Development Team

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Environmental Sciences

Analytical Chemistry Bomb Calorimetry Paper No 2: Analytical Chemistry Module 20: Bomb Calorimetry

Development Team

Principal Investigator

&

Co- Principal Investigator

Prof. R.K. Kohli

Prof. V.K. Garg &Prof.Ashok Dhawan Central University of Punjab, Bathinda

Paper Coordinator Dr. J. N. Babu,

Central University of Punjab, Bathinda Content Writer

Dr. J. N. Babu

Department of Chemistry,

Central University of Punjab, Bathinda Content Reviewer Dr. J. N. Babu,

Central University of Punjab, Bathinda Anchor Institute Central University of Punjab

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Analytical Chemistry Bomb Calorimetry

Description of Module

Subject Name Environmental Sciences Paper Name Analytical Chemistry Module

Name/Title Bomb Calorimetry Module Id EVS/AC-II/20 Pre-requisites

Objectives

To study the basics of bomb calorimetry and know the following about self generated questions.

1. What is GCV and NCV?

2. What is first law of thermodynamics and its application to calorimetry?

3. What is a thermodynamic path and process?

4. What are the different types of thermodynamic processes?

5. How does a bomb calorimeter work?

6. How is the calorific value of gaseous fuel?

7. What is the principle of Boy’s calorimeter and Junker’s calorimeter?

8. What are the applications of bomb calorimeter?

Keywords

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Module 5: Bomb Calorimetry

Objectives: To study the basics of bomb calorimetry and know the following about self generated questions.

1. What is GCV and NCV?

2. What is first law of thermodynamics and its application to calorimetry?

3. What is a thermodynamic path and process?

4. What are the different types of thermodynamic processes?

5. How does a bomb calorimeter work?

6. How is the calorific value of gaseous fuel?

7. What is the principle of Boy’s calorimeter and Junker’s calorimeter?

8. What are the applications of bomb calorimeter?

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Module 20: Bomb Calorimetry 1. Introduction

Heat is a form of energy which cannot be measured directly. Thus the science of calorimetry deals with the measurement of the heat of a process based on the temperature change as the parameter of choice for the system under controlled conditions. The definition of the processes is wide, covering all physiochemical phenomena in the environment. However, the present context of calorimetry would discuss only the heat of combustion, which is commonly associated with fuels and nutritive foods as gross calorific value (GCV). The determination of the calorific value is very important in this energy efficient world, particularly for environmental and energy management applications, food and nutrition etc. The calorific value is the amount of heat liberated during the process of combustion per unit weight of the fuel, commonly expressed in MJ/kg for fuels and Kcal/g for nutritive purposes.

Apart from calorific value determination, calorimetry is applicable in the determination of the net calorific value (NCV), heat of combustion, heat of formation, sulphur content in fuels.

As the energy form of heat could not be measured directly, in calorimetry, the temperature change is the parameter for the study of heat during the combustion process. The process involves the heat exchange between known amount of water and the reaction system. The heat exchanged is relayed in terms of the temperature change of the water. The heat transferred to water is directly proportional to the rise in temperature of water. The constant of proportionality is known as the heat capacity of water, which is defined as the amount of heat required to raise the temperature of water 1 kg of water by 1^oC.

Thus, calorimetry requires the understanding of the basic thermodynamics for evaluation of the process and its heat energy. Thus, in the subsequent section, the basic thermodynamics, calorimetry process thermodynamics, principle of bomb calorimetry, Boy’s calorimeter and Junker’s calorimeter are discussed with their applications.

2. Thermodynamic Basics

The thermodynamic processes in universe are required to isolated by defining the following a. System: A system is defined as a quantity of matter or a region in space chosen for study.

b. Surrounding: The mass or region outside the system is called the surrounding.

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c. Boundary: the real or imaginary surface that separates the system from its surroundings.

(a) Closed System (b) Open System (c) Isolated System Figure 1: Thermodynamic system, boundary and surrounding.

2.1 Types of System

Based on the system and its interaction with surrounding through the boundary, system may be classified as (Figure 1)

a. Closed system: Processes where the system does not exchange mass with the surrounding but can exchange energy with the surrounding, i.e., no mass can cross the boundary of the system.

Thus, the mass in the closed system if fixed and does not undergo any change during the process. As the system tends to have mass as constant, the volume is subjected to expand or compress as energy in the form of work or heat could cross the boundary.

b. Open System: Open system is a selected region in space which involves mass flow as well as energy flow across the boundary. For example beaker containing water, whereby a salt could be added to the system or water evaporated from the system whereby both mass change as well as energy transfer is observed during the process. Compressor in a fridge is another example, whereby the refrigerant is circulated from compressor to the external coil and back to the compressor, thus comprising of both mass and energy transfer.

c. Isolated System: Isolated system is one which involves neither mass flow nor energy flow across the boundary. For example, hot water placed in a well insulated thermos flask.

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d. Rigid System: This is a closed system which has only heat transfer between the system and its surrounding.

e. Adiabatic System: Open or closed system which do not exchange heat with its surrounding.

All these systems are bound to exist in a state where all the properties of the system are defined by fixed value. These properties of the state of the system could be classified as extensive of intensive properties. Extensive properties are those properties which depend on the size of the system e.g. mass, volume and energy. On the other hand, intensive properties are those properties which are independent of the size of the system e.g. temperature, pressure and density.

2.2 Thermodynamic Process and Path

Any change in these properties, leads to a change in the state of the system. The change in the state of the system from initial state A to final state B is called a process. However, during the change of state from A B, the system may have passed through series of states during the process which is called the path of the system.

Figure 2: Thermodynamic process and path

The processes in Thermodynamics can be classified under one of the following:

1. Isothermal Process: The processes where the temperature of the system is kept constant.

2. Isochroic Process: The process where the volume of the system is kept constant.

3. Isobaric process: The process where the pressure of the system is kept constant.

4. Adiabatic Process: The process where there is no heat exchange between the system and the surrounding

5. Isenthalpic Process: The process where there is not enthalpy change of the system 6. Isentropic Process: The process where there is no entropy change of the system.

2.3 First Law of Thermodynamics and Heat Measurement Path

Process State A

State B

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As heat is an immeasurable form of energy directly, the first law of thermodynamics provides the explanation for the evaluating the heat energy associated with a process.

First law can be stated as

“Energy can neither be created nor destroyed, however can be converted from one form to another.”

The quantitative expression for the first law of thermodynamics can be provided assuming that only pressure volume work is done by the system

U= qsys +w eqn. 1

Where U represents the internal energy change of the system, qsys is the heat absorbed by the system

w is the work done by the system and is given by w = - Pext . V

If the process is carried out under constant volume conditions, the work done by the system w=0.

Thus, the first law expression for energy is reduced to

U = qsys eqn. 2

Where, heat absorbed by system is equal to the heat released by surrounding, i.e.,

qsys = -qsurr => U = - qsurr eqn. 3 equation 3 is the expression for the heat measured under the constant volume conditions. However, all the combustion processes are carried out under constant pressure conditions. Thus, the thermodynamic term ‘enthalpy’ is used for processes in under constant pressure conditions, which is defined by

H = U +PV

H = U + PV) = U + PV + VP eqn. 4 Where, PV = 0, as volume is constant, thus,

H = U + PV) = U + VP eqn. 5

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If the pressure under constant volume condition for combustion is constant, i.e., the amount of gaseous components remain constant during the reaction, then change in enthalpy would be equal to change in internal energy. However, in case of combustion like in most of the cases the gaseous products are formed during the process, thus in such cases, PV could be replaced by nRT in the enthalpy expression in equation. 4 i.e.,

H = U + nRT) eqn. 6

H = U + n.RT + nRT ≈U + n.RT eqn. 7 Where, n = number of gaseous products – number of gaseous reactants

Thus, n, could be positive (more number of gaseous products formed in comparison to the number of gaseous reactants consumed in the process) or could be negative (gaseous product decrease upon completion of the process). Based on n, the enthalpy would deviate from internal energy of the system.

3. Calorimetry

Calorimetry is an important field of analytical chemistry which deals accurately measuring heats of reaction.

3.1 Calorimeter: Designs and Uses

The present work would discuss the design and use of the three calorimeters namely a. Bomb Calorimeter

b. Boy’s Calorimeter c. Junker’s Calorimeter

Bomb calorimeter is used for solid and liquid sample analysis for heat of combustion or gross calorific value determination. On the other hand, the Boy’s Calorimeter and Junker’s calorimeter are used for the analysis of gaseous fuel.

3.2. Bomb Calorimeter:

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Heat of combustion is determined by using a bomb calorimeter, whereby the heat obtained from the combustion of sample under high oxygen pressure conditions to ensure the complete combustion of the sample is carried out. The energy released by the combustion of the sample is absorbed by a measured volume of heat absorbing medium, whereby the temperature rise is noted. The general view of a bomb calorimeter is given in Figure 3.

Figure 3: A general view of a bomb calorimeter with its important functional components

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A bomb calorimeter comprises of four components

a. Bomb: The bomb is a strong, thick walled steel/alloy vessel which is screw opened for inserting the sample and removing the product of combustion. The bomb is constructed in such a manner to resist a pressure upto 3000 psig, though it is operated at half the maximum pressure limit. The bomb is provided with filling valves for filling the bomb with oxygen under high pressure conditions and for releasing the residual gases upon combustion at the end of the test before opening the bomb vessel. The bomb would be provided with two electrodes to connect the ignition wire and a connector in the outer end to connect to a current supply system. A crucible holder for holding the liquid or the solid samples. The bomb is made acid resistant as to ensure that the acid formed by oxidation of nitrogen and sulphur present in the sample as well as hydrochloric acid formed from chlorine in sample do not harm the container life and operation.

b. Calorimeter Bucket: The calorimeter bucket are carefully designed so that it can hold water as per the methods requirement generally 2 litres of water as well as a stirrer, a thermometer and the bomb submerged in the water in such a manner that it does not interfere with /short circuit the electrical supply on the bomb. The stirrer included should itself not introduce its own mechanical energy in the form of heat. Buckets are polished on outer finish to minimize the adsorption and emission of radiant heat.

c. Calorimeter Jacket: The bomb and the bucket are held in the calorimeter jacket which serves as a thermal shield, controlling any heat transfer between the bucket and the surrounding. The jackets minimize the effect of air draft, radiation and most importantly the temperature changes during the heat transfer during the calorimetry. In a plain bomb calorimeter, there is a air jacket between the calorimeter jacket and the bucket. However several other jacketing systems are available in the advanced bomb calorimeters which enable the calorimeter to function in adiabatic or isoperibol mode. In an adiabatic system the jacket temperature is adjusted continuously, using water filled jacket equipped with heater or water circulator, so as to establish a thermal equilibrium with the bucket. The heat in the adiabetic mode evaluation is given by the expression as given in equation 8.

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𝐻_𝑜 𝑎𝑑𝑖𝑎𝑏𝑒𝑡. = ^{𝑐 (𝑇}^𝑓^−𝑇^𝑖^{)− 𝑄}^𝑓

𝑚 eqn 8

However in the isoperibol mode, the jacket temperature is controlled and held constant throughout the experiment while the bucket temperature rises. The difference between the monitoring in the adiabatic calorimetry and isoperibol calorimetry are brought out in Figure 4. A correction e.g.

Regnault-Pfaundler correction factor (ξ) (equation X) is applied to account for the heat leak resulting from the difference in the temperature between bucket and the jacket. The enthalpy in isoperibol conditions could be given by equation 10.

𝜉 = 𝜃 [Δ_Z[^𝑇^𝑠^+𝑇^𝑒

2 + ∑^𝑍_𝑍^𝑒^−Δ^𝑧𝑇

𝑎−Δ𝑧 ] − (𝑍_𝑒+ 𝑍_𝑎) ^𝑇^𝑠^−𝑇^𝑒

2 ] − (𝑍_𝑒− 𝑍_𝑎)^𝑇^𝑠^{− 𝑇}^𝑒

𝑍_𝑠− 𝑍_𝑒 eqn 9 𝐻_𝑜 𝑖𝑠𝑜𝑝. = 𝑐 (𝑑𝑇+ 𝜉)− 𝑄_𝑓

𝑚 eqn 10

Figure 4: The temperature monitoring difference between (a) adiabetic calorimetry (b) isoperibol calorimetry.

d. Thermometer: Precise temperature measurement is essential in bomb calorimeter. The Beckmann Thermometer with a least count of 0.01^oC was used in earlier studies. However with advancement in technology platinum resistance thermometer, quartz oscillator and thermistor based system have all being efficient and used in bomb calorimetry quiet efficiently with improved automation with a resolution of 0.001^oC.

3.2.1. Bomb Method of Analysis a. Sample Preparation

20 21 22 23 24 25

0 2 4 6 8 10 12 14 16

Temperature of Water Temperature Adiabetic Jacket

Time (in min) Temperature (inoC)

20 21 22 23 24 25

0 2 4 6 8 10 12 14 16 18 Time (in minutes) Temperature (inoC)

Outer Jacket Temperature

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a. Solids: In case of solid samples, if the sample is intact, it is weighed as such upto a maximum of one gram. However, in samples which show improper combustion are required to be powdered by grinding in a mixer. The powdered materials are weighed upto not more than 1 g, and then pelletized with a powder pellet press. The solid pellet is put in a pre-weighed sample holder and weighed again. The difference in weight of the sample holder to that of sample holder with pellet sample would be the actual amount of sample utilized in the analysis.

b. Liquids: In case of liquids, the sample is prepared using capsule method. Plastic capsules are available in the market, the capsules are purchased in bulk and the calorific value of the capsule is determined. The liquid samples are filled in capsules and used upon weighing the sample for the analysis. The capsules are loaded into the sample holder. However, incase of non-volatile liquid, the capsule is not required for the analysis. The samples are directly weighed in the sample crucible and transferred to the bomb.

b. Assembling the bomb:

a. Place the sample holder containing the sample in the sample place holder attached to one of the electrodes.

b. Measure 10 cm of ignition wire and weigh the wire. Connect the wire across the two electrodes in the calorimeter top hanging down and in good contact with the sample but not the cup.

c. Many Bomb calorimeter recommend the contact if sample in sample holder with a cotton thread of measured length ca 10 cm hanging from the ignition wire.

d. Carefully fit the bomb head containing the sample in sample holder with the electrodes facing down into the cylinder of the bomb. Screw the bomb tightly.

e. Attached the oxygen inlet to the bomb and fill the bomb with oxygen upto 30 + 2 atm pressure.

c. Preparation of the Calorimeter Apparatus:

a. Place the bucket at the appropriate prescribed place in the jacket of the calorimeter b. Place the bomb in the calorimeter at the prescribed appropriate place in the bucket.

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c. Attach the electrodes to the electrical supply as marked on the outside of the bomb.

d. Add two litres of water measured using a measuring cylinder at an appropriate temperature to the bucket from the sides of the bucket. Ensure that the bomb is sufficiently submerged in the water and that the electrode short circuit is averted.

e. Close the calorimeter. Put the motorized stirrer at its place.

f. The Thermometer or thermocouple is inserted into the space provided ensuring that the mercury bulb completely submerges in the water in the bucket.

g. Gently put on the stirrer.

d. Starting the experiment

a. Begin reading the temperature of the system at every 30 second interval till the rise in the temperature of the water bath is about 0.001^oC in 15 seconds. This temperature is the initial reading for the sample.

b. Upon reaching this temperature stability, the sample is ignited by pressing the ignite button, whereby the current flows in the circuit igniting the sample inturn.

c. Continue taking the temperature readings every 30 seconds till the temperature rises and becomes constant.

d. Plot the graph of the temperature with reference to time.

e. Post Completion care

a. Switch off the stirring device and take out the device from the calorimeter.

b. Raise the thermometer on its stand and remove the calorimeter lid.

c. Unplug the electrode connection and take out the bomb from the bucket and place it on the laboratory table.

d. Slowly release the pressure in the bomb, open it and measure the length and weight of the wire in case the nichrome wire is used of igniting.

e. Empty dry the bucket.

f. This procedure is required to be repeated with standard sample as well to determine the heat capacity of the calorimeter.

3.2.2 Calculate the calorific value of the sample

The calorific value of the sample is analyzed using bomb calorimetry.

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3.2.2.1 Determination of the calorimeter constant:

The calorimeter constant is the amount of heat required to increase the temperature of the calorimeter by 1^o.C

To evaluate the same

QBA = Literature reported value

Qwater = 2000 * 4.184 * T mBA (in g)QBA - Qwater = Qcalorimeter

where, mBA is the mass of benzoic acid combusted in the calorimeter Calorimeter Constant (C) = Qcalorimeter/ T Where, Qcalorimeter is the heat absorbed by the calorimeter

3.2.2.2 Determination of Heat of combustion of sample:

Qsam = 2000 * 4.184* (T2 - T1) + C. (T2-T1) Where, C is the calorimeter constant

T1 = Initial temperature of the calorimeter before ignition of sample T2 = final temperature of the calorimeter upon combustion of sample

U (kJ/mol) = Qsam * Mol. Wt. / mass of the sample combusted

H = U + ngRT

Problem 1: A bomb calorimeter containing 900 grams of water was calibrated by burning a sample of benzoic acid (C6H5COOH), whose heat of combustion is –3227 kJ/mol. When 1.890 g of benzoic acid is burned in the calorimeter, the temperature of the water and the calorimeter increases by 8.32°C.

Using these data, calculate the calorimeter constant for this calorimeter in J/ºC.

Solution

QBA (kJ/g) = Qcombustion /Mol wt. = 3227 / 122 = 26.451 kJ/g mQBA = 26.451 kJ/g * 1.89 g = 50.767 kJ

Qcalorimeter = m.QBA - Qwater = 50.767 kJ – (900 * 4.184 * 10^-3 * 8.32)

= 50.767 – 31.300 kJ = 19.467 kJ

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Calorimeter Constant (C) = Qcalorimeter/ T C = 19.467 / 8.32 = 2.340 kJ / ^oC = 2340 J/^oC

Problem 2: A 0.500 g sample of naphthalene (C10H8) is burned in a bomb calorimeter containing 650 g of water at an initial temperature of 20.00ºC. After the reaction, the final temperature of water is 26.4ºC. The heat capacity of the calorimeter is 420 J/ºC. Using these data, calculate the heat of combustion of naphthalene in kJ/mol.

Solution

Calorimeter Constant (C) = Qcalorimeter/ T

 Qcalorimeter = Calorimeter Constant (C) * T

 Qcalorimeter = 420 * 6.4 = 2688 J = 2.688 kJ

Qwater + Qcalorimeter = m.Qnapthalene

Qnapthalene = 650 * 4.184 * 10^-3 * 6.4 + 2.688 kJ

Qnapthalene = 17.405 + 2.688 kJ / 0.5 = 40.186 kJ

Heat of combustion = - 20.186 * 128 = - 5143.81 kJ/mol

3.2.3. Corrections in Bomb Calorimetry:

1. Fuse wire correction: The fuse wire contributes its heat generated as the current flows thorough it. This heat liberated by ignition of fuse wire is required to be subtracted from the total heat generated by the analyte as this is an external energy added voluntarily to the system.

In case using the cotton thread of uniform measurement, the heat contributed due to the combustion of thread would also required to be subtracted from the total heat generated.

2. Acid Correction: The processes in the bomb in particular the combustion of nitrogen and sulhur contribute to the formation of oxides shich readily reacts with water vapours to provide a heat of reaction. Thus the amount of heat generated in the reaction is required to be corrected by subtraction from total heat liberated.

SO3 + H2O  H2SO4 + heat

NO2 + NO3 + H2O  2HNO3 + heat

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This correction amounts to 9.414 and 5.983 J/mg for S and nitrogen in the fuel respectively.

3. Cooling Correction: Upon achieving the maximum temperature of the bomb, the rate of cooling of the calorimeter given by dT/dt (^oC/min) determined and the actual time for cooling is recorded. The cooling correction, (dT/dt) x t is added to the rise in temperature of the calorimeter.

Thus based on this three corrections the modified heat expression would be

Qsam = ((2000 * 4.184) +C) * (T2 - T1+ Cooling Correction)

U (kJ/mol) = (Qsam – Acid correction – Fuse Correction) * Mol. Wt. / mass of the sample combusted

3.2.3. Boy’s Calorimeter

Boy’s gas calorimeter is used for the determination of the calorific value of gaseous fuel. This apparatus named after the inventor, Sir Charles Vernon Boy’s (1918). The instrument consists of a gas burner with an arrangement to control and measure the gas flow rate. The burner burns inside the calorimeter. The calorimeter container has a cooling coil arrangement with flowing water. A rotameter is provided to measure the flow rate of water. Two thermometers are arranged one at the inlet and one at the outlet of the water flowing through the coil. The heat from the burner flows up thorough the inner containers of the calorimeter. These inner containers are wrapped with copper coils for carrying water from outside thorough the rotameter and upto a measuring cylinder for measuring the water thorough the circulation in the calorimeter. Meanwhile due to the condensate of the fuel combustion in the calorimeter is also collected in a measuring cylinder.

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Figure 4: Boy’s Calorimeter for calorific value analysis of gaseous fuels Experimentation:

1. The circulation of water and burning of gaseous fuel are continued for 15 minutes to warm up the calorimeter.

2. The rate of fuel burning and water circulation are adjusted so that the water exits the apparatus at atmospheric pressure.

3. The flow rate of water and gaseous fuel is recorded.

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4. The temperature of the incoming as well as outgoing water is recorded upon stabilization of the calorimeter water and gaseous fuel flow rate.

5. The weight of the water condensate obtained is determined upon completion of the experiment.

Recorded Parameters:

a. Vol. of gas burnt at STP in time “t” = V m³

b. Wt. of water passed through the coil in time “t” = W kg c. Temp. of incoming water = T1oC

d. Temp. of outgoing water = T2oC e. Wt. Of condensed steam = W’ kg Calculations

Heat absorbed by circulating water= W*4.184*(T2-T1) kJ Heat produced by the combustion of fuel = Qsample

Heat produced = Heat absorbed Thus,

Qsample = W*4.184*(T2-T1)

3.2.4 Box and Junker’s Calorimeter:

Box and Junker’s calorimeter is another most widely used calorimeter for the analysis of calorific value of gaseous fuel. The calorimeter is fixed on a tripod stand having leveling screws to keep the Calorimeter in perfectly vertical position.

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Figure 5: Junker’s calorimeter and its working

The calorimeter mainly consists of three components namely

a. Gas combustion chamber: The chamber comprises of a provision to insert a burner, gas flow measurement apparatus. The chamber is provided with the provision to monitor the exhaust gas temperature.

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b. Heat exchanger: It is designed for maximum efficiency for heat transfer from the calorimeter inside to the water flowing thorough the jacket surrounding the gas combustion chamber.

c. Water flow system: An overflow device through which excess water drains out is attached with the water and the rise in temperature of the water is measured at near the outlet of the water jacket.

3.2.4.1 Principle of working and analysis:

It works on the Junker's principle of burning of a known volume of gas and imparting the heat transfer with maximum efficiency to steadily flowing water and finding out the rise in temperature of a

measured volume of water.

Calorific Value of Gas X Volume of Gas = Volume of water X Rise in Temperature, is then used to determine the Calorific Value of the Gas (assuming that heat

capacity of water is unity).

Let V = vol. of gas collected at S.T.P. In certain time ‘t’

W = Wt. of water collected in that time ‘t’

T1 = Temp. of incoming water T2 = Temp. of outgoing water

𝐻𝐶𝑉 = 𝑊 (𝑇₂− 𝑇₁) / 𝑉

𝑉 𝑘𝐽/𝑚³

m = Mass of steam condensed in certain time ‘t’ in graduated cylinder from V m³ of gas.

Latent heat of steam = 2456 kJ/kg Thus,

𝐿. 𝐶. 𝑉. = [𝐻𝐶𝑉 – 𝑚 𝑥 2456]

𝑉 𝑘𝐽/𝑚³

3.3. Application of Combustion Calorimeter:

The combustion calorimetry is applied to various fields of nutrition, energy and environmental analysis. Few of the applications are enlisted below

3.3.1. Determination of calorific value of solid/liquid fuels:

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Calorific Value is defined as the amount of heat released per unit weight of substance upon complete combustion. Calorific value is the characteristics feature of a fuel. The units of calorific value used for common reporting of fuel characteristics are kcals/kg, KJ/g, or MJ/kg. Some of the fuel and their characteristic calorific value is enlisted in table 1.

Table 1: Calorific value of various fuels Sr.

No.

Fuel Calorific Value in (KJ/g)

1 Hydrogen 150

2 Methane 55

3 LPG 50

4 Kerosene oil 48

5 Charcoal 33

6 Wood 17

There exist two types of calorific values as follows:

a. Higher calorific value (HCV) or Gross calorific value (GCV): It is defined as the amount of heat evolved when a unit weight (or volume in the case of gaseous fuels) of the fuel is

completely burnt and the products of combustion cooled to NTP (with water vapour condensed as a result).

b. Lower Calorific Value (LCV) or Net Calorific Value (NCV): It is defined as the amount of heat evolved when a unit weight (or volume in case of gaseous fuels) of the fuel is completely burnt and the water during the combustion is in vapour phase, as does the other products of combustion.

LCV is related to HCV by the relation:

LCV = HCV – Latent heat of water vapour formed

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LCV = HCV- mass of hydrogen *9 * Latent Heat of Steam

Where the latent heat of steam is 587 cal/kg or 2.456 kJ/kg, for water vapor formed at 15^oC.

The unit of calorific value and their conversion factors are as given in equation 3.

1kcal/kg = 4.186 J/g = 4.186 kJ/kg = 1.8 B.Th.U/lb = 2.2 C.H.U/lb for solid/liquid fuels 1 kcal/m³ = 4.186 kJ/m³ = 0.1077 B.Th.U/ft³ for gaseous fuels

Where B.Th.U and C. H. U. are defined as British Thermal Unit and Centigrade Heat Unit, respectively.

The fuels calorific value is determined using bomb calorimeter experiment and is given by GCV/HCV (kJ/kg) = ((4.184𝑊 + 𝐶) (𝑇2 − 𝑇1) )

𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑓𝑢𝑒𝑙 𝑠𝑎𝑚𝑝𝑙𝑒 (𝑖𝑛 𝑔) Where, W = weight of water in g, taken in the bomb calorimeter C is the calorimeter constant

T1 = Initial temperature of the calorimeter before ignition of sample T2 = final temperature of the calorimeter upon combustion of sample

3.3.2 For gaseous fuel using the boy’s calorimeter is given by Qsample = HCV * V Where V = total volume of gas flow added

Substituting, the bomb calorimetric expression for heat change as given in equation HCV = W*4.184*(T2-T1) / V kJ/m³

Latent Heat of Water vapour = 2456 J/g or kJ/kg

Wt. of water condensed from 1m³ of gas = W’/V kg/m³ Where, W’ is the weight of the water condensate collected So, Latent Heat of steam per m³ of gas = 2456 x W’/V kJ/m³

LCV of fuel = HCV- Latent Heat of steam per m³ LCV= (HCV - 2456*W’/ V)

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3.3.3. Determination of sulphur in coal:

Sulphur content in fuel is an essential criteria to be estimated for its use as a fuel in various

application. This element critically evolves as SO2 upon combustion. SO2 is known for causing the London smog conditions and is require an additional set-up of scrubbers as air pollution control device, to quench the SO2 in the flue gas.

Thus, it is quintessential to analyze sulphur. Though elemental analysis is the method usually used for sulphur determination. However, an alternative standard method for determination of sulphur is to oxidize the fuel in a bomb calorimeter under a moist condition created in the bomb. The sulphur oxides formed in the bomb condenses in the bomb itself. Thus, the ash from the bomb calorimeter is extracted with dil. HCl. The % of ‘S’ is estimated by the BaSO4 gravimetric analysis as prescribed in module : gravimetric analysis and the sulphur percentage evaluated as follows:

𝑆𝑢𝑙𝑝ℎ𝑢𝑟 (%) = 𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑃𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑡𝑒 (𝑖𝑛 𝑔) 𝑥 32

𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑎𝑙 𝑐𝑜𝑚𝑏𝑢𝑠𝑡𝑒𝑑 (𝑖𝑛 𝑔) 𝑥 233 𝑥 100

Bibliography

1. Atkins, P., & De Paula, J. (2013). Elements of physical chemistry. Oxford University Press, USA.

2. I. Lampercht, Handbook of Thermal Analysis and Calorimetry: From Macromolecules to Man, volume 4, Elsevier 1999

3. Stig Sunner, Margret Månsson Combustion Calorimetry: Experimental Chemical Thermodynamics Volume 1, Pergamon, 1979.

4. Silbey, R. J., Alberty, R. A., & Bawendi, M. G. Physical Chemistry 4^th Edition, 2001, Wiley New York.