19/Feb/2019 Bomb Calorimeter Lab Report

THERMODYNAMICS 2nd Year Mechanical Engineering

Presented by: Patrick Livingstone

Module: Thermodynamics

Presented to: Tom Roach

Table of Contents:

Introduction: .....................................................................................................................................1

Objectives: .......................................................................................................................................1 Theory on Bomb Calorimeter: .........................................................................................................1 Apparatus: ........................................................................................................................................2 Procedure: ........................................................................................................................................3 Data Collected:.................................................................................................................................6

Calculations: ....................................................................................................................................7 Errors: ............................................................................................................................................11 Conclusions: ...................................................................................................................................11

References: .....................................................................................................................................11

Table of Figures: Figure 1. Bomb Calorimeter Diagram ............................................................................................ 2 Figure 2. Images of the Crucible..................................................................................................... 2 Figure 3 The Bomb ......................................................................................................................... 3 Figure 4 Bomb Calorimeter Apparatus ........................................................................................... 3 Figure 5. Crucible Prepared for Bomb ............................................................................................ 3 Figure 6. Bomb Closed ................................................................................................................... 4 Figure 7. Opening the Bomb ........................................................................................................... 5

List of Tables: Table 1: Data Collected during Bomb Run ..................................................................................... 6 Table 2: Calorimeter Observations ................................................................................................. 7 Table 3: Boiler Observations. ......................................................................................................... 9

Page | 1

Introduction:

The aim for this lab report is to study and examine the first law of thermodynamics which states

that heat is a form of energy, and thermodynamic processes are therefore subject to the principle

of conservation of energy. This means that heat energy cannot be created or destroyed. We hope

to examine this law and carry out an experiment and report on its conclusions in relation to the

first law of thermodynamics.

Objectives:

There are two main objectives to this experiment, these objectives are:

• Calculate the calorific value of the woodchip boiler.

• Calculate the efficiency of the woodchip boiler.

The main aim in this experiment & report is to calculate the efficiency of the woodchip pellet

boiler.

Theory on Bomb Calorimeter:

• Newtons First Law of Thermodynamics states that the change in the internal energy ΔU of

a closed system is equal to the amount of heat Q supplied to the system, minus the amount

of work W done by the system on its surroundings.

• Calorimetry is the science of measuring quantities of heat, as distinct from temperature.

The instruments used for such measurements are known as calorimeters. The most common

type of calorimeter is the oxygen bomb calorimeter. The Calorific Value of a sample may

be broadly defined as the number of heat units liberated by a unit mass of a sample when

burned with oxygen in an enclosure of constant volume.

• These measurements are obtained by burning a representative sample in a high-pressure

oxygen atmosphere within a metal pressure vessel – called a bomb. The energy released

by this combustion is absorbed within the calorimeter and the resulting temperature change

within the absorbing medium is noted. The calorific value of the sample is then calculated

by multiplying the temperature rise in the calorimeter by a previously determined energy

equivalent determined from previous tests with a standardizing material.

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Apparatus:

Figure 1. Bomb Calorimeter Diagram

.

Figure 2. Images of the Crucible

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Figure 3. The Bomb

Figure 4. Bomb Calorimeter Apparatus

Procedure:

1. Prepare the sample in the bomb, wrap the fuse wire through the fuel and as shown in image

below.

Crucible

Fuel

Fuse Wire

Figure 5. Crucible Prepared for

Bomb

Page | 4

2. Close the bomb up and prepare to record the results.

3. Place the bomb in the calorimeter bucket, secure the bomb in the correct position and

proceed to the following stage.

4. Fill the calorimeter bucket with water.

5. Final settings.

6. Read and record temperatures.

7. Stand back from the calorimeter and fire the bomb.

Figure 6. Bomb Closed

Page | 5

8. Record the change in temperature.

9. Open the Bomb to see that the fuel is burned.

10. Check the Fuse wire and make sure it has burned out and you know it is a success.

13

13.5

14

14.5

15

15.5

16

16.5

17

17.5

18

0 5 10 15 20 25 30 35

Tem

per

atu

re (

ºC)

Time - Minutes

Temperature / Time Bomb Calorimeter

Bomb Fired

Figure 7. Opening the

Bomb

Page | 6

Data Collected:

Bomb Calorimeter Data Collected

Temperature allowed to stabilize Bomb Fired

Time (Minutes) Temperature (°C) Time (Minutes) Temperature (°C)

1 13.847 15.5 14.629

2 13.939 16 15.658

3 13.985 16.5 16.242

4 14.005 17 16.672

5 14.038 17.5 16.972

6 14.054 18 17.14

7 14.072 18.5 17.282

8 14.087 19 17.372

9 14.101 19.5 17.435

10 14.114 20 17.477

11 14.127 20.5 17.515

12 14.14 21 17.537

13 14.152 21.5 17.551

14 14.165 22 17.564

15 14.177 22.5 17.574

23 17.583

23.5 17.59

24 17.595

24.5 17.6

25 17.603

25.5 17.606

26 17.609

26.5 17.612

27 17.614

27.5 17.616

28 17.619

28.5 17.621

29 17.623

29.5 17.625

Started at 10:25 am 30 17.627

Ignited at 10:40 am 30.5 17.629

Finished at 10:57 am 31 17.631

Fuel (grams) 1.8 Grams 31.5 17.633

Water (kilograms) 2 Kilograms 32 17.635

Table 1: Data Collected during Bomb Run

Table 1: Data Collected during Bomb Run

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Calculations:

The following data is recorded during the operation of the calorimeter.

a. Time of firing

b. Time when the temperature reaches 60% of the total rise.

c. Time at which the temperature is constant.

ta. Temperature at time of firing.

tc. Temperature at time c.

r1. Rate at which the temperature was rising during the 5 min period prior to firing.

r2. Rate at which the temperature was rising after time c.

c3. Centimeters of fuse wire consumed in in firing.

W. Energy equivalent of the calorimeter.

M. Mass of the sample in grams.

Data from Experiment:

Calorimeter Observations

a. Time of firing 10:25:00 am

b. Temperature reaches 60% of the total rise. 10:41:45 am

c. Time at which the temperature is constant. 10:57:00 am

ta. Temperature at time of firing. 14.629°

tc. Temperature at time c. 17.635°

r1. Rate of temperature rise in the 5 min period prior to firing. 0.0126°/min

r2. Rate at which the temperature was rising after time c. 0°/min

c3. Centimeters of fuse wire consumed in in firing. 7cm

W. Energy equivalent of the calorimeter. 2426 Cal/°K

M. Mass of the sample in grams. 1.8g

Table 2: Calorimeter Observations

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Temperature Rise: The net correct temperature rise is calculated by using the following equation.

𝛥𝑡 = 𝑡𝑐 − 𝑡𝑎 − 𝑟1(𝑏 − 𝑎) − 𝑟2(𝑐 − 𝑏)

And calculated:

𝛥𝑡 = 17.635 − 14.629 − 0.0126(16.75) − 0.0126(15.25)

𝛥𝑡 = 2.9871

Gross Heat of Combustion: To compute the gross heat of combustion the following formula is

used.

𝐻𝑔 =(Δt)(𝑊) − ((2.3)(𝑐3))

𝑚

𝐻𝑔 =(2.987)(2426) − ((2.3)(7))

1.8

𝐻𝑔 = 4016.86 𝑐𝑎𝑙/𝑔

1cal/gram = 4.187kJ/kg

𝐻𝑔 = (4016.86)(4.187)

𝐻𝑔 = 16818𝑘𝐽/𝑘𝑔

Data from Wood Pellet Boiler:

15

20

25

30

35

40

45

50

55

60

65

0 50 100 150 200 250 300 350 400

Tem

per

atu

re (

°C)

Time - Minutes

Temperature/ Time Wood pellet Boiler

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Heat Produced by the Fuel:

As the fuel is burned it produces heat energy and can be calculated as follows:

𝑄 = (𝑚)(𝐻𝑔)

Q. Energy Produced

mf. Mass of Fuel Used

Hg. Calorific Value of the Fuel (Determined in Experiment One

Heat Exported from the Boiler to the Fluid:

When water is used to transfer heat from the boiler the heat transfer can be expressed as:

𝑄𝑓 = (𝑚)(𝑐𝑝)(𝛥𝑇)

Q. Energy out of the boiler

mb. Mass flow of water through the boiler (kg/min)

cp. Specific Heat (J/kg oK)

ΔT. Temperature difference between inlet and outlet of the boiler (oC)

Boiler Efficiency:

Boiler Efficiency related to the boiler’s energy output compared to the boiler’s energy input can

be expressed as boiler efficiency (%) = 100 heat exported by the fluid / heat provided by the fuel.

Boiler Observations

c. Time at which the temperature is constant. 09:41:00 am

ta. Temperature at time of firing. 17.1979°

tc. Temperature at time c. 61.3843°

ΔT. Temperature rise in the Boiler 44.1864°

mf. Mass of the Fuel Used. 10.7 kg

mb. Mass Flow 10.9 kg/min

Cp. Specific Heat for Water. 4186 J/kg°K

Table 3: Boiler Observations.

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Calculations:

The total fuel used during the run was 10.7Kg and using the calorific data produced in the first

experiment the total heat that can be produced by the fuel is as follows:

𝑄𝑓 = (𝑚)(𝐻𝑔)

𝑄𝑓 = (10.7)(16.818 × 106)

𝑄𝑓 = 179.953 × 106𝐽

The boiler was run for 280 minutes the following is the total heat energy measured at the boiler

outlet:

𝑄𝑏 = (𝑚)(𝑐𝑝)(𝛥𝑇)

𝑄𝑏 = 154.938 × 106𝐽

With these values the efficiency of the boiler can be determined as follows:

𝑄𝑏

𝑄𝑓× 100 = % 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

179.953 × 106

154.938 × 106× 100 = % 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

86.1% = % 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

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Errors:

To understand the errors correctly it is first necessary to calculate the percentage error of the values

obtained. To do this the following formula is used:

𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 × 100 = % 𝐸𝑟𝑟𝑜𝑟

In the first part of the experiment the calorific value of the fuel was determined to be 16.82 MJ/kg

however there may be some error in this value as a recent study by COFORD which the Council

for Forest Research and Development Ireland is lists the average calorific value of Irish wood fuel

to be 19.24 MJ/kg. This produces an error of:

16.82 −19.24

19.24 × 100 = −12.58%

Due to some difficulties experienced with displaying the experiment to a large group of students

refrigerated water was used for the experiment, this may have caused the ambient temperature

within the calorimeter to be somewhat unstable prior to firing the bomb. Also due to a lack of time

the experiment was cut short and the temperature was not given enough time to ensure it had

peaked. A combination of these factors may have led to the error in the result obtained.

In the second part of the experiment the boiler was determined to be 86.1% efficient. Given that

the values used to determine the heat produced by the fuel were taken from experiment one, a

slight error is to be expected. Other errors may have occurred due to the frequency of the data

samples. The temperatures and flowrate data were sampled once per minute and for greater

accuracy it would have been better to sample once per second. Also, the accuracy of the

temperature and flowrate sensing equipment are not determined within the scope of this

experiment. A combination of these factors will have led to the error observed.

Conclusions:

To conclude this experiment, it can be shown that the calorific value of the wood fuel was not

determined with any measure of accuracy. Going forward it would be necessary to mitigate as

many of the errors as possible to yield a more accurate result. The errors in the initial experiment

led to errors observed while determining the efficiency of the boiler. This emphasizes the need for

careful preparation before the experiments are carried out to ensure accurate and useable results.

References:

• http://www.coford.ie/media/coford/content/publications/projectreports/cofordconnects/Calorific%20value

%20of%20Irish%20woodfuels..pdf

• https://www.livescience.com/50881-first-law-thermodynamics.html