SpecificHeat Capacity                             18/01/18 Introduction: The aim of this experimentwas to determine the specific heat capacity of water and copper. Theory:Bydefinition the specific heat capacity of any substance is the energy requiredto change the temperature of 1kg of the substance by 1 Celsius  The amount of energyrequired depends on the substance as different substances have differentspecific heat capacities, as show in the table 1 below. Substance c in J/gm K c in cal/gm K or Btu/lb F Molar C J/mol K Aluminum 0.

900 0.215 24.3 Bismuth 0.123 0.0294 25.7 Copper 0.386 0.

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0923 24.5 Brass 0.380 0.092 … Gold 0.126 0.

0301 25.6 Lead 0.128 0.0305 26.4 It was only less than 400 years ago whenhumanity began to grasp the idea of specific heat capacity. Joseph Black, a chemist and lecturer at theUniversity of Glasgow during the 18th century, was the first personto hypothesise the idea of latent heat and specific heat capacity.

He realisedthat when ice is heated to melting point, there is no temperature change in themixture of water and ice, instead the volume of water in the mixture increasedwhen the temperature increased. This realisation eventually led to the theory oflatent heat, and from there to the generalization of specific heat capacity  Equation 1.0 below relates the heat addedto a substance with its specific heat capacity. Q =  Where: – –       Q is the amount of heatadded (J)-       m is the mass of thematerial (Kg)-       –       c is the specific heatcapacity () By rearranging equation 1,0, A value forspecific heat capacity can be calculated with equation 1.1, shown below.   c=  (1.1) A change of temperature (will naturally result in a change of heat energy, so equation1.1 can also be represented in the form: c =  (1.

2)Where is the change of heat energy with temperature.  As time went on, physicists dove deeperinto thermodynamics and obviously dove deeper it specific heat. During the early19th century a new law was hypothesised by two French physicists.

This law is the law of Dulong and Petit and was named after the scientists thatcreated it. This law states that the molar heat capacities for the majority ofelemental solids are around 25. This at a glance may not seem like anything out of the ordinary,however when compared with the specific heat capacities of elemental solids adistinct difference is noticed. This can be seen in table 1 above. Unlike the molarspecific heat capacities (C) the specific heat capacities (c) do not hoveraround a set value. The only difference when calculating the molar and specificheat capacities is that instead of using the mass of the material, the numberof moles multiplied by the molar mass per mole is used The total mass of a material can be givenby the number of moles (n) multiplied by the molar mass per mole (M), Shown inequation 3.0 below.  m = nM (3.

0When substituted into equation 1.0:                                                             Q= (3.1) The molar head capacity (C) is equal toMolar mass per mole (M) multiplied by the specific heat capacity(c), shown inequation 3.2 below. C = McQ = (3.2) The law of Dulong and Petit comes from adeeper analysis of the difference of expressing the specific heat of anelemental solids as energy per unit mass and as energy per mole.

The law states that the atoms in 1 moleis the same in all elemental substances. So on the atomic level, roughly thesame amount of heat is required to increase the temperature of an elementalsolid by a specific amount  Apparatus:     Diagram 1 (modelled after Figure 1, page 3 .) Equipmentused:-       Digitalthermometer                                                                                                  -Glass beaker-       Electric kettle                                                                                                                 – Copper rod-       Digital timer                                                                                                                    -Thermally insulated gloves-       Digital scales                                                                                                                   -Insulating foam                        MethodThe experiment was broken up intotwo parts. Part 1 was to determine the specific heat capacity of water and part2 was to determine he specific heat capacity of copper.  Part 1Part 1 consisted of firstly, filling the kettle with 1 litre of tapwater and recording the initial temperature of the water. The thermometer wasthen placed inside the kettle. Then the temperature changes of water during 15second intervals were recorded with the thermometer and timer, until the waterbegan to boil.

After this the Energy transferred to the kettle at each timeinterval was calculated. Agraph was then plotted with the values of energy and temperature. Finally, thespecific heat capacity of water was calculated using the gradient of the graphand the mass of the water. Part 2Part 2 consisted of firstly, replacing the water in the kettle with newtap water and recording the mass of the copper rod.

After this the copper rod wassuspended via the string inside the kettle. The kettle was then switched on.While the water was boiling a beaker was filled with 200ml of cold water andplaced on top of a block of insulating foam. When the water began to boil thecopper rod was removed and placed inside the beaker, ensuring that it did nottouch any sides of the beaker. At the same time the thermometer was placedinside the beaker, ensuring it did not touch anything but the water.

The copperrod was then removed when the temperature of the water had settled. Thistemperature is the temperature which water and copper are at thermalequilibrium.ResultsPart 1 Temperature Time (seconds) Energy (Joules) 20.0 0.00 0 31.1 15.

0 4.14 38.8 30.

0 8.28 47.6 45.0 1.

24 57.7 60.0 1.66 77.7 75.

0 2.07 90.0 90.

0 2.48 94.1 105 2.90 98.1 120 3.31 99.2 135 3.73 100.

1 150 4.14 101.1 165 4.

55 Table 2  The energy transferred to the kettle was calculated using equation 3below:Energy = Power.TimeQ = P (3.0)The power of the kettle ranged from 2520 to 3000 Joules, So an average ofthis was calculated and used to calculate the Energy values. =      = = 2760 W Agraph of the energy transferred to the kettle against the temperature was thenplotted.    Graph 1Part 2   Mass of copper rod (Kg) Initial water temperature Equilibrium temperature Heat energy(J) 0.436 21.3 21.

9 503  Table 3  The value usedfor the heat energy will be explained in the next segment of the report.       Analysis: Part 1 Energy:Theenergy at each time interval was calculated using equation 3.0. The followingis a sample calculation of the energy at 15 seconds.

                                                            Q = P                                                             Q= 2760 W. 15s                                                            Q= 41400J = 4.14JTheuncertainty in Q would be the percentage uncertainty of the power and the timeadded.Thepercentage error at 15 seconds for the time and the temperature are 0.

6% and 0.3%respectively. Thus, the percentage uncertainly in the energy at this time is .                                      Q =  4.

14J = =  4.14J                                                 Fromequation 1.1 it can be seen that the specific heat capacity if water would be thegradient of the graph divide by the mass of the water. In this experiment, thegradient of the graph would be the specific heat capacity of the tap water.

                                                                              c =               c =     (  1 litre of water was used in theexperiment and 1 litre of water is almost exactly 1 kg. The gradient of thegraph can be calculated using simple mathematics.                                                                                                                        Gradient =                                                                Gradient =                       Gradient =  4190 The reason to which why the gradient isthe specific heat capacity is since the mass is 1kg, the value of the gradientwill not change.                                                                                    c =  c =  c =  4190 The uncertainty for the specific heatcapacity is calculated similarly to how the uncertainty in the energy wascalculated. Firstly, the average energy and temperature was calculated, shownbelow.                                                                                                                               J                                                              The percentage uncertainty of the energyand temperature are  and .                                                                        c = 4190 4190                                                                                                                                                                                                                          Part 2Equation1 was used to calculate the specific heat capacity for the copper rod as well. Thereason for using 503J for the heat energy is because at the equilibrium temperatureof the water and copper ( 21.

9 the heat energy transferbetween the copper rod and the water would be constant, so the heat energy ofthe water would equal the heat energy of the copper rod and can be calculatedwith equation 1.0, shown below.                                                                                                                                                    Q(water) = 4190×0.

200×0.6                                                                               = 502.8 J = 503JAsQ water = Q copper at thermal equilibrium, the specific heat capacity can thenbe calculated using equation 1.1, shown below.                                                            c (copper) =                                                                         =1920 The uncertainty would be the sum of allthe individual percentage uncertainties.

The uncertainties in the energy, massand temperature are  respectively, thus the uncertaintyin the specific heat capacity of copper is   C = 1920            Conclusion Both experiments were successfullyfulfilled the overall aim, this being obtaining values for the specific heatcapacity of water and copper. Part 1The accepted value for the specificheat capacity of water in  is 4.186  as the experiment used kilograms on conversion it becomes . This is very close to the value calculated during thisexperiment. However, there are still a few variables that could be controlled ina better manner. The biggest source of error is that the kettle was slightly openwhen conducting the experiment. This resulted as steam being released from thekettle as it was heated.

As a result of this the mass of the tap waterdecreased by a certain amount as during the course of the experiment. This wouldalter the value obtained for the specific heat capacity. Ideally the temperature of the watershould be measured with the kettle top closed. This could be done with awireless thermometer that sends the temperature values to a computer as thewater boils, or the amount of energy that was used to cause the phase changeform tap water to steam could be calculated, this having the name latent heat.

Thislatent energy at each time interval could then be added accordingly to each calculatedenergy value. Another big source of error is humanjudgement. This experiment was meant to be carried out by 2 Individuals, A andB, but due to a constraint in numbers it was only carried out by 1 individual,C. So ideally A would look at the timer and B at the thermometer. A would notifyB every time interval. In this case, C was doing both things simultaneously,which resulted in errors in the precision of the temperature at each timeinterval. Part 2 Theaccepted specific heat capacity of copper is 0.385  when converted to kilogramsit becomes 385 .

It is obvious to see that the value obtained or the specificheat capacity of copper from this experiment is nowhere near the acceptedvalue. This gigantic difference has occurred either due to a multitude oferrors in the experiment or a calculation error. The first cause of error is the positioningof the equipment.

Ideally when the copper rod is removed from the kettle it shouldbe instantly suspended in the glass beaker. Hover during the experiment theglass beaker was positioned on at the end of the table. So during this distancethe copper rod was already being cooled. This error could be minimalized by ensuringthe beaker is positioned as close as possible to the kettle.  To conclude, the result obtained for part 1 was within the uncertaintyof the accepted value.

So it can be considered as a valid experiment, howeverthis is not to say that the experiment was conducted as well as it could havebeen. There were still a multitude of errors that could have been dealt with in a better manner. For example, ensuringthe sufficient number of individuals are conducting the experiment.On the contrary, the result obtained for part 2 is nowhere close tothe accepted value. It is difficult to identify any major experimental uncertaintiesin the experiment as it followed the method thoroughly.

So it must be acalculation error, however after calculating the values repeatedly the valuesobtained were constant. 

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