A bomb calorimeter is an instrument used to determine the heat of combustion generated when a weighed amount of fuel is burned in a controlled environment. The colorimeter device allows for a controlled ignition of a multitude of fuels whilst constantly measuring the temperature of combustion. These temperature measurements are then converted to an energy output for the fuel [3]. This experiment entails the testing of five different fuels.
AIM OF THE EXPERIMENT
The aim of the bomb calorimeter experiment is to determine the heat capacity of a specific mass of a combustible fuel and from this determine the specific heat capacity of the fuel. The five fuels that will be tested are:

Petrol
Diesel
Methylated Spirits
Paraffin
Ethanol

APPARATUS
The following apparatus are used to perform the bomb calorimeter experiment:

Calorimeter
Filling Station (Oxygen)
Oxygen
Vessel
Preparation Stand
Sartorius Balance
Firing Cotton
Combustible Fuels – Petrol (0.5g)
Diesel (0.5g)
Methylated Spirits (0.5g)
Paraffin (0.5g)
Ethanol (0.5g)
Computer to Record Results

Figure 3 Bomb Calorimeter Apparatus [2]eco group.jpg
THEORETICAL BACKGROUND
In the following section the relevant literature that pertains to this experiment will be presented.
Bomb Calorimeters
The bomb calorimeter used in the practical experiment was the CAL2K-ECO bomb calorimeter. In the past calorimeters used a mass of water to insulate the combustion vessel, the temperature increase of the water surrounding the vessel was then used to calculate the energy increase due to combustion. The following figure depicts the general layout of a water insulated bomb calorimeter.
0008n041.gif
Figure 4 Wet Bomb Calorimeter [4]
This large body of water surrounding the bomb calorimeter provides stability to the system. New advanced in calorimeter systems have lead to the development of dry isothermal calorimeter systems [3]. This new development allows for greater accuracy as changes in water volume affect the experimental results. The lack of water surrounding the colorimeter removes an experimental parameter and improves the results. The dry vessel used in this experiment utilises a conductive aluminium shell which is shrunk fit on to the vessel. Temperature sensors are then placed equally between the vessel and the conductive aluminium casing [3].
The vessel is purged and filled with oxygen at a pressure of 3 MPa, this provides an oxygen rich environment for the reaction to take place.
The calorimeter used in this experiment has the following specifications: [2]

Operating Temperature: 0 – 60ËšC
Temperature Resolution: 0.000001ËšC
Repeatability: 0-1%
Resolution: 0.001 MJ/Kg

Combustion Equations
Ethanol
When ethanol is combusted in an oxygen rich environment the following complete combustion equation is yielded:

Ethanol: C2H5OH
Oxygen: O2
Combustion Equation:
C2H5OH + 3O2 = 2CO2 + 3H2O + Heat

Diesel
When diesel is combusted in an oxygen rich environment the following complete combustion equation is yielded:

Regular Pure Diesel: C12H23
Oxygen: O2

Combustion Equation:

4C12H23+ 71O2 = 48CO2 + 46H2O + Heat

This equation represents the combustion of pure diesel which is not practical as diesel contains many additives and chemicals that will affect the combustion equation.
Petrol
When petrol is combusted in an oxygen rich environment the following complete combustion equation is yielded:

Regular Pure Petrol: C8H18
Oxygen: O2
Combustion Equation: 2C8H18+ 25O2 = 16CO2 + 18H2O + Heat

The above equation pertains to pure petrol. Petrol comes in many different forms with different octane ratings that would significantly change the chemical combustion equation.
Specific Heat Capacity
The specific heat capacity of a substance is the amount of energy that is required to raise a mass of 1 kilogram of the substance by 1ËšC or 1K. The heat capacity of a substance can be measured by the constant pressure specific heat (Cp) or the constant volume specific heat (Cv)
The constant pressure specific heat allows for the measuring of the change in enthalpy of a substance at a specific temperature change. [6]
The constant volume specific heat allows for the determination of internal energy at a constant volume over a change in temperature. [6]
For the purpose of this experiment the constant volume specific heat will be calculated although the constant pressure specific heat for uncompressible solids and liquids yields similar results. [6]
The amount of energy required to raise the temperature of a mass of a substance is calculated using the following formula:
Q = CvmΔT [6]
Where Q: Heat Added (MJ/Kg)
Cv: Constant Volume Specific Heat (KJ/Kg.K)
m: Mass of substance (Kg)
ΔT: Change in temperature (K)
Rearranging the equation for the purpose of this experiment yield the following equation with the specific heat as the subject of the formula:
METHOD
The following method was followed in order to perform the bomb calorimeter test:

The calorimeter crucible was cleaned and placed on the sartorius balance.
The balance was then zeroed in order to take into account the mass of the crucible.
Approximately 0.5g of the combustible fluid is then placed in the crucible.
The crucible with the combustible fluid is then weighed on the balance and the mass of the fluid recorded.
The mass of the fluid is then entered in to the calorimeter.
The crucible was then placed on the setup station where the crucible is fitted with firing cotton and the firing wire.
This setup is placed in the vessel where it is then filled with 3 MPa’s of pure oxygen.
The vessel was then placed in the calorimeter and the testing sequence was initiated.
After the test was completed the results were recorded into an excel file automatically by the calorimeter.

RESULTS
Petrol
On the 12th of April 2010 petrol of 0.58g was placed into the bomb calorimeter and the following results were produced:

Table Calorimeter Results for Petrol
Parameter
Value
Mass of Sample
0.58g
Minimum Temperature
22.3011ËšC
Maximum Temperature
38.98523ËšC
Change in Temperature (Max. Temp – Min. Temp)
16.68413ËšC
Specific Energy Released
37.0041 MJ/Kg

Figure 6 Graph Representing Sample Temperature vs. Time for Petrol
Using the results obtained from the bomb calorimeter a table was generated in order to calculate the heat capacity as well as the specific heat capacity of the fluid sample. The following table presents the results:

Table Theoretical Calculations for Petrol
Parameter
Formula
Value
Change in temperature (ΔT)
ΔT = Max. Temp – Min. Temp
16.68413ËšC
Specific Energy Released (U)
From Data
37.0041 MJ/Kg
Mass of sample (m)
Recorded in experiment
0.58g = 0.00058Kg
Specific Heat Capacity (Cv)
Cv = U/ΔT
2.217922 KJ/Kg.K
Heat Capacity (Cv.m)
Cv.m = (U.m)/ΔT
1.286395 J/K

From the table above the bomb calorimeter for 0.58 grams of petrol yielded the following results:
Specific Heat Capacity: 2.217922 KJ/Kg.K
Heat Capacity (0.58g Petrol): 1.286395 J/K
Diesel
On the 12th of April 2010 diesel of 0.5269g was placed into the bomb calorimeter and the following results were produced:

Table Calorimeter Results for Diesel
Parameter
Value
Mass of Sample
0.5269g
Minimum Temperature
25.84436ËšC
Maximum Temperature
44.15795ËšC
Change in Temperature (Max. Temp – Min. Temp)
18.31359ËšC
Specific Energy Released
43.4423 MJ/Kg

Figure 6Graph Representing Sample Temperature vs. Time for Diesel
Using the results obtained from the bomb calorimeter a table was generated in order to calculate the heat capacity as well as the specific heat capacity of the fluid sample. The following table presents the results:

Table Theoretical Calculations for Diesel
Parameter
Formula
Value
Change in temperature (ΔT)
ΔT = Max. Temp – Min. Temp
18.31359ËšC
Specific Energy Released (U)
From Data
43.4423 MJ/Kg
Mass of sample (m)
Recorded in experiment
0.5269g = 0.0005269Kg
Specific Heat Capacity (Cv)
Cv = U/ΔT
2.372135 KJ/Kg.K
Heat Capacity (Cv.m)
Cv.m = (U.m)/ΔT
1.249878 J/K

From the table above the bomb calorimeter for 0.5269 grams of diesel yielded the following results:

Specific Heat Capacity: 2.372135 KJ/Kg.K
Heat Capacity (0.5269g Diesel): 1.249878 J/K

Methylated Spirits
On the 15th of April 2010 methylated spirits of 0.5865g was placed into the bomb calorimeter and the following results were produced:

Table Calorimeter Results for Methylated Spirits
Parameter
Value
Mass of Sample
0.5865g
Minimum Temperature
23.59523ËšC
Maximum Temperature
36.40363ËšC
Change in Temperature (Max. Temp – Min. Temp)
12.8084ËšC
Specific Energy Released
27.8794 MJ/Kg

Figure 6 Graph Representing Sample Temperature vs. Time for Methylated Spirits
Using the results obtained from the bomb calorimeter a table was generated in order to calculate the heat capacity as well as the specific heat capacity of the fluid sample. The following table presents the results:

Table Theoretical Calculations for Methylated Spirits
Parameter
Formula
Value
Change in temperature (ΔT)
ΔT = Max. Temp – Min. Temp
12.8084ËšC
Specific Energy Released (U)
From Data
27.8794 MJ/Kg
Mass of sample (m)
Recorded in experiment
0.5865g = 0.0005865Kg
Specific Heat Capacity (Cv)
Cv = U/ΔT
2.17665 KJ/Kg.K
Heat Capacity (Cv.m)
Cv.m = (U.m)/ΔT
1.276605 J/K

From the table above the bomb calorimeter for 0.5865 grams of methylated spirits yielded the following results:
Specific Heat Capacity: 2.17665 KJ/Kg.K
Heat Capacity (0.5865g Methylated Spirits): 1.276605 J/K
Paraffin
On the 16th of April 2010 paraffin of 0.5262g was placed into the bomb calorimeter and the following results were produced:

Table Calorimeter Results for Paraffin
Parameter
Value
Mass of Sample
0.5262g
Minimum Temperature
23.47467ËšC
Maximum Temperature
42.94966ËšC
Change in Temperature (Max. Temp – Min. Temp)
19.47499ËšC
Specific Energy Released
46.2688 MJ/Kg

Figure 6 Graph Representing Sample Temperature vs. Time for Paraffin
Using the results obtained from the bomb calorimeter a table was generated in order to calculate the heat capacity as well as the specific heat capacity of the fluid sample. The following table presents the results:

Table Theoretical Calculations for Paraffin
Parameter
Formula
Value
Change in temperature (ΔT)
ΔT = Max. Temp – Min. Temp
19.47499ËšC
Specific Energy Released (U)
From Data
46.2688 MJ/Kg
Mass of sample (m)
Recorded in experiment
0.5262g = 0.0005262Kg
Specific Heat Capacity (Cv)
Cv = U/ΔT
2.375806 KJ/Kg.K
Heat Capacity (Cv.m)
Cv.m = (U.m)/ΔT
1.250149 J/K

From the table above the bomb calorimeter for 0.5262 grams of paraffin yielded the following results:
Specific Heat Capacity: 2.375806 KJ/Kg.K
Heat Capacity (0.5262g Paraffin): 1.250149 J/K
Ethanol
On the 19th of April 2010 ethanol of 0.5204g was placed into the bomb calorimeter and the following results were produced:

Table Calorimeter Results for Ethanol
Parameter
Value
Mass of Sample
0.5204g
Minimum Temperature
21.69235ËšC
Maximum Temperature
40.87241ËšC
Change in Temperature (Max. Temp – Min. Temp)
19.18006ËšC
Specific Energy Released
45.5869 MJ/Kg

Figure 6 Graph Representing Sample Temperature vs. Time for Ethanol
Using the results obtained from the bomb calorimeter a table was generated in order to calculate the heat capacity as well as the specific heat capacity of the fluid sample. The following table presents the results:

Table Theoretical Calculations for Ethanol
Parameter
Formula
Value
Change in temperature (ΔT)
ΔT = Max. Temp – Min. Temp
19.18006ËšC
Specific Energy Released (U)
From Data
45.5869 MJ/Kg
Mass of sample (m)
Recorded in experiment
0.5204g = 0.0005204Kg
Specific Heat Capacity (Cv)
Cv = U/ΔT
2.376786 KJ/Kg.K
Heat Capacity (Cv.m)
Cv.m = (U.m)/ΔT
1.236879 J/K

From the table above the bomb calorimeter for 0.5204 grams of ethanol yielded the following results:
Specific Heat Capacity: 2.376786 KJ/Kg.K
Heat Capacity (0.5204g Ethanol): 1.236879 J/K
DISCUSSION OF RESULTS
The results from the bomb calorimeter were collated into a table and compared to theoretical results. The calorimeter results and the theoretical results were then compared and a percentage error calculated.
Table Comparisons of Calorimeter Results and Theoretical Results [1]

Fuel
Specific Heat Capacity (Calorimeter)
Specific Heat Capacity (Theory)
Percentage Difference (%)
Petrol
2.217922 KJ/Kg.K
2.22 KJ/Kg.K
0.093604
Diesel
2.372135 KJ/Kg.K
2.01 KJ/Kg.K
18.0167
Methylated Spirits
2.176650 KJ/Kg.K
2.40 KJ/Kg.K
9.30625
Paraffin
2.375806 KJ/Kg.K
2.13 KJ/Kg.K
11.5402
Ethanol
2.376786 KJ/Kg.K
2.30 KJ/Kg.K
3.33852

The specific heat calculated for petrol using the bomb calorimeter yielded a resultant specific heat of 2.217922KJ/Kg.K, this was compared to the theoretical value of 2.22KJ/Kg.K. The percentage difference between theoretical and practical results was only 0.094% and the result can therefore be regarded as relatively accurate.
The percentage difference between theoretical values and practical values for ethanol yielded a difference of 3.34%. This difference in calculated specific heat is possibly due to the theoretical value being taken at an ambient temperature of 20ËšC whilst the calorimeter value was taken at 21.69ËšC. The error calculated for ethanol is in the acceptable range.
The specific heats calculated for the other three samples (Diesel, Methylated Spirits, Paraffin) all yielded large experimental errors. The large errors produced may be due to the mass of sample used and measured. Once the samples were decanted into the crucible they began evaporating. Once the mass of the sample was measured it still needed a fuse added to the sample and the sample needed to be placed into the vessel. This reduced the mass of the sample and may have given an inaccurate result.

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CONCLUSION
From the results obtained from the bomb calorimeter practical the results were comparable to those from other literature sources. The percentage error for two of the five tests yielded accurate results where as the other three test showed an error ranging from 9 – 18%. This error was justified by experimental errors from the mass entered into the bomb calorimeter as well as differences in atmospheric temperature between the practical results and the results in the relevant literature researched.
 
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