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Faculty of ACES Department of Engineering and Mathematics Mechanical Engineering Laboratory (Sheaf – 4028)

Measurement of the Specific Heat Capacity of a Metal Specimen

Sheffield Hallam University

Department of Engineering and Mathematics

For the attention of: Andrew Garrard

Report author: James Lennard

Report author ID: 24016334

Module name & code: Engineering Principles 16-4019-00S-A-20145

Course name: Materials Engineering

Date: 01.12.14

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Abstract This report has been produced to calculate the specific heat capacity of a set of specimens of unknown materials in order to determine their compositions.

Each specimen was heated to close to the boiling point of water before being transferred to a calorimeter containing water at room temperature. By measuring the change in temperature of the metal and of the water in the calorimeter, the specific heat capacity was determined because the masses of the specimens and water were known.

Once the specific heat capacity for each specimen had been calculated, the materials of them were determined by comparing the calculated results to multiple sources listing the true values of specific heat capacity for a range of known materials. Selecting materials with true values of specific heat capacity close to the results obtained allowed for the materials to be identified.

Some of the data obtained was very accurate, with only a 9.9% difference between the calculated and actual value for specific heat capacity, and some of the data had many errors affecting the results and therefore with lower reliability. The largest percentage difference was found to be 43.5%.

The materials of the specimens were determined to be Lead, Copper and Aluminium, and so the aims of the experiment (to identify the materials using specific heat capacity) were met.

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Nomenclature

Ms = Mass of the specimen

Mc = Mass of the calorimeter (when empty, inclusive of mass of stirrer and lid)

Mw = Mass of water (at initial temperature)

Cps = Specific heat capacity of specimen

Cpw = Specific heat capacity of water

Tis = Initial temperature of specimen

Tiw = Initial temperature of water

Tfs = Final temperature of specimen

Tfw = Final temperature of water

SHC = specific heat capacity

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1.Contents

Abstract 2 ........................................................................................................................

Nomenclature 3 ..............................................................................................................

1. Introduction 5 .............................................................................................................

2. Background Theory 5 ................................................................................................

3. Procedure 6 ...............................................................................................................

4. Results 8 ...................................................................................................................

5. Discussion 10 ............................................................................................................

6. Conclusions 15 ..........................................................................................................

7 References 16.........................................................................................................

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2.

1. Introduction The specific heat capacity, cp of a material is the amount of heat energy required to heat one kilogram of that material by 1ºC or 1K. It is a physical property that varies from one material to another.

A calorimeter is a container, usually well insulated, which allows measurement of temperature changes of its contents to be measured. If a hot specimen is placed in cooler water inside a calorimeter, the temperature of the specimen will fall, while that of the water will rise as the heat energy is transferred from one to the other. If there are no heat losses from the calorimeter, the temperature of the system will reach equilibrium i.e. the temperature of the specimen, water and calorimeter will be the same.

1.1 Aim of the Experiment

To measure the specific heat capacity of a metal sample using a calorimeter.

2. Background Theory

If the heat losses from the calorimeter are small, this heat transfer can be expressed as:

Heat energy lost by the specimen = Heat energy gained by the water.

Or

mscps (Tinitial specimen - Tfinal specimen) = mwcpw (Tfinal water - Tinitial water)……(1)

where = mass of specimen (kg) = mass of calorimeter (kg) = mass of water in the calorimeter (kg) cps = specific heat capacity of specimen (J kg-1 K-1) cpw = specific heat capacity of water (J kg-1 K-1)

= initial temperature of the specimen ºC = final temperature of the specimen ºC = initial temperature of the water ºC = final temperature of the water ºC

and equation (1) becomes = mscps△Ts = mwcpw△Tw……(2)

where △Ts = (Tinitial specimen - Tfinal specimen) and △Tw = (Tfinal water - Tinitial water)

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3. Procedure To begin with, a table was produced so that all results could be recorded clearly and easily. The mass, specific heat capacity and initial and final temperatures of the specimens and the water were recorded, in addition to the mass of the calorimeter. An example of the table produced is given below (Table 1):

Once the table was produced, a heater was used to heat a beaker of deionised water to the boiling point (100°C), as shown in Figure 1. Deionised water was used to ensure that the value for the specific heat capacity of water used in later calculations was accurate, so to minimise any associated errors. The first metal specimen was randomly selected, weighed using an electronic balance and then placed in the beaker until it reached the same temperature as the water, identified using the digital temperature probe, again shown in Figure 1. This took around ten minutes. The maximum temperature of the specimen was recorded in Table 1 as its “initial temperature”. The mass of the specimen was also recorded appropriately. The balance had a precision of 1g, and therefore an error of ±0.5g, and the temperature probe had a precision of 0.1°C and a resulting error of ±0.05°C*.

Whilst the submerged metal specimen was being heated, the calorimeter was placed on the balance and weighed (when empty); including the mass of its lid and stirrer. Its mass was recorded.

After the calorimeter’s mass had been determined, the lid was removed and it was half filled with room temperature, deionised water, before replacing the lid and weighing it again. The difference between the original and the new mass was found, to give the mass of water added. The mass of water was recorded, and the temperature probe was used to determine its initial temperature. Both of these values were suitably recorded.

Upon completion of adding the water to the calorimeter, the first metal specimen was now sufficiently heated and was quickly yet carefully transferred from the beaker to the calorimeter using the hooked, metal rod (once its initial temperature had been measured and noted). This stage had to be performed fast so

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Specimen Ms (kg)

Mc (kg)

Mw (kg) Cps (Jkg-1K-1)

Cpw (Jkg-1K-1)

Tis (K) Tfs (K) Tiw (K) Tfw (K)

1

2

3

Table 1

Figure 1: the digital temperature probe (left) and heated beaker containing the metal specimens (right).

that the specimen did not dissipate large quantities of heat energy to its surroundings, yet carefully so as to not damage the interior of the fragile calorimeter. When the specimen was fully inserted, the hook was removed; and the lid, stirrer and thermometer probe quickly replaced, in order to minimise heat losses and to detect the temperature change in the water. Again, this part of the procedure had to be fast because there was a large volume of water surrounding the comparatively small metal specimen, meaning that it would cool quickly, and only a small temperature change would take place. The maximum, steady temperature of the water was recorded in the table as “final temperature”. This value is the same for the final temperature of the metal specimen, as the temperatures of the specimen and water approach each other until they reach the same value, and at which point are said to be in ‘thermal equilibrium’ (Liddle and Loveday, 2008). These values were both recorded in the table.

The procedure was then complete for the first metal specimen. Equation 2 was rearranged in order to determine the specific heat capacity of the specimen, which can then be compared to a database of metals and their respective specific heat capacities in order to determine their composition.

Equation 2:

mscps△Ts = mwcpw△Tw

when rearranged, Equation 3 is derived to determine the specific heat capacity of the metal:

Cps = (mwcpwΔTw)/(msΔTs) (Equation 3)

The procedure was then repeated using a different specimen of the same composition in order to further increase the reliability of the data, before reporting the procedure for the two remaining specimens of differing compositions.

*Temperatures were measured in °C, but recorded in K for proper scientific practise.

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4. Results For each material composition, two specimens were available, that were similar in appearance and apparent density. They were assumed to be made of the same material, and so the procedure was conducted for each, and the data was recorded in the table according to either the first or second specimen, labelled “specimen a” and “specimen b” respectively.

Physical Quantities

Specific heat capacity of water = 4187Jkg-1K-1

Example Calculations - Specimen 1a

1K = 1°C + 273.15

Cps = (mwcpwΔTw)/msΔTs ΔTw = 294.95K - 292.75 = 2.2K Ts = 294.95K - 373.15K = 78.2K Cps = (0.1kg x 4187Jkg-1K-1 x 2.2K) / (0.099 x 78.2K) = 118.983Jkg-1K-1

From the data recorded in Table 2, values for specific heat capacity for each material (specimens 1, 2 and 3) were calculated in. These calculated values were then compared to known values of specific heat capacities for a range of materials, in order to help identify the materials involved. Although the masses of the specimens varied for each material, the values for the specific heat capacity should be approximately the same, as these values are material properties and are extensive - meaning that the values can be scaled up or scaled down accordingly to the amount of mass involved (Valencia and Quested, 2009).

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Specimen Ms (kg)

Mc (kg)

Mw (kg) Cps (Jkg-1K-1)

Cpw (Jkg-1K-1)

Tis (K) Tfs (K) Tiw (K) Tfw (K)

1a 0.099 0.965 0.100 118.983 4187.000 373.150 294.950 292.750 294.950

1b 0.105 0.965 0.100 116.196 4187.000 372.750 297.250 295.050 297.250

2a 0.085 0.965 0.100 217.506 4187.000 373.150 296.150 292.750 296.150

2b 0.054 0.965 0.100 336.660 4187.000 372.350 298.650 295.450 298.650

3a 0.029 0.965 0.100 754.798 4187.000 372.950 298.350 294.450 298.350

3b 0.030 0.965 0.100 724.526 4187.000 373.050 299.850 296.050 299.850

Table 2

1a 1b 3a2b2a 3b

Figure 2 - the specimens used.

Example Calculation of Percentage Difference

% difference = (△SHC / Original Value) x 100

= ((129Jkg-1K-1 - 119Jkg-1K-1) / 129Jkg-1K-1) x 100 = 7.765% = 7.8%

Specimen Calculated SHC (Jkg-1K-1)

Proposed Material

Actual SHC[1]

(Jkg-1K-1)

Actual SHC[2]

(Jkg-1K-1)

△% (Calculated and Actual[1])

△% (Calculated and Actual[2])

1a 118.983 Lead 129.000 128.000 7.765 7.045

1b 116.196 Lead 129.000 128.000 9.926 9.222

2a 217.506 Copper 385.000 385.000 43.504 43.504

2b 336.660 Copper 385.000 385.000 12.556 12.556

3a 754.798 Aluminium 897.000 900.000 15.853 16.134

3b 724.526 Aluminium 897.000 900.000 19.228 19.495

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1 - Actual values taken from Engineering Toolbox

2 - Actual Values taken from GSU

Table 3

5. Discussion

Following the procedure and conducting the experiments described allowed for the specific heat capacity of the materials to be calculated, in order to determine the material that was used. Materials have unique values for specific heat capacity, so once the specific heat capacity has been calculated, the value can be compared to those of known materials. Specific heat capacity is the amount of energy (in Joules) required to raise the temperature of 1kg of substance by 1K or 1ºC. The higher the specific heat capacity value, the more energy is required in order to raise its temperature.

The specific heat capacity in the experiment was determined by using a known mass of water, with a specific heat capacity of 4187Jkg-1K-1, and placing a heated specimen within it and measuring the temperature change. This is possible because of the fact that the specimen and water are in direct contact with each other - and the laws of thermodynamics govern that the two are in equilibrium and so will both approach the same temperature.

Ultimately, the metal will cool from its initial temperature to its final temperature as heat is transferred to the water surrounding it, and vice versa the water will be heated slightly from its original temperature to its final temperature as heat is transferred into it. This slight increase in temperature of the water and significant decrease in temperature of the specimens can be explained by water’s ability to receive lots of heat energy and hardly be affected (because of its high specific heat capacity). The final temperature of the water is the final temperature of the metal specimen. By measuring these factors, the metal’s specific heat capacity was obtained and compared to various tables from a multiple sources in order to determine its composition. The materials were identified as shown below, and this data is summarised in Table 3.

Identifying the Material Composition of Specimen 1

Specimen 1a and 1b were calculated to have similar values for specific heat capacity.

1a = 119.0Jkg-1K-1, and 1b = 116.2Jkg-1K-1.

According to Engineering Toolbox’s “list of specific heat capacities for common substances”, the specific heat capacity for Lead is 129.0Jkg-1K-1, and according to Georgia State University’s HyperPhysics website, this value is 128.0Jkg-1K-1 (Tipler, 1999). These values seem reasonable and are are within experimental error of the values obtained for specimen 1 in Table 1. The value for specific heat capacity for Gold is closer to the calculated values for specimen 1, with GSU stating its value to be 126Jkg-1K-1, however the test pieces were dull-grey in colour, whereas Gold is typically golden in colour with a shiny surface finish meaning that it can be ruled out as a possible candidate for its material.

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If the material for specimen 1 is Lead, then the specific heat capacity of specimen 1a is 7.8% lower than the value obtained from Engineering Toolbox, and 7.0% lower than that obtained from GSU.

Specimen 1b is 9.9% lower than the value obtained from Engineering Toolbox and 9.2% lower than the value taken from GSU.

Values for both specimens 1a and 1b are have similar percentage differences to the actual values, meaning that it is a good assumption to state that specimen 1 is Lead.

Identifying the Material Composition of Specimen 2

Specimen 2a and 2b were calculated to give very different values for specific heat capacity:

2a = 217.5Jkg-1K-1, and 2b = 336.7Jkg-1K-1.

These values are far apart, and this could be caused by the fact that the masses of specimen 2a and 2b were 31g different, meaning that it is impossible to tell which value is the most accurate to use. Specimen 2a’s calculated value for specific heat capacity is not dissimilar to that of Silver according to both Engineering Toolbox and GSU (235.0Jkg-1K-1 and 236.0Jkg-1K-1 respectively). Assuming that specimen 2a is in fact Silver, the calculated value is 7.4% lower than the value from Engineering Toolbox and 7.8% lower than the value for specific heat capacity according to GSU. Silver however is silver in colour and is an “incredibly lustrous metal” (Theodore Gray, 2012), whereas the specimen was brown in colour and relatively dull.

More likely however, specimen 2a is made of Copper (based on appearance only), with a specific heat capacity value of around 385.0Jkg-1K-1 (according to the Engineering Toolbox and GSU). If the material was Copper, the calculated value differed from the actual value by 43.5%, which is a huge percentage difference. If the specimen is made of Copper, then huge errors were involved in the procedure in order to bring about such a large difference.

Specimen 2b had a very similar appearance to specimen 2a; and the two had similar apparent densities (2b was around half the size of 2a, and had roughly half the mass) and so the two were assumed to be the same material. There doesn't appear to be any anomalous results shown in Table 2 in terms of temperature changes which could explain the huge difference in calculated values between specimen 2a and 2b. If, like 2a, specimen 2b is assumed to be Copper, then the calculated value for specific heat capacity differs from the actual value by 12.6% - which is a more reasonable difference when taking into account experimental errors.

Identifying the Material Composition of Specimen 3

Specimen 3a and 3b were calculated to have very similar values of specific heat capacity.

3a = 754.8Jkg-1K-1, and 3b = 724.5Jkg-1K-1. � of �11 18

The fact that these results are close together indicates some accuracy in the procedure and means that the data is reliable to a certain degree. Specimens 3(a and b) were silver in appearance, and had bright, shiny surfaces. 3a could be Titanium - whose specific heat capacity is 523Jkg-1K-1, resulting in a percentage difference of 30.7%.

However, specimen 3a could also be Aluminium - with an actual specific heat capacity between 897Jkg-1K-1 (Engineering Toolbox) and 900Jkg-1K-1 (GSU). Supposing specimen 3a is Aluminium, there is a percentage difference between the actual value taken from Engineering Toolbox and the calculated value of specific heat capacity of 15.9%, which is more accurate than supposing the specimen is made of Titanium. The percentage difference between the calculated value and the actual value taken from GSU is 16.1%. This further supports the idea that the material is Aluminium. Without comparing the specific heat capacities, it is difficult to identify Titanium and Aluminium as they are both lightweight and silver in colour.

Similarly, specimen 3b can be assumed to be Aluminium, however there would be a larger percentage difference than specimen 3a if this was true. There is a 19.2% difference between the calculated specific heat capacity and the value obtained from Engineering Toolbox, and a 19.5% difference between the calculated value and the actual value taken from GSU.

Sources of Error

There are many sources of error that could have affected the results and therefore increase the uncertainty of this particular experiment. To begin with, the measuring equipment will be discussed.

When recording the mass of the specimens, calorimeter, beaker and water, an electronic balance was used. The balance had a precision of 1g, meaning that it could not produce any smaller readings than this figure. For example, a mass of 1.49g will have been displayed as 1g, and a mass of 1.5g will have been displayed as 2g, despite a marginal difference between the two. The uncertainty associated is therefore ±0.5g - meaning that every value recorded using this equipment could be an additional 0.5g or smaller by 0.5g. In order to calculate the specific heat capacity for each specimen, several values of mass were used, all with an uncertainty of 0.5g. The largest possible percentage error for the balance is given by :

(limit of accuracy/largest measurement taken) x 100

The largest specimen mass recorded using the balance (and therefore associated with this error) was 105g. The largest value of error associated with the specimen masses is therefore

(0.5g/105g x 100) = 0.48%.

The actual value for mass could be 104.5g or 105.5g.

The digital thermometer also had an error associated with it. The maximum precision it could produce was 0.1ºC or 0.1K. Similarly to the balance, the actual values for

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temperature could be bigger or smaller than the equipment could show, with an uncertainty of 0.05ºC.

As a maximum percentage, this error is:

(0.05/100 x 100) = 0.05%.

The actual value for temperature could be 100.05ºC or 99.95ºC.

The effects of these errors on the masses and temperatures and resulting specific heat capacities are shown in Table 4.

Maximum Cps = (maxmwcpwmaxΔTw)/minmsminΔTs Minimum Cps = (minmwcpwminΔTw)/maxmsmaxΔTs

Other factors could have further affected the results of the investigation. A large source of error will have been caused by heat losses that are unaccounted for in the equations and data. For example, the stirrer that was used to stir the hot contents of the calorimeter was used for every repeat experiment - without having time to cool fully. This would mean that extra heat is transferred to the next system, and that heat was taken away from the previous system. The net effect of this is that one experiment would cool quickly and to a lower temperature and one experiment would show a slower rate of cooling and a slightly higher end temperature.

In addition to this, heat would have also been lost to the environment, through the stirring rod and the metal hook (used to transport the specimens), and through the hole in the lid of the calorimeter. The stirrer and hook were made of metal and were therefore conductive - meaning that heat will have transferred from the hot water in the calorimeter, through the stirring rod/hook and then to the environment. The hole in the calorimeter would have allowed for hot air (heated by the water in the calorimeter) to escape to the atmosphere by convection - again causing losses to occur.

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Specimen Ms (g) Mw (g) Tis (K) Tfs (K) Tiw (K) Tfw (K) Minimum Cps (Jkg-1K-1)

Maximum Cps (Jkg-1K-1)

1a 99.00 ±0.50

100.00 ±0.50

373.15 ±0.05

294.95 ±0.05

292.75 ±0.05

294.95 ±0.05

112.30 125.81

1b 105.00 ±0.50

100.00 ±0.50

372.75 ±0.05

297.25 ±0.05

295.05 ±0.05

297.25 ±0.05

109.69 122.88

2a 85.00 ±0.50

100.00 ±0.50

373.15 ±0.05

296.15 ±0.05

292.75 ±0.05

296.15 ±0.05

208.55 226.65

2b 54.00 ±0.50

100.00 ±0.50

372.35 ±0.05

298.65 ±0.05

295.45 ±0.05

298.65 ±0.05

321.10 352.66

3a 29.00 ±0.50

100.00 ±0.50

372.95 ±0.05

298.35 ±0.05

294.45 ±0.05

298.35 ±0.05

718.40 852.19

3b 30.00 ±0.50

100.00 ±0.50

373.05 ±0.05

299.85±0.05

296.05 ±0.05

299.85 ±0.05

689.48 761.02

Table 4

Mass was also affected by uncertainties. The first instance in the procedure where a change in mass could have been influenced was the excess water left behind inside the calorimeter between readings. This residual water could have been stuck to the interior of the calorimeter because of the cohesion of water, and the extra mass may not have been detected by the balance because of the 1g precision. To minimise this effect during the experiment, the calorimeter was inverted and shook vigorously three times between investigations of each specimen.

In a similar fashion, excess water (used to heat the metals) may have remained on the specimens as they were transferred to the calorimeter - again increasing the mass of the system without detection. When combined, the total effect of extra mass may have altered the results to appear as though the metal specimens had a slightly lower specific heat capacity than they actually have - as there would have been more water within the calorimeter to dissipate heat energy stored within the metals.

Large Scale Applications of Specific Heat Capacity

Specific heat capacity is of vast importance when considering material selection, and thus the results show that data obtained experimentally can be modelled and extrapolated into real world situations.

The results of this investigation show the variation in specific heat capacity between several metals. The data shows that for Lead, this value is relatively small, meaning that only a small amount of energy (around 118J) is required to raise its temperature by 1ºC. By observing this result, it is obvious that Lead is not suitable for applications such as heat proof combustion engine linings etc., in which the system is exposed to high temperatures. These temperatures would easily deform the Lead and potentially destroy the engine.

In addition to this, these data help show the most suitable materials for certain applications - for example water. Water has a comparatively high specific heat capacity (4187Jkg-1K-1), meaning that lots of energy is needed in order for the temperature rise significantly and ultimately for the system to get hot. Because of this property of water, it makes a suitable coolant in industry, such as water cooled power stations, computer systems and resistors - as lots of energy can be transferred to it before it begins to get hot (Smith and Kim, 2001).

Processing data of this kind allows for engineers to model materials in certain applications under certain environments in order to test their suitability for a particular role.

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6. Conclusions The aims of the investigation were to identify the specific heat capacities of unknown metal specimens in order to determine the metals involved. Conducting the experiment allowed for the metals to be identified to a good level of accuracy and confidence, and so the aims of the experiment were met.

By analysing the data obtained, the three different specimen materials were identified as Lead, Copper and Aluminium. The largest percentage difference between the specific heat capacity of the supposed Lead specimen and the true value was 9.9%, giving a large confidence in the assumption. The largest percentage difference for the apparent Copper specimen and its true value was found to be 43.5% - which is a huge difference. The final specimen analysed was assumed to be Aluminium - and the largest difference between obtained and actual specific heat capacities was 19.5%.

The least amount of confidence in the results was associated with specimens 2a and 2b, which were assumed to be the same material; yet had a difference in specific heat capacities of 119.2Jkg-1K-1. By drawing comparisons from multiple sources, the two specimens could have both been the same material, which seems likely due to the same physical appearances. Error s associated with mass could have resulted in the large differences in specific heat capacity, as the two specimens also differed by 31g.

In conclusion, the data alone provided some relatively reliable information that resulted in accurate assumptions of the materials involved. The procedure was found to have several associated errors however, and therefore the information was found to have substantial errors. Other information, such as colour and physical appearance noted during the investigation helped to support ideas and suggestions raised by the collected data, e.g. specimen 2 had a similar specific heat capacity to that of Silver - however its brown colour eliminated this possibility. Repeating the procedure with a larger number of specimens made of each material would have helped reduce uncertainties and increase the accuracy of this experiment.

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7 References

1 - Liddle, Andrew and Loveday, Jon, Oxford University Press, The Oxford Companion to Cosmology

2 - Valenica, J.J. and Quested, P.N., ASM International, Metals Process Simulation: Thermophysical Properties vol. 22B p.18-32

3 - The Engineering Toolbox, specific heat capacity of some common substances, 2009, http://www.engineeringtoolbox.com/specific-heat-capacity-d_391.html

4 - Tipler, Paul, Freeman, Physics for Scientists and Engineers, 4th Ed, http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html

5 - Gray, Theodore, Black Dog, The Elements: a visual exploration of every element in the Universe, p.Ag - Silver

6 - Smith, Robin and Kim, Jin-Kuk, Chemical Engineering Science: Cooling water system design, p.3641-3658

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Assessment Grid

The Assessment Grid shows how you will be awarded marks for the respective sections of the report.

(Please add the Assessment Grid to your report at the end)

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Final Marks Sheet

You will be awarded marks for this lab according to the following scheme.

(Please add this page to your report at the end)

________________________________________________________

Lab Book (10%)

Recording of work, engagement in the task, punctuality - /10 (0 or 5 or 10 marks will be recorded by tutor according to their personal judgement) _______________________________________________________

Report

Introduction / Objectives / Theory (20%) - ( N o Mark) (This has been written for you. Please include the given text)

Procedure (10%) - /10

Results (20%) - /20

Discussion and Conclusions (30%) - /30

Presentation (20%) - /20 (Including Abstract, Nomenclature, Contents page, References and correct use of English) ________________________________________________________

Total - /90

Percentage Mark - % ________________________________________________________

Note: The final mark, awarded out of a total of 90 (as above), is converted to a percentage mark for the write-up Lab. The % mark will appear under My Grades for this lab report.

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