• Measure the heat of combustion of Biofuels per unit mass or per unit mole, in oxygen using the Bomb Calorimeter.
• Understand the differences in the heat of combustion between different fuels (including oxygenated fuels such as alcohol).
• Understand the effect of incomplete combustion on the heat of combustion.

Heat of combustion is a very important parameter in choosing fuels for vehicles from transportation to rocket propulsion. A higher heat of combustion usually implies higher engine efficiency and propulsion performance.

Heat of combustion depends on the thermodynamic process and the final combustion products. There are two different ways to define the heat of combustion depending on whether the combustion process occurs at constant volume (e.g. gasoline engine) or at constant pressure (e.g. gas turbine engine). For constant volume combustion, if the initial temperature is the same as the final temperature, the change of internal energy will be converted to thermal energy: the heat of combustion at constant volume

Equation 1

Here Q is the total heat and U the total internal energy, and R and p indicate the initial reactants and the final products respectively. Similarly, for constant pressure combustion with the same initial and final temperatures, the change of enthalpy will be converted to thermal energy: the heat of combustion at constant pressure

Equation 2

Here H is the total enthalpy, H = U + pV, P is the pressure, and V is the total volume. Therefore, from above definition, the difference in the heat of combustion between the constant pressure and the constant volume combustion is

Equation 3

Here n is the total mole number, T is the gas temperature, and R is the gas constant.

Let us consider the constant volume combustion of one mole of hydrocarbon fuel in oxygen. The ideal chemical reaction (completely burned) can be written as

Equation 4

where is the stoichiometric coefficient, which means the number of moles of oxygen required to burn a mole of fuel completely. If we can measure the combustion heat release Q, the heat of combustion (q) can be simply calculated by

Equation 5

where m is the mass of fuel. Therefore, the question becomes how to ensure the complete combustion and how to measure the combustion heat release Q. To ensure a complete combustion of fuel, the amount oxygen must be larger than the oxygen required for complete oxidization of fuel. For example, for methane (CH4) combustion in oxygen, the combustion reaction in Eq. 4 becomes

Equation 6

Therefore, one mole CH4 needs two moles of oxygen to completely consume CH4 and form CO2 and H2O. The stoichiometric fuel/oxygen ratio can therefore be given by

Equation 7

In fuel lean and fuel rich cases, the fuel/air ratio (FAR) are respectively less and larger than the stoichiometric FAR. As such, it is convenient to use the ratio of actual FAR to the stoichiometric FAR to determine whether the mixture is fuel rich or fuel lean. This ratio is termed the mixture equivalence ratio,, and is defined as

Equation 8

, Fuel rich

, Stoichiometric

, Fuel lean

Therefore, larger, equal, and less than unity denotes fuel rich, stoichiometric, and fuel lean conditions, respectively,. Thus, from the above discussions and Eq.4, to completely consume the fuel in a combustion process, the oxygen mass (see Eq. 4) must be

Equation 9

In fact, in the experiment, you know the mass of fuel () and chamber volume V. The amount of oxygen is determined by the oxygen pressure in Eq.9. To measure the heat release Q for constant volume combustion, Eq.1 tells you that you need a system that has a very large heat capacity to absorb the combustion heat release and to keep the final temperature very close to the initial temperature.

Measuring the temperature rise of the calorimeter due to the combustion of fuels requires a thermistor, precision 10k ohm resistor, breadboard and the 4.8V Photon power supply. A thermistor is a temperature sensitive resistor where its resistance is inversely proportional to temperature. We will be using a Pasco thermistor wand (Figure 1). It’s resistance is 10k ohms at 21 deg C.

Figure 1: Pasco thermistor wand

We will be using a Voltage Divider Circuit. The transfer function for this circuit is:

Equation 10

Where is the voltage out of the junction between and
is the Pasco Thermistor
is the 10kOhm precision resistor
is the 4.8V power supply from the Photon
Construct the circuit in the following Schematic:

Figure 2: Voltage divider circuit schematic

Then connect the output of the voltage divider to the "A1" pin on the photon as shown in figure 3.

Figure 3: Photon Circuit

Bio-Diesel Test Batch, Recipe and Procedure
• Potassium Hydroxide (KOH) – 2.45g
• Canola Oil – 500mL
• Methanol – 100mL

Experimental Equipment
• Thermocouple
• Matlab Program "BiofuelsThermistor.m"
• Blender
• Weight Scale
• Transfer Pipette (4mL)
• Glass Beaker (500mL)
• Glass Beaker (1L)
• Pyrex Dish
• Bomb Calorimeter
• Oxygen Supply
• Fuse Wire

Safety

Methanol and Potassium Hydroxide (Methoxide when combined) are dangerous chemicals. Methanol if ingested can cause blindness and death. Potassium Hydroxide (KOH) can cause severe burns. Wear protective gloves and eye protection. Do not wear shorts or open toe shoes. In other words, minimize exposed skin. If these chemicals do contact your skin, rinse thoroughly with water.

Carefully pour 500mL of Canola oil into the 1L glass beaker. Set this aside for now.

Now let’s make the Methoxide. Carefully pour 100mL of Methanol into the 500mL beaker. Weigh out 2.45g of Potassium Hydroxide into the Pyrex dish. Be as accurate as you can. Add the KOH to the Methanol and gently swirl until all the KOH is dissolved.

Pour the Canola oil into the blender. Add the Methoxide and secure the lid tightly. Turn the blender on in pulse mode to start then continue to stir using the low setting. Continue blending for 1 min.

Pour this disgusting concoction into the 1L Nalgene container and secure the lid.
Now you must wait at least 24 hours to allow the Glycerin to separate from the Bio Diesel. The Glycerin will settle to the bottom.

The calibration involves the operation of the calorimeter on a standard fuel sample (e.g. benzoic acid) from which the energy equivalent or effective heat capacity can be determined. The effective heat capacity (C) of the bomb calorimeter is the heat required to raise its temperature by one degree, expressed in cal/K. With your photon connected with the voltage divider circuit and thermistor, download and open the BiofuelsThermistor.m matlab code.

Example of calibration: By assuming a complete combustion and that the change of the heat capacity of the gas mixture before and after combustion is negligible compared with total heat capacity of water and calorimeter, the effective heat capacity can be obtained by the ratio of total heat release to the change of the temperature before and after the combustion.

Equation 11

where,
C: energy equivalent of the bomb calorimeter (cal/K),
q : heat of combustion of the standard fuel sample per unit mass at constant volume combustion in oxygen (e. g. benzoic acid q = 6,318 cal/g),

: mass of the standard fuel sample (g),
: length of the wire (cm),
: heat of combustion per centimeter of the ignition wire (2.3 cal/cm),
ΔT = change of temperature before and after combustion (K).

Figure 4: Bomb calorimeter schematic

It’s a good idea to start with the high purity carbon as your first fuel sample. Note that complete combustion will require at least enough oxygen to satisfy the stoichiometric reaction, but usually more oxygen is required to actually achieve complete reaction. Therefore, you need to know how much oxygen is required from the stoichiometric mass ratio of fuel to oxygen. A bottle of charcoal along with several other fuels will be provided. Measure out about 1 gram using the top-loading balance. The oxygen pressure is measured using a pressure transducer mounted on the oxygen tank. The readout is located on the bench and is calibrated in atmospheres. After preparing the bomb and turning the mixer on, run the program to collect about 1 min of base line water temperature data, then ignite the fuel. Typical temperature rises are 2 – 3 degrees C over about 10 min. Analyze your raw data in matlab plotting temperature vs. time.

Choose different fuels (at least one solid and two liquid fuels) in the lab and follow the experimental procedure described above. The heat of combustion (gross heat of combustion) can be computed from the measured temperature change, effective heat capacity, and burned length of the fuse wire by rewriting the above equation as

Equation 12

Compare your results with those published in standard reference works.

Not all of the fuel becomes CO2 and condensed H2O in the final products. For example, some of fuel may be partially oxidized into CO or form soot. As a result, the heat of combustion will be lower than the ideal case. In addition, pressure will affect the final products via the changes of the collision rate between molecules and the chemical equilibrium.

Fuel may be contaminated by other substances. For example, when coal containing sulfur is burned not all the sulfur is oxidized as SO2 but instead carried further to SO3 which combines with water vapor to form H2SO4. Some of the nitrogen in the bomb atmosphere is also oxidized and combined with water to form HNO3. A correction of 13.8Kcal/mol for HNO3 and 1.4K cal/mol for each gram of sulfur converted to H2SO4 is generally applied. We will ignore the energy released from the heat of formation of these two side reactions.

The fuse-wire generates heat through ohmic losses it presents in the firing circuit and by the heat of combustion of the portion of wire burned. The heat input from the firing circuit will be the same as when standardizing the calorimeter so this requires no correction. However, it would be found that the amount of wire consumed from test to test varies. This is a simple correction and therefore must be included in your determination of the calorific value of fuels. A correction of 2.3 cal /cm should be subtracted from your measurement as shown in Equation 12.

The bomb is surrounded by a quasi-adiabatic enclosure. Therefore, a more accurate measurement is obtained by considering the preperiod and postperiod portions of the temperature vs. time curve. By measuring temperature changes as a function of time before and after the rise period an estimation of the heat transfer through the enclosure can be obtained. The resultant “t” is referred to as the net corrected temperature rise. We will assume no heat is lost or gained by the calorimeter.

Use the compressibility factor (Z) to determine the validity of the ideal gas law when calculating the molar amount of oxygen in the bomb at high pressures.

If a part of the water formed from combustion is not condensed, how will the heat of combustion change?

You will be required to submit your results in the form of a lab report

Care must be taken to stay within the design limits of the apparatus. NOT MORE THEN ONE GRAM OF CARBON (7,824 cal or 393.5 kJ/mole) EQUIVALENT of a combustible material may be burned in the oxygen atmosphere of the bomb.

The oxygen pressure is RESTRICTED TO LESS THAN 2.0 MPa (20 atm).