Therefore, the inverse of the gradient gives
∆E/∆Θ which equals specific heat capacity times mass. Dividing both
sides by the mass will give the specific heat capacity
(mass/gradient). These calculations will be carried out for both the
lines and the average will give the resultant, most accurate value for
the specific heat capacity.

The following apparatus will be used:

* copper block

* electric balance

* data book

* bubble wrap

* cotton wool

* 12V, 8.5A DC power supply

* wiring

* various sized polythene beakers

* masking tape

* oil

* stop clock

* ammeter

* voltmeter

* two temperature probes and displays

* alcohol thermometer

* heat-proof mat

* distilled water

* 200ml measuring cylinder

* immersion heater

Sensitivity:

Electric balance ± 0.5 g

Ammeter ± 0.005 A

Voltmeter ± 0.005 V

Temperature probe ± 0.05°C

Alcohol thermometer ± 0.5°C

Stop clock ~+1 s (± 0.005 s)

Measuring cylinder ± 0.5 ml

The electric balance is suitably accurate especially for the
calculations that would be made. When measuring in kilograms, it is
sensitive to four decimal places. The ammeter and voltmeter are highly
sensitive digital electronic devices that offer a high degree of
sensitivity unparalleled by other lab. equipment. It was decided upon
to use the temperature probes to measure temperatures due to their
very high sensitivity. It is also much easier to read their digital
displays at a glance and, unlike traditional alcohol thermometers,
there is no danger of parallax error with the digital probes. However,
after the experiment was carried out and the temperature probes were
calibrated with by boiling water, they were found to be very
inaccurate. When the water boiled an alcohol thermometer showed the
temperature to be around 99°C, but the two temperature probes measured
about 94°C. It is reasonable to expect this difference to be
consistent throughout the temperature range so that the error is still
only about -5-6°C in the temperature range in which the experiment was
conducted. In addition, the variable that must be measured is
temperature change, so an error such as this should have a negligible
effect on results and the following conclusions. As such, it was
decided that, on balance, the temperature probes' higher sensitivity
would be of greater use in the experiment anyway. The stop clock
measures accurately to 0.01 s giving a potential error of ± 0.005 s
but, as it has to be read by a human and the reading on the display
noted down by hand, this can be extended up to almost plus 1 s.
However, as the temperature changes at a fairly slow rate and readings
are only taken every thirty seconds, this could not have a significant
effect on the quality of the results garnered.



Accuracy:
=========

The power supply can be set to various voltage settings - for this
experiment, 12V was chosen. However, due to various factors such as
internal resistance, this stated value is often different to the true
voltage in the circuit and the voltage across the heater. Because of
this, a voltmeter was used to measure the actual voltage and this has
the advantage of being far more accurate than the value claimed by the
power supply. An electric heat supply is very accurate as, due to the
E = IVt formula, the amount of energy put into the copper can be
measured very precisely - it is far superior than other methods of
heating the substances such as with a Bunsen or hot water. Also, the
copper block was cylindrical because this is a similar shape to the
shape of the cylindrical electric heating element and this will mean
that the heat is spread fairly evenly through the metal. The amount of
energy can be measured digitally and the number of joules transferred
at any given time can be calculated.

Variables:

* Energy put into the copper block - This is the independent
variable that will be controlled to see how the other variables
are affected.

* Room temperature - Any change in room temperature between the two
lessons will be very small and any effect this may have on the
results will be negligible.

* Room pressure - The experiments will take place at the same
altitude and roughly the same air pressure. There will be very
little difference between the two repeats.

* Temperature of copper block - The starting temperature of the
copper block will depend on the room temperature and hence, should
be almost the same in both experiments. This is also the dependent
variable and the change in temperature will be measured throughout
the experiment.

* Temperature of distilled water - This is another dependent
variable. The change in temperature of the water will also be
measured during the experiment and combined with the other results
taken in order to find the specific heat capacity. Similarly to
the copper block, the starting temperature of the water should not
change much and affect the results.

* Temperature range - For both experiments roughly the same amount
of heat energy will be supplied for the same length of time to
make sure that the temperature range is kept fairly constant. This
is because specific heat capacities of copper and water vary
slightly according to temperature, as does the rate of heat loss.
In addition, at higher temperatures the resistance of the circuit
will increase and the water could evaporate.

* Insulation - for the repeat of the experiment, the same insulation
will be used to ensure that minimal heat loss is set at a constant
rate for each test and will not vary.

* Measuring devices - The same measuring devices (including, among
others, temperature probes and displays, ammeters, voltmeters)
will be used for all repeats to ensure that the readings obtained
are consistent and do not affect the results or introduce
anomalies.

* Material - throughout the experiment, the same copper block of the
same mass will be used. This is to ensure no error is introduced
due to a different material with a different density and other
properties or the mass being different resulting in more energy
being required to raise the temperature for each degree
centigrade.

Safety:

Because of the hazardous nature of the experiment, special care must
be take to adhere to safety guidelines and avoid accidents. When the
heater is turned on, the hot element must never be touched
unprotected, as it gets very hot indeed. It should also be remembered
that the element stays very hot for a period after the power has been
switched off. Due to the insulation, the copper will be much hotter to
the touch than the outside of the flask and allowances must be made
for this. The ammeter and voltmeter must always be set to the correct
settings before they are turned on so as to avoid dangerously fusing
them due to current surges. Water is also dangerous as, when spilled,
it can get very slippery. In addition, when calibrating temperature
sensors by boiling water, special care must be taken due to the
hazardous nature of boiling water and especially steam. Finally, care
must always be taken will electrical apparatus particularly when water
is nearby.


Skill C

Results:



Experiment One
==============



Experiment Two
==============

Mass of copper block/kg: (± 0.0005 kg, ± 0.4982%)

1.0035

1.0035

Volume of distilled water/l: (± 0.0005 l, ± 0.1786%)

0.272

0.288

Starting voltage/V: (± 0.005 V)

8.76

8.89

Final voltage/V: (± 0.005 V)

8.74

8.89

Average voltage/V: (± 0.005 V, ± 0.006%)

8.75

8.89

Starting current/A: (± 0.005 A)

3.73

3.79

Final current/A: (± 0.005 A)

3.69

3.77

Average current/A: (± 0.005 A, ± 0.013%)

3.71

3.78

Power (IV)/W (J/s): (±0.006 + ± 0.013 = ± 0.019%)

32.46

33.60


Experiment one
--------------

Measurement

Sensitivity

Average Value

Error

Metal temperature

Temperature

± 0.05°C

23.50°C

0.21%

Water temperature

Temperature

± 0.05°C

11.10°C

0.45%

Electrical Energy

Power

-

-

0.02%

Time

+ 1.00 s

1290.00 s

0.08%

Total: 0.10%

Water energy

Specific heat capacity

taken to be zero

4192.50 J kg-1 K-1

0.00%

Mass

± 0.50 g

272.00 g

0.20%

Temperature change

2 x ± 0.05°C

11.10°C

0.90%

Total: 1.10%

'True' energy

(Electrical energy - water energy)

Electrical energy

-

-

0.10%

Water energy

-

-

1.10%

Largest error: 1.10%


Experiment one
--------------

Time/s

Metal temperature/°C

Water temperature/°C

Electrical energy/J

Water energy/J

'True' energy/J

(±0.08%)

(± 0.21%)

(± 0.45%)

(± 0.10%)

(± 0.92%)

(± 0.92%)

0

13.3

10.6

0

0

0

30

13.8

10.6

974

0

974

60

15.4

10.6

1948

0

1948

90

17.7

10.6

2922

0

2922

120

20.3

10.6

3896

0

3896

150[*]

23.0

10.6

4869

0

4869

180

25.1

10.6

4869

0

4869

210

26.4

10.6

4869

0

4869

240

26.9

10.6

4869

0

4869

270

27.0

10.7

4869

114

4755

300

27.1[†]

10.7

4869

114

4755

330

27.1

10.7

4869

114

4755

360

27.0

10.7

4869

114

4755

390

26.9

10.7

4869

114

4755

420

26.8

10.7

4869

114

4755

450

26.7

10.7

4869

114

4755

480

26.6

10.7

4869

114

4755

510

26.5

10.7

4869

114

4755

540

26.4

10.7

4869

114

4755

570

26.3

10.8

4869

228

4641

600

26.2

10.8

4869

228

4641

630

26.1

10.8

4869

228

4641

660

26.0

10.8

4869

228

4641

690

25.9

10.8

4869

228

4641

720

25.8

10.8

4869

228

4641

750

25.7

10.8

4869

228

4641

780

25.6

10.8

4869

228

4641

810

25.5

10.8

4869

228

4641

840

25.4

10.9

4869

343

4527

870

25.3

10.9

4869

343

4527

900

25.2

10.9

4869

343

4527

930

25.1

10.9

4869

343

4527

960

25.0

10.9

4869

343

4527

990

24.9

10.9

4869

343

4527

1020

24.8

10.9

4869

343

4527

1050

24.8

11.0

4869

457

4412

1080

24.7

11.1

4869

571

4298

1110

24.6

11.1

4869

571

4298

1140

24.5

11.1

4869

571

4298

1170

24.5

11.1

4869

571

4298

1200

24.4

11.1

4869

571

4298

1230

24.3

11.1

4869

571

4298

1260

24.2

11.1

4869

571

4298

1290

24.1

11.1

4869

571

4298

1320

24.0

11.1

4869

571

4298

1350

23.9

11.1

4869

571

4298

1380

23.9

11.2

4869

685

4184

1410

23.8

11.2

4869

685

4184

1440

23.7

11.2

4869

685

4184

1470

23.6

11.2

4869

685

4184

1500

23.6

11.2

4869

685

4184

1530

23.5

11.2

4869

685

4184

1560

23.4

11.2

4869

685

4184

1590

23.3

11.3

4869

800

4070

1620

23.2

11.3

4869

800

4070

1650

23.2

11.3

4869

800

4070

1680

23.1

11.3

4869

800

4070

1710

23.0

11.3

4869

800

4070

1740

23.0

11.3

4869

800

4070

1770

22.9

11.3

4869

800

4070

1800

22.8

11.4

4869

914

3955

1830

22.7

11.4

4869

914

3955

1860

22.7

11.4

4869

914

3955

1890

22.6

11.4

4869

914

3955

1920

22.6

11.4

4869

914

3955

1950

22.5

11.4

4869

914

3955

1980

22.4

11.5

4869

1028

3841

2010

22.3

11.5

4869

1028

3841

2040

22.2

11.5

4869

1028

3841

2070

22.1

11.5

4869

1028

3841

2100

22.0

11.5

4869

1028

3841

2130

21.9

11.5

4869

1028

3841

2160

21.8

11.5

4869

1028

3841

2190

21.7

11.6[‡]

4869

1142

3727

2220

21.6

11.6

4869

1142

3727

2250

21.5

11.6

4869

1142

3727

2280

21.5

11.6

4869

1142

3727

2310

21.4

11.6

4869

1142

3727

2340

21.3

11.6

4869

1142

3727

2370

21.3

11.6

4869

1142

3727

2400

21.2

11.5

4869

1142

3727

2430

21.2

11.5

4869

1142

3727

2460

21.1

11.5

4869

1142

3727

2490

21.0

11.4

4869

1142

3727

2520

20.9

11.4

4869

1142

3727

2550

20.8

11.4

4869

1142

3727

2580

20.7

11.4

4869

1142

3727


Experiment two
--------------

Measurement

Sensitivity

Average Value

Error

Metal temperature

Temperature

± 0.05°C

23.42°C

0.21%

Water temperature

Temperature

± 0.05°C

12.42°C

0.40%

Electrical Energy

Power

-

-

0.02%

Time

+ 1.00 s

1740.00 s

0.06%

Total: 0.08%

Water energy

Specific heat capacity

taken to be zero

4192.50 J kg-1 K-1

0.00%

Mass

± 0.50 g

288.00 g

0.17%

Temperature change

2 x ± 0.05°C

12.42°C

0.81%

Total: 0.98%

'True' energy

(Electrical energy - water energy)

Electrical energy

-

-

0.08%

Water energy

-

-

0.98%

Largest error: 0.98%


Experiment two
--------------

Time/s

Metal temperature/°C

Water temperature/°C

Electrical energy/J

Water energy/J

'True' energy/J

(±0.06%)

(± 0.21%)

(± 0.40%)

(± 0.08%)

(± 0.98%)

(± 0.98%)

0

13.2

11.6

0

0

0

30

14.1

11.6

1008

0

1008

60

16.3

11.7

1895

121

1774

90

18.3

11.7

2903

121

2782

120

21.5

11.7

3912

121

3791

150[§]

24.9

11.7

4920

121

4799

180

26.5

11.7

4926

121

4805

210

27.2

11.7

4926

121

4805

240

27.4

11.7

4926

121

4805

270

27.5[**]

11.7

4926

121

4805

300

27.5

11.8

4926

242

4684

330

27.4

11.8

4926

242

4684

360

27.4

11.8

4926

242

4684

390

27.3

11.8

4926

242

4684

420

27.2

11.8

4926

242

4684

450

27.1

11.8

4926

242

4684

480

27.0

11.9

4926

363

4564

510

26.9

11.9

4926

363

4564

540

26.8

11.9

4926

363

4564

570

26.8

11.9

4926

363

4564

600

26.6

11.9

4926

363

4564

630

26.5

12.0

4926

484

4443

660

26.4

12.0

4926

484

4443

690

26.3

12.0

4926

484

4443

720

26.3

12.0

4926

484

4443

750

26.2

12.0

4926

484

4443

780

26.1

12.0

4926

484

4443

810

26.0

12.0

4926

484

4443

840

25.9

12.0

4926

484

4443

870

25.8

12.0

4926

484

4443

900

25.7

12.1

4926

605

4322

930

25.6

12.1

4926

605

4322

960

25.5

12.1

4926

605

4322

990

25.5

12.1

4926

605

4322

1020

25.4

12.1

4926

605

4322

1050

25.3

12.1

4926

605

4322

1080

25.2

12.1

4926

605

4322

1110

25.1

12.1

4926

605

4322

1140

25.0

12.1

4926

605

4322

1170

25.0

12.1

4926

605

4322

1200

24.9

12.2

4926

726

4201

1230

24.8

12.2

4926

726

4201

1260

24.7

12.2

4926

726

4201

1290

24.7

12.2

4926

726

4201

1320

24.6

12.2

4926

726

4201

1350

24.5

12.2

4926

726

4201

1380

24.5

12.2

4926

726

4201

1410

24.4

12.3

4926

847

4080

1440

24.3

12.3

4926

847

4080

1470

24.2

12.3

4926

847

4080

1500

24.2

12.3

4926

847

4080

1530

24.1

12.3

4926

847

4080

1560

24.0

12.3

4926

847

4080

1590

23.9

12.4

4926

968

3959

1620

23.9

12.4

4926

968

3959

1650

23.8

12.4

4926

968

3959

1680

23.7

12.4

4926

968

3959

1710

23.7

12.4

4926

968

3959

1740

23.6

12.4

4926

968

3959

1770

23.6

12.5

4926

1089

3838

1800

23.5

12.5

4926

1089

3838

1830

23.5

12.5

4926

1089

3838

1860

23.4

12.5

4926

1089

3838

1890

23.3

12.5

4926

1089

3838

1920

23.3

12.5

4926

1089

3838

1950

23.2

12.5

4926

1089

3838

1980

23.2

12.5

4926

1089

3838

2010

23.1

12.5

4926

1089

3838

2040

23.1

12.6

4926

1210

3717

2070

23.0

12.6

4926

1210

3717

2100

22.9

12.6

4926

1210

3717

2130

22.8

12.6

4926

1210

3717

2160

22.8

12.6

4926

1210

3717

2190

22.7

12.6

4926

1210

3717

2220

22.7

12.6

4926

1210

3717

2250

22.6

12.7

4926

1331

3596

2280

22.6

12.7

4926

1331

3596

2310

22.5

12.7

4926

1331

3596

2340

22.5

12.7

4926

1331

3596

2370

22.4

12.7

4926

1331

3596

2400

22.4

12.7

4926

1331

3596

2430

22.3

12.7

4926

1331

3596

2460

22.3

12.7

4926

1331

3596

2490

22.2

12.8

4926

1452

3475

2520

22.2

12.8

4926

1452

3475

2550

22.1

12.8

4926

1452

3475

2580

22.1

12.8

4926

1452

3475

2610

22.0

12.8

4926

1452

3475

2640

22.0

12.8

4926

1452

3475

2670

21.9

12.9

4926

1572

3354

2700

21.9

12.9

4926

1572

3354

2730

21.8

12.9

4926

1572

3354

2760

21.8

12.9

4926

1572

3354

2790

21.7

12.9

4926

1572

3354

2820

21.7

12.9

4926

1572

3354

2850

21.6

12.9

4926

1572

3354

2880

21.6

12.9

4926

1572

3354

2910

21.5

12.9

4926

1572

3354

2940

21.5

12.9

4926

1572

3354

2970

21.4

13.0

4926

1693

3233

3000

21.3

13.0

4926

1693

3233

3030

21.3

13.0

4926

1693

3233

3060

21.2

13.0

4926

1693

3233

3090

21.2

13.0

4926

1693

3233

3120

21.2

13.0

4926

1693

3233

3150

21.1

13.0

4926

1693

3233

3180

21.1

13.0

4926

1693

3233

3210

21.0

13.1

4926

1814

3112

3240

20.9

13.1

4926

1814

3112

3270

20.9

13.1

4926

1814

3112

3300

20.8

13.1

4926

1814

3112

3330

20.7

13.2[††]

4926

1935

2991

3360

20.6

13.2

4926

1935

2991

3390

20.5

13.1

4926

1935

2991

3420

20.4

13.1

4926

1935

2991

3450

20.4

13.0

4926

1935

2991

3480

20.3

13.0

4926

1935

2991

Turning points/anomalies:

The first graph to follow shows how the temperature of the metal rises
during and after heating and then begins to cool. This is because the
heater is turned off and, as the copper's surroundings are colder,
heat energy is dissipated. The temperature of the copper continues to
rise after the heater has been switched off because the heater is
still giving out heat energy as the element itself cools off.
Similarly, the temperature of the water continues to rise even though
the copper is already cooling because, as the copper cools, it gives
out energy which heats the water. As seen in the graph, the copper
cools slightly faster in the first experiment. This was probably
because there was a slight difference in the efficiency of the
insulation due to a human error and thus, the cooling rate was
slightly higher. Also, it is possible that the room temperature could
have been lower producing a greater temperature difference and same
effect of faster cooling.

In the second experiment, the water started off 1°C warmer than in the
first experiment even though the copper block was at the same
temperature. This difference is insignificant because only the
temperature change is important but, nevertheless, could be attributed
to the very inaccurate temperature probes. However, there are no real
anomalies and the two experiments give such similar results that no
further repeats were needed.



Procedures adapted:
===================

In addition to what had been planned, the temperature probes were
calibrated with boiling water as described above. The inaccuracy this
exposed helps to explain some systematic errors in the procedure.
Also, because the water took so long to begin to cool, each experiment
took much longer to perform than had been expected. Because of this,
there was only enough time for two experiments to be carried out. This
is because the copper had to cool in between so that roughly the same
temperature range could be tested. In addition, much care was taken to
ensure that the insulation was suitably loose around the copper and
the beakers. Cotton wool and bubblewrap are good insulators because
they have many air pockets which have a very low heat conductivity.
This helps to significantly slow down conduction and convection
through the medium. It was made certain that the insulation was not
wrapped too tightly around the beaker with the masking tape as this
would compress the insulating materials too much and squash the air
pockets which provide such good insulating properties. Finally, extra
insulation was added to the top of the beaker because the heat loss
from the top was underestimated. This is especially important
considering that water was being heated and could evaporate and that
hot air expands and becomes less dense which causes it to rise.




Skill D

Processing:

The specific heat capacity is found from the formula ∆E = ∆Θ x c x m.
The gradients of the linear lines in the second graph give the
temperature change per joule of energy supplied (∆Θ/∆E). This is
measured in °C J-1. The inverse of the gradients is the energy per
degree centigrade of temperature change (∆E/∆Θ) measured in J °C-1.
The measurement in J °C-1 simply has to be divided by the mass of the
metal to find the specific heat capacity measured in J kg-1 °C-1.

Its percentage error is equal to the percentage error of the
temperature change plus that of the 'true' energy plus that of the
mass.

Experiment one: (2 x ± 0.21%) + (± 1.10%) + (± 0.50%)= ± 2.01%

Experiment two: (2 x ± 0.21%) + (± 0.98%) + (± 0.50%) =

The process for finding the specific heat capacity of copper is shown
below:

Experiment one: (0.0025)-1 ¸ 1.0035 = 398.60 J kg-1 °C-1 ± 2.01%

Experiment two: (0.0027)-1 ¸1.0035 = 396.07 J kg-1 °C-1 ± 1.90%

\ Average specific heat capacity: 383.84 J kg-1 °C-1 ± 1.96%

It is also possible to extrapolate the cooling of the curve back to
find the maximum temperature that would have been reached allowing for
the constant cooling of the copper and then calculate the specific
heat capacity. This is possible because the rate of cooling as the
copper is heated is proportional to the average temperature during the
linear temperature increase. By finding the rate of cooling after the
maximum temperature has been reached and using a cooling formula, it
is possible to find what the maximum temperature change would have
been if all cooling had been eliminated. Then, putting this value into
the formula ∆E = ∆Θ x c x m, the specific heat capacity, c, could have
been found. However, by its nature, this method is less accurate than
finding the gradient of the linear section as described above. This
preferential method allows for much greater precision.

Conclusion:

Is has now been found that the specific heat capacity of copper is
about 384 J kg-1 °C-1 in the range of 10°C to 30°C. However, allowing
for the ~-5°C offset of the temperature probes, this is probably
closer to the range between 15°C and 35°C. The specific heat capacity
definitely cannot be quoted to any decimal places as it already has a
~± 2.0% error due to equipment sensitivity, as well as experimental
errors. Also, because a difference of 0.001 in the gradient of the
second graph will result in a change of about ± 16 J kg-1 °C-1, a
greater degree of accuracy is misleading. According to a physics data
book, the specific heat capacity of copper is 385 J kg-1 °C-1. This is
very close to the result achieved, showing that the experiment was
very successful and that the results are particularly reliable. The
result procured from the two experiments was only 0.26% below the
recognised value for copper's specific heat capacity. Also, the R2
values for the lines of best fit are both 0.99 which is very close to
the optimum of 1.00 showing that the results are very accurate.

Qualitative discussion of limitations, errors and conclusion:

The experiment was limited by the inability to completely remove any
heat loss at all. This probably accounted for most of the errors in
the results. Even though the purpose of the distilled water was to
measure the heat loss, this is very hard with the equipment provided
and is also very imprecise. The insulation itself is heated up
slightly by the hot metal and only a small percentage of the lost
energy heats up the water. It is very hard to completely insulate the
copper block and reduce heat loss any further. Also, copper was chosen
as it has a relatively low heat capacity. This is because it is a
solid at room temperature and has a high density. The metallic copper
atoms are closely packed and, when heated, begin to vibrate
vigorously. As the atoms are so close to the neighbouring atoms, these
vibrations easily travel through the material and hence, heat is
conducted easily resulting in a low specific heat capacity. Copper has
a high heat conductivity and hence, requires little energy to raise
its temperature. Conversely, if the material has a very high specific
heat, lots of power is required which would greatly increase the rate
of heat loss and it would also take a large length of time to provide
enough energy to sufficiently heat the object, during which it will
have cooled a lot.

The inaccuracy of the temperature probes was only discovered after the
experiments had been carried out and could have contributed to any
errors in the results. However, as the data value being measured was
temperature change, assuming the temperature offset was fairly
constant over a large range, this should not have affected the results
so far as to make them unreliable.

The heating element and the conduction oil each have their own
specific heat capacity and require energy to heat up and transfer
energy into the copper block. As specific heat capacities change
slightly with temperature, more minor errors could have been included
in the calculated results. Despite this, the temperature range tested
was quite small and, as such, any effect should be negligible. In
experiments of this type, human errors in making measurements always
factor in. Also, many assumptions were made, including the current and
voltage changing regularly, no water evaporating, the block being pure
copper and that the voltmeters and ammeters were accurate as well as
sensitive.

The value achieved from the experiment was slightly lower than the
'official' specific heat capacity of copper. Because it is so hard to
measure all the heat lost, it was expected that the value achieved
from the experiment would be higher than the recognised measurement.
This is because the energy change recorded would have been higher than
the true amount of energy transferred (∆E) to the copper. Hence, as
the mass and temperature change were the same, the specific heat
capacity would be measured as being higher too (∆E = ∆Θ x c x m). The
reason why the value found from this experiment was actually lower was
probably mainly due to human error and the temperature probes. Perhaps
more importantly, the heater was not hot when it was first turned on
and needed some power to heat up the element at the beginning of each
experiment as well as having to heat the oil. In addition, there may
have been a small difference in ambient room temperature which could
have had an effect. All these small factors in combination may have
been enough to reduce the measured specific heat capacity enough so
that it was slightly lower than the recognised value.

The results are also limited due to the very low gradients of the
second graph caused by the large amount of energy that was required to
increase the temperature by a small amount. As explained above, this
meant that a small change in the gradient would affect the specific
heat capacity calculated by a quite a large amount. By using a
spreadsheet program to precisely calculate the gradient, any human
error in accurately finding the gradient was eliminated. However, as
the lines of best fit do not pass through the origin by quite a large
intercept, this indicates that there was quite a large systematic
error. Again, this is likely to have been caused by the inaccuracy of
the temperature probes. Also, there is a little deviation of points
and their error boxes from the lines of best fit as correlation is not
perfect. This is probably due to human error and the limited
sensitivities of the measuring instruments and apparatus and only has
a small effect. Taking averages helps to even out any small errors
such as these in each of the experiments.

Despite a seemingly large number of limitations to the reliability of
the conclusion, ample consideration was made for many of the errors.
The high quality of the graphs that were procured shows that the
experiment was very successful and the small difference between the
accepted value and the one calculated is evidence of this. As any
inaccuracies were minimised, the conclusion is dependable and likely
to be correct. The most was made of the equipment provided and heat
loss was controlled as well as possible, meaning that the results
achieved were the best they could be under such conditions.

Modifications:

Should the experiment be carried out again with fewer restrictions on
the apparatus allowed, greater control over the heat loss could have
been achieved. Research could be conducted into the insulating
properties of different materials to discover the best insulators. A
much better was of measuring heat loss could be developed and also,
vacuums could be utilised. A simple piece of vacuum apparatus, even
something similar to a simple Thermos flask, would be sufficient to
cut out the vast majority of heat loss. This is because conduction and
convection as modes of energy transfer require a medium and hence,
cannot occur through a vacuum. This would mean that the only heat loss
to account for would be the heating of excess air within the vacuum
container and electromagnetic infrared radiation. Even this can be
limited by the use of silvering to reflect radiation that is escaping.

Special equipment could be used to keep the power constant so that the
energy transferred can be measure more accurately. Also, the heater
and any conduction medium such as oil would be warmed up first so that
energy is not wasted heating up the element used to transfer energy
into the copper block. More accurate and more sensitive measuring
devices could be used and the tests would be carried out over exactly
the same temperature range. Also, this range would be made smaller to
reduce to possibility of changing specific heat capacities affecting
results.

Should more time be available, many more repeats could be carried out
so that the average would give even more accurate results. In
addition, the temperature probes would be calibrated before performing
the experiment to ensure they were suitably accurate and sensitive.
This combined with much more sensitive measuring instruments would
help in reducing in-built errors.

Finally, all measuring devices could be linked up to a computer which
would record all the variables and draw a graph of the results of the
experiment as it took place. This would have numerous advantages.
Firstly, any human error in making readings at certain times would be
eliminated as a computer can perform several high-level tasks
simultaneously - all the readings could be taken at precisely the same
time and recorded with no delays. All of this would be automated and
could occur at much more regular intervals, meaning that smoother
graphs could be constructed. Human intervention need not even be
required and repeats could be carried out without user commands. The
power could be constantly monitored, kept constant and any
fluctuations noted and regarded in calculations. Another advantage is
that the data could be plotted while the experiment went on meaning
that any anomalies could instantly be spotted and the appropriate
repeats be organised. Furthermore, the apparatus would not have to be
touched in between repeats so that there would be very no difference
between the conditions and no errors introduced because of humans.

How to Cite this Page

MLA Citation:
"Finding a Material's Specific Heat Capacity." 123HelpMe.com. 30 Sep 2014
    <http://www.123HelpMe.com/view.asp?id=121785>.




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