1435 - الجامعة التكنولوجية · 2018-01-19 · observed and boyle’s law is...

-

Republic of Iraq

Ministry of Higher Education

and Scientific Research

University of Technology-Electromechanical

Department

1435 2014

August 28 2014 Lab. of Thermodynamics Electromechanical Eng. Dept Dr. Kassim K. A.

Title Page No.

Experiment No. (1): Boyle's Law 1

Object 1

Background 1

Apparatus 2

Theory 5

The method/procedure 9

Reading and requirements 10

Requirements 11

Calculations 12

Discussion 14

Experiment No. (2): The specific heat capacity 15

Purpose 15

Background 15


ii

The apparatus 17

Theory 21

Experimental procedure 27

Discussion 30

Experiment No. (3): Adiabatic exponential index of Oxygen 31

Objective 31

Introduction 31

Apparatus 33

Theory 35

Procedure 40

Results 41

Calculation of standard deviation and percentage

error43

Discussion 44

Experiment No. (4): Mechanical heat pump 45

Objectives 45

Background 45


iii

Safety features 46

Theory 48

Apparatus overview 51

Cycle of operation 55

Set up and instruction/procedure 57

Readings and calculations 58

Discussion 60

Experiment No. (5): Bomb Calorimeter 61

Objectives 61

Introduction 61

General description of the bomb calorimeter 62

Theory 69

Gross and net heats of combustion 71

The readings 73

Calculation of standard deviation and percentage

errors74

Procedure of bomb calorimeter experiment 76


iv

Possible problems 82

Plotting the data 83

Calculation, results and discussion 85

Parting comments 86


[1]

Object:

To learn and verify the relationship between volume and pressure

according to Boyle's law.

Back ground:

The absolute pressure exerted by a given mass of an ideal gas is inversely

proportional to the volume it occupies if the temperature and mass of gas remain

unchanged within a closed system. Mathematically, Boyle's law can be stated as

= … … … … … … … … … ( )

In this equation, “P” represents pressure, “V” signifies volume and “C” represents

a constant (fixed) number.

Notes: There are numerous number of units used worldwide for representing

the pressure such as,


[2]

( ), = , = , = , = ,

, = , = , = , atm = 101.325 .

In certain occasions however, (i.e. blood pressure) the unit of pressure used is

mm Hg or cm Hg,…and so forth.

Apparatus:

There are many devices suitable for conducting such an experiments are

illustrated in Figure (1). However the apparatus used in this particular experiment

is given in Figure (2). It mainly consists of two glass/plastic’ tubes (limbs)

connected together by a rubber tube (hose) to give it flexibility during movements

up and down, and getting a shape of a u-tube mercury manometer. The glass tube

(AB) fitted with a tap by which the top end of this limb can be closed during the

experiment. While the other end (bottom) is connected by a length of rubber tubing

to an open end glass tube (CD).The open end (top of limb, CD) of the manometer is

exposed to the atmosphere. Consequently the atmospheric pressure ( ) must be

added to the pressure exerted by the column of mercury. The first step in this

experiment is thus to measure the atmospheric pressure using the manometer

containing no trapped air.

However, during the experiment a sample of air is trapped in the closed end of

the manometer (part AX). Carefully measure the heights of the columns of mercury

and the column of trapped air. (The trapped air has artificially been given a light

green color in Figure (2). Use this data to calculate the volume of the trapped gas

and the pressure.


[3]

Figure (1): Different types of devices used to verify Boyle’s Law.


[4]

Figure (2): The apparatus used for verifying the Boyle's Law.


[5]

Theory:

It is apparent that Equation (1) is an equation of the second degree, since the

left side is the product of two variable quantities. When the pressure is plotted as a

function of the volume, an equilateral hyperbola, as shown in Figure (3), below is

obtained.


[6]

The actual pressure may be thought of as consisting of the atmospheric or

barometric pressure plus an added pressure P due to the difference in the

heights of mercury levels in both limbs (h), the algebraic sign of the added pressure

depending upon whether the actual pressure is above or below atmospheric

pressure. Thus, Eq. (1)may therefore be re-written as;

= ( ) =

If one considered the absolute pressure is higher than the atmospheric pressure then

the negative sign is dropped and only the positive sign remains. Hence,

= + ( ) = + … (2)

Where, represents mercury’s density and g denotes the

acceleration of gravity . .

But, according to the Boyle’s Law we can write,

= + ( ) =

or

+ ( ) = …………………….. (3)

Where, h in cm Hg represents the difference in height between the top level of

mercury (point Y and point X) in the right limb (CD) .

= = .


[7]

Here, A represents the cross-sectional area of the gas/air tubes, which will be

considered constant (= k) and L denotes the difference in height between points A

and X shown in Figure (2). Thus, equation (3) becomes:

+ ( ) =.

Hence,

=.

. =.

.

= ……………………..…… (4)

where, the number 76 denotes the barometric reading in cm Hg at time of the

experiment, = and = are another constants.

By placing = , the above equation becomes

= ……………………..……….…… (5)

Where, represents the mercury height in the barometer during the experiment, its

value at sea level is around .

It will be seen that Eq. (5), being of the first degree, is the equation of a straight

line. If, then, not the actual pressure P but merely the added pressure p or h be

plotted as ordinates and the reciprocal of volume, or X, be plotted as abscissas,

the resultant curve should be a straight line [Figure(4)]. If the curve is produced


[8]

downward until it intersects the pressure axis, i.e., when x or equals zero, the

intercept on the p/h-axis gives immediately the negative of the barometric pressure

at the time of the experiment. This is obvious from Eq. (5) for if x is placed equal

to 0, then

= ……………………………..….. (6)

While this portion of the present experiment is designed ostensibly to furnish a

check upon the approximate validity of Boyle’s law, it also furnishes a splendid

example of a study of both graphical and analytical representation and

interpretation of experimental data.

Figure (4): Typical relationship between h and of a fixed mass and constant temperature of pressure above and below atmospheric pressure.

,

O

, , ( )

N

Atmospheric pressure

B


[9]

The method/procedure:

To study Boyle’s law; a fixed mass of air confined/trapped in a glass tube is

kept at room temperature and subjected to various pressures, ranging from half to

double atmospheric pressure. A series of corresponding pressures and volumes are

observed and Boyle’s law is checked by noting the constancy of their products. The

data can be plotted in several graphical forms as mentioned in the theory above, the

interpretation of which also indicates the validity of Boyle’s law.

By referring to Figure (2), the method considered to carry out this experiment

adopts the following steps, the temperature and the mass of the air will be assume

constant:

1. Lower the tube AB as much as possible and raise the limb CD until the mercury levels X and Y are visible.

2. Record the scale reading of these levels and also the scale reading of A. The inside of the closed end of the tube AB.

3. Alter the pressure by suitable adjustment (moving up or down) of both limbs of the apparatus over the largest ranges of pressure and volume of which the apparatus is capable. Continue to do so until data is obtained for at least ten different pressures. Notice that sometimes the column of mercury on the left is higher than that on the right and sometimes the reverse is true. Why does this occur? Make sure you take this effect into account in calculating the pressure.

4. For each pair of volume-pressure values, enter the data in the table and plot two graphs. One of them equivalent to Figure (3) in which the volume on the x-axis versus corresponding total pressure on the y-axis, while the other one should be equivalent to Figure (4) in which the reciprocal of the volume on the x-axis versus h on the y-axis. Note: The origin of the graphs should be (0,0). Choose a suitable scale for each axis so that the data points fill the graph as completely as possible. Remember to label each axis and give the

graph a title. Then, carefully examine the plot and determine the value of atmospheric pressure.


[10]

Readings and requirements:

The experiment readings may be summarized in the following table:

No. of reading = , cm , ( ) = ,

= = + = +

1

2

3

4

5

6

7

8

9

10

The table above shows pressure and volume data for a set amount of gas at a

constant temperature. The fourth column represents the value of the constant C for

this data and is always equal to the pressure multiplied by the volume. As one of

the variables changes, the other changes in such a way that the product of

always remains the same. In this particular case, that constant is

?? atm · ml. You can fill this column by knowing the cross-sectional area of the

lift limb where the air is trapped.


[11]

Requirements:

Curved line such as Figure (3) is hard to recognise, so you should plot the

pressure (P or h in cm Hg) as ordinates against corresponding values of the

reciprocal of volume (ie. or ) as abscissa as shown in the typical Figure of this

kind, Figure (4). This time the points lie close to a straight line. This means

pressure is directly proportional to 1/volume or pressure is inversely proportional to

volume.

Whereas,

= .

= .

or

= . . … … … … … … … … … … … … … ( )

According to this equation, if one plot of h against yields a straight line,

Boyle's law is verified and the negative intercept on the h-axis is numerically equal

to 76 cm Hg, that represents the atmospheric pressure. However, number 76

appears in Equation (7) is not just a constant, instead it may be varied from one

place to another depends on the value of atmospheric pressure at the time of the

experiment.


[12]

Calculations:

From the Figure that will result off your data find the value of B

which represents the atmospheric pressure or height of mercury column

representing the barometric reading.

When, cm Hg the value of

= . ( ) = .

You can use the slope of the line appears in Figure (4) to calculate the mass of

trapped gas/air. It is also important to remember that this requires that the

temperature be constant. That means you have to change the pressure and volume

slowly! However if temperature does not remain constant, a figure more or less

similar to the following one [Figure (5)] will be found. In such a case Boyle’s Law

is no longer applicable.


[13]


[14]

Discussion:

1. What would happen where the pressure was very small?

2. What would happen where the volume was very small? 3. Are the statements aforementioned realistic or not? 4. What experimental factors are assumed to be constant in this experiment? 5. Is the relationship between pressure and volume direct or indirect? Explain. 6. What would you notice when you calculate [ P.V (= pressure x volume)] for

each set of results?

7. What does the slope of the line appears in the graph between pressure and reciprocal of volume represents?

8. What does the relationship between pressure and volume called?

9. Calculate the average value of the ’ . = ’ and the average deviation.

10. The relative percent error (uncertainty) in this constant can be determined as:

Relative percent error = (Average deviation/Average value) =100%

or

% = %


[15]

Purpose:

To determine the specific heat of solid metal (to demonstrate the

relationship between matter and energy involving heat, mass, specific heat and

temperature).

Background:

Heat is energy transferred from one body to another solely as a result of the

temperature differences between bodies. The unit of energy used in the metric

(MKS) system is the joule. However, the calorie, which is equivalent to 4.184 J, is

perhaps more commonly used. The calorie is the amount of heat needed to raise the

temperature of one gram of water by , for example, from . to

. . One property of a material that composes a body is known as specific heat

capacity, often abbreviated to specific heat. Specific heat, usually indicated by the

symbol C, is the amount of heat required to raise the temperature of one gram of


[16]

the substance by one degree Celsius. From the definition of the calorie, it can be

seen that the specific heat of water is or . Therefore, the amount

of heat, Q, needed by an object that is made of material of an amount of mass ,m,

with specific heat equal to C in order to raise the temperature of that object by an

amount T is:

= = . .

My prediction is that the metal with the least massive atoms will heat up more

quickly because they require less heat energy to make the molecules move around

and heat up.

Calorimetry is the science of measuring the heat of chemical reactions or

physical changes. Heat is the transfer of energy. While temperature is a physical

property of matter that quantitatively expresses the common notions of hot and

cold.


[17]

The apparatus:

By referring to Figure (1) , the apparatus used in this experiment consists of

the following parts:

1. Calorimeter/vessel set [metal vessel/ calorimeter of 37 liter volume that

represents the water bath and it is well thermally insulated from its

surroundings by Styrofoam, Foam , Polyester , Cork , Wood or any other

suitable insulator, so no heat is gained from (except that from the electric

heater) or lost to the surroundings.

2. AC 220 - 240 V Electric heater with total power rating of 1000 W (=1 kW),

it has 100% efficiency. This means that the quantity of heat energy given out

is equal to the electrical energy put in.

3. Electric mixer used to stirred gently the water around to evenly distribute the

energy given off by the electric heater.

4. Digital or mercury thermometer to measure the water temperature.

5. Movable part at the top surface of the calorimeter used to insert the metal or

metal alloy that you want to determine its specific heat inside the calorimeter

and also to fill it with distiller water.

6. Drain water tap to pour the water from the vessel after finishing the

experiment.


[18]

7. Suitable electric switches to turn the electric heater and the stirrer motor on

and off.

8. Two meters fixed on the outside of the calorimeter (not shown) one of them

to measure the eclectic voltage while the other is used to measure the

consumed ampere.

9. Digital or any suitable stop watch to measure the time.

10. Samples of aluminum and copper block. Their masses should be measured

carefully before or during the experiment in kg. In this experiment =

. .

11. Distiller water of appropriate volume, 37 liters in the present case.

12. Electronic balance/scale (not shown), measures to of a gram in order

to measure the mass of the metal (copper and aluminum) samples and the

mass of the water if necessary.


[19]

Figure (1): Typical experimental set-up for determining the heat capacity of metals.


[20]

FIGURE (2): Aluminum and copper samples.

FIGURE (3): Specific heat and conductivity of different materials..


[21]

Theory:

Before the heat capacity of metal can be determined, it is worthable to have a

quick look to Figure (3). It shows that different materials have different specific

heat capacity and conductivity. It also shows that material with low specific heat

has high conductivity and vice versa, i.e. silver and water.

Now to determine the heat capacity of a copper or aluminum it is necessary

to know the mass of the inner container of the vessel/calorimeter without the

insulator ring and lids along with its heat capacity [thermal worth of the vessel

(mass of the vessel times its specific heat capacity = = )], the value

can be found by first performing the experiment without the metal . This means that

the experiment should be carried out in three parts.

Part one:

In this case the heat added by the electrical heater should be gained by the

vessel and the water in it. Mathematically speaking:

= + = + …………………… (1)

Where, represents the add heat from electrical resistor that immersed in a

known mass of distilled water contained in an insulated vessel. When a current I

passes between two points of a conductor between which there is a potential


[22]

difference of, V, during a period of time , , the quantities of power, P, and heat

energy, Q , supplied to the vessel and its contents can be determined as:

= = = ,

Where, I = current in ampere, V = voltage in volt and R = resistance in ohm.

The total heat added to the water in time, is then,

= . = = = …..…..(2)

If the heat is added continuously, the temperature will increase linearly and the

slope of a temperature versus time plot will be related to the specific heat.

Thus, equation (1), can be rewritten as:

= = + or

= + = + Hence,

= ……………………..….…..(3) Where, subscripts V and W denote vessel and water respectively, m signifies

mass in kg and is the temperature deference in Kelvin or Centigrade (Celsius).

While k represents thermal worth of the vessel (= = ).

The only unknown in equation (3) is the thermal worth of the vessel “k”,

while ..

and , this by considering

density of water = . The experiment should be repeated several


[23]

times using different parameters. And you should always get the same

value of k in within the experimental error.

However, to minimize any error if it exists due to the idealistic or any other reasons

the average mean value of k is to be determined. Thus equation (3) should be

adopted at least four times on a prescribed temperature interval around three degree

centigrade/Kelvin. Then, a mean value of k can be found from those four or more

values. This value that should be used as a final and accepted value of k.

Table (1): shows the main reading of part (1).

No. of reading I, amp V, volt

, ,

,= , ,

1

2

3

4

5

6

=


[24]

Part two:

Once the thermal worth “k” of the vessel has been determined, it is possible

to experimentally determine the heat capacity of copper block by using the same

method mentioned in part one above, but this time the energy generated by the

electric heater is transferred to the vessel itself, water and copper block . Thus,

= = + + or = + + Hence,

= ( )…………….…….(4)

Here, subscript C signifies copper.

The copper mass appears in this equation should be given in the experiment.

Thus the only unknown in this equation is in .

, and it can be easily

evaluated. As it was mentioned in part one, the experiment should be repeated

several times using different parameters. You should always get the same value of

within the experimental error.

Again, to minimize the error in its value due to the idealistic the average mean

value of it is to be determined. Thus equation (4) should be adopted at least four

times on a minimum temperature interval of around three degree centigrade or

Kelvin. Then, a mean value of can be found from those four or more values.


[25]

Table (2): shows the main reading of part (2).


, ,

,= , , , .

1 2 3 4 5 6

=

Part three:

Once the previous two parts are performed, it is possible to experimentally

determine the heat capacity of aluminum (Al) block , , by using a method similar

to that mentioned in part two, but this time the energy generated by the electric

heater is transferred to the vessel itself, water and aluminum block instead of

copper block. Hence,

= = + +

or

= + +

From which,

= ( ) …………..….…….(5)


[26]

Here, the subscript A means aluminum. Thus, the only unknown in this

equation is in .

, that can be easily determined. And as it is mentioned in

parts one and two, the experiment should be repeated several times using different

parameters. And in each time you should always get the same value of within

experimental error.

However, to minimize the error in value due to the idealistic or any other

reason, the average mean value of have be determined. Thus equation (5)

should be adopted at least four times on a minimum temperature interval of around

three degree centigrade or Kelvin. Then, a mean value of can be found from

those four or more values.

Table (3): shows the main reading of part (3):


, ,

,= , , .

1

2

3

4

5

6

=


[27]

Experimental procedure:

1. Fill the vessel/calorimeter with appropriate amount of distiller water (=37

liters =37 kg). (Note: De-ionized water can have many dissolved substances

that do not result in ions, yet are present nonetheless, potentially altering any

future calculations. However, distilled water is very pure and contains only

water molecules, and this very reason it was used in this experiment.)

2. Clamp the thermometer through suitable hole in place so it rests in the

center of the water. Monitor and record the temperature of the water (before

and after switching on the electric heater).

3. Measure the initial temperature of the water, and record.

4. Switch on the electric stirrer to slowly and carefully stir the water.

5. Switch on the electric heater to heat the water inside the vessel.

6. Use the ammeter and voltmeter (together with a stop-watch) to find the

quantity of electrical energy put into the heater.

7. Allow a few minutes for the temperature of whole apparatus including water

to increase by at least three degree centigrade, then record the time taken to

reach this condition using the available stop watch.

8. Repeat the previous step as many times as you can in the time available

using certain deference in temperature. In each step the temperature and time

involved must be recorded, so as the voltage and amperes.


[28]

9. Using equation (3) and your collected data, calculate the thermal worth “k”

of the vessel. Record your results.

10. Weigh the mass of the metal sample [Figure (2)]. Record your

measurements in kg.

11. Once the thermal worth “ k ” of the vessel determined, you should continue

with the experiment. In this time you have to repeat all instruction above, but

after you have put the copper sample inside the vessel/calorimeter.

12. Again and to minimize the error due to the idealistic assumptions and to

eliminate sources of random and systematic errors, a mean average value of

the specific heat capacity of copper should be determine.

13. Using equation (4) and your collected data, calculate the specific heat of

Copper, record your results.

Using the percent error equation and the theoretical values of specific

heat, determine the percent error for the copper sample tested and see how

accurate you are in your measurements during the lab.

You can now compare your measured specific heat of copper to the

known specific heat of copper = . to see how accurate

you are in your measurements.


[29]

% =

………………………………………………………..…...(6)

A percent error of 1.05 % is acceptable given the equipment used. If

your rough value deviates by more than a factor of ten from the expected

one, then review your calculation and/or consider repeating the experiment if

possible.

14. Repeat all above instructions 1 to 13 excluding steps 8 and 12, while step 9should be done for aluminum (Al) instead of copper.

15. Using equation (5) and your collected data, calculate the specific heats of aluminum. Record your results.

16. Turn off the source of heat. 17. Compare your results found in this step with the standard value by

calculating the percentage errors using equation (6) , but in this time use the

specific heat capacity of aluminum instead of copper. Again a percent error

of 1.05 % is acceptable given the equipment used.

18. Leave this water in the calorimeter/vessel for a suitable time to cool down,

then empty it through the drain tap and dry it.


[30]

Discussion:

1. If the determined values of the specific heat capacities of copper or

aluminum blocks are differ from their standard values given in literature, in

your opinion what are the main source of errors?

2. Do substances that heat up quickly normally have high or low specific heat

capacity?

3. Discuss any unwanted heat loss or gain that might have affected your

results?

4. How do the specific heats of the samples compare with the specific heat of

water?

5. Some possible sources of error could have been in the thermometers not

being accurately read, the heat lost to the air was not factored in, also

possibly altering the results.


[31]

Objective:

To measure the specific heat ratio [the ratio of the heat capacity at constant

pressure ( ) to the heat capacity at constant volume ( )] or the heat capacity

ratio or adiabatic index of Oxygen ( ) by simulating an adiabatic expansion of

Oxygen contained in a pressurized vessel at room temperature.

Introduction:

The experiment was conducted in order to determine the adiabatic index of

Oxygen at room temperature by allowing the Oxygen in a pressurized vessel to

expand very briefly, during a quick opening and closing action of a large valve, so

that there is no opportunity for significant heat exchange and ensured that the


[32]

expansion could be considered as adiabatic. An adiabatic process is a process that

occurs without the transfer of heat between a system and its surroundings.

Adiabatic processes are primarily and exactly defined for a system contained by

walls that are completely thermally insulating; such walls are said to be adiabatic.

An adiabatic transfer is a transfer of energy as work across an adiabatic wall or

sector of a boundary.

Pressure readings were recorded before and immediately after the expansion.

The pressurized vessel contents were then allowed to come back to room

temperature and the final pressure was recorded. Pressure was the best quantity to

monitor, as compared to temperature or specific volume, and therefore, an equation

relating the adiabatic index to those three pressures had to be derived. The

derivation required the application of the First Law of Thermodynamics to the

adiabatic expansion process and the use of the Ideal Gas Law, assuming that

Oxygen behaves as an ideal gas. The relationship between the heat capacity at

constant volume and internal energy was also used in the derivation. An average

value for the adiabatic index was determined using the results from several trials

and the standard deviation and percentage error analyzed to verify the reliability of

the experiment.


[33]

Apparatus:

Figure (1) shows a typical apparatus used in performing this experiment. It

consists of an Oxygen tight vessel, which can be opened to the atmosphere through

a large bore ball valve at its left end. It also has connections to a high pressure

Oxygen cylinder through certain types of hose and valves, which allows its internal

pressure to be increased. The apparatus has three valves at the top of the Oxygen

cylinder (in reality there is no need to use three valves of any kind instead one

valve is quite enough). Anyhow these valves play major control on the flow of

Oxygen from the cylinder to the vessel. There are two pressure gauges, one of them

at the top of the vessel that shows the pressure in the vessel, while the other gauge

is at the top of the cylinder shows the pressure in the cylinder. There are numerous

different apparatuses that can be used to determine the adiabatic exponential index

of oxygen/gas/air. Their explanations are out the scope of the present experiment.

For more information however, student can visit lots website that are available in

the internet.


[34]

Figure (1): Typical perfect gas expansion apparatus.


[35]

Theory:

Consider a system that contains an ideal gas and is restricted to performing

only mechanical (P-V) work. Furthermore, assume that the system is thermally

insulated from the surroundings ( = . ). These conditions describe what is

called an adiabatic expansion. The heat capacity ratio may then be determined

experimentally using a two step process:

1. An adiabatic reversible expansion from the initial pressure to an

intermediate pressure ( , , ) ( , , ).

2. A return of the temperature to its original value at constant volume,

:

( , , ) ( , , )

If the system undergoes an infinitesimal change of state, the change in

internal energy will be given by:

= ………………………………..…(1)

Here, U denotes internal energy, T is absolute temperature and the subscript V

represents constant volume.

From the 1st Law of thermodynamics for an adiabatic process one can show that:

=

Since, Q = 0.0 = . , (adiabatic)


[36]

= …………………………….……(2)

For an ideal gas undergoing a reversible change of state, we have:

…………………..…….………….(3)

, = = , substituting into the above equation, yields:

……………………..……..….(4)

In aforementioned relationships, symbols W, P, V, m and R are respectively

represent work, pressure, volume, mass and gas constant.

Now, substituting equation (4) into Eq. (2), yields:

=

dividing both sides by ( ) gives:

= ………………………..……….….(5)

Since the expansion has an initial and final conditions associated with it

( , ) ( , ), we can integrate Eq. (5):

= …………….………………..(6)

Where the subscripts 1 and 2 are respectively denote initial and final (in present

experiment this state represent the intermediate) conditions of the process

considered.

If we assume that the specific heat capacity at constant volume , , is constant over

the temperature range (a reasonably good approximation for relatively small


[37]

changes in temperature) , then can be removed from the integral, and evaluation

of each integral in Eq. (6) yields:

= ………………...…(7)

To make further progress, recall that for an ideal gas, the state equation is applied at

the two ends of the process in the form:

= ………………………………………..…(8)

And therefore,

or

+

Hence,

+ ………. ……………....(9)

Now,

= ( ) =

Where, is the adiabatic exponential index and is the specific heat capacity at

constant pressure.

Substituting into Eq. (9) yields,

+ ( ) ( ) ……(10)

From which,


[38]

+ ………….…(11)

Hence,

= …………………….……..….(12)

Now the second half of the process (from state 2 to state 3, that is constant volume

process) is used to express the volume ratio in terms of measurable quantities (i.e.

pressure): First recall that: = = and because of pressures can be

measured directly in the experiment, one has to replace the ratio of volumes in Eq.

(12) with a ratio of pressures between the final and starting states (constant

temperature process 3-1) as:

= = = …………...……..….(13)

Substituting into Eq.(12) gives:

= …………………………..….(14)

= = …………....(15)

Using Eq. (15) , enable us can determine by measuring the initial pressure of

the gas, atmospheric pressure, and the resulting pressure after the expansion occurs.

Typical P-v and P-T diagrams of this experiment are shown in Figure (2).


[39]

Figure (2): Typical P - v and P – T diagrams of the perfect gas expansion for the present experiment.


[40]

Procedure:

By referring to Figure (1), the experimental procedure may be

summarized as follows:

1. Perform the general start up procedure. Make sure all valves are closed. 2. Before starting the experiment, the atmospheric pressure should be measured

using the barometer or any other suitable means. This is needed to determine the absolute pressure in the pressurized vessel.

3. Connect the Oxygen cylinder with the pressurized vessel through certain gauges, valves and hoses.

4. Close the large bore ball valve at the left end of the vessel, then open all three valves at the top of the Oxygen cylinder, so Oxygen will flow from the high pressure cylinder to the low pressure vessel. When the gauge pressure

on the vessel reached approximately , the Oxygen valves on the cylinder should be closed. A slight fall in pressure will be observed afterwards, accounted by the fact that the vessel contents were cooling to room temperature. The pressure was therefore allowed to stabilize and was recorded as the starting/initial pressure .

5. The large bore ball valve on the pressurized vessel is then opened and closed very rapidly, with a snap action, to allow amount of Oxygen to escape from the pressurized vessel to the surrounding, simulating a very quick expansion. While the opening-closing action was done, the minimum value of pressure indicated on the vessel was recorded as an intermediate pressure, .

6. Again, the vessel contents are allowed to return to the ambient temperature so the final pressure, , could be recorded..

7. The absolute pressures , and are then calculated by adding the value for atmospheric pressure to , , and respectively.


[41]

Results:

All experimental data and calculation of adiabatic index are to be represented in the following table,

Table (1): Experimental data with calculated values for adiabatic index.

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6

Atmospheric pressure,

,

Starting pressure (gauge) ,

,

Starting pressure (absolute) ,

,

Intermediate pressure (gauge) ,

,

Intermediate pressure (Absolute)

, ,

Final pressure (gauge) ,

,

Final pressure (gauge) ,

,

Calculated adiabatic index ,


[42]

The experimental data collected from each trial has to be laid out as in Table

(1) above. The relevant absolute pressures, P1, P2 and P3, have also been tabulated

and have been used in calculating the adiabatic index, . The formula used for this

calculation has been derived in the theory section and has to be evaluated for the

first trial using equation (15).The calculation of adiabatic index for Trial 1 should

be given here in details. While its values from other trial are not need to be shown

here. The above was repeated for all trials and their relevant values of that have

to be given in table should be at least up to four significant decimal figures (i.e.

1.4023).


[43]

Calculation of standard deviation and percentage error:

To see how accurate you are in your measurements during the laboratory, determine the standard deviation of the experiment’s, denoted by as:

= ( ) ………………………..(16)

Where, is the mean adiabatic index, it has a single value and N the number of

values in the sample.

Table (2) Working for calculation of .

No. ( ) ( ) 1 2 3 4 5 6 Total

Table (2) shows the values for the square of the differences and their sum.

The value of can therefore be easily evaluated using Eq. (16).

Then the % error can be calculated using the standard deviation and the

mean value of obtained as;

% = ………………………………(17)

A percentage error of less than 1.5% is relatively low and implies that the

values recorded were very precise.


[44]

Discussion:

1. Discuss any source of errors that could have affected the accuracy of your

results.

2. If there are some sources of errors, how do you think they can be revealed or

minimized their effects?

3. What are the main assumptions that you adopted in this experiment , state

whether they are realistic or not?.

4. Steady Figure (2) and then plot the T-s diagram of the experiment without

using numbers, in a way similar to that used in plotting Figure (2).


[45]

Objectives:

i) To demonstrate the performance of a heat pump in both heating and

cooling modes(how heat can be transferred from a cooler place to a hotter

place.

ii) To achieve an understanding of the Second Law of Thermodynamics as

applied to a heat pump in both heating and cooling modes.

Background:

Part of the argument that we cannot expect growth to continue indefinitely is

that efficiency gains are capped. Many of our energy applications are within a

factor of two of theoretical efficiency limits, so we can’t squeeze too much more

out of this orange. After all, nothing can be more than 100% efficient. Well, it turns

out there is one domain in which we can gleefully break these bonds and achieve


[46]

far better than 100% efficiency: heat pumps (includes refrigerators). Even though it

sounds like magic, we still must operate within physical limits, naturally.

Heat is the flow of energy between two things at different temperatures. A

heat pump, rather than creating heat, simply moves heat. It may move thermal

energy from cooler place into the warmer/hotter place, or from the cooler

refrigerator interior into the ambient air. It pushes heat in a direction counter to its

normal flow (cold to hot, rather than hot to cold). Thus the word pump.

It has been estimated that at least 85% of the refrigeration processes in use

today are powered by vapor compression systems. The applications embrace many

varied disciplines including catering, public health, architecture, food storage,

transport, food processing, …etc.

Safety Features:

Refrigerant 12 used in the heat pump is incombustible and non-toxic so that

leakages of refrigerant arising from an accident or from student abuse will not

cause any harm (except perhaps to the ozone layer).

To eliminate the possibility of an excessive refrigerant pressure from

occurring in the condensing coil a differential pressure switch is fitted in the

refrigerant circuit. The switch will isolate the compressor drive motor. The

maximum condenser pressure is marked on the dial of the pressure gauge. The

compressor motor is protected by thermal overload relays and a thermal switch.


[47]

Should the compressor be switched on under conditions of high load e.g. a high

compression ratio across the compressor, the motor starting current will also be

high and there is a risk of the compressor and motor being stalled. Under these

conditions the relay will go open circuit and isolate the motor. To protect the resin

insulation of the motor windings the internal temperature of the compressor casing

must not exceed the fusion temperature of the resin. The purpose of the thermal

switch attached to the inside of the casing is to isolate the motor under conditions

of excessive casing temperature. In both situations described above, allow the

compressor to cool before attempting to re-start.

There is no moving part associated with the apparatus, so there is no kinetic

energy hazard. The compressor is the only component of apparatus that will

become hot. It can exceed ) and therefore is a thermal energy hazard. Avoid

touching the compressor while the apparatus is in operation. The copper tubes and

water piping can become hot, but can be touched and are not a significant thermal

hazard. If any electrical components of the apparatus overheat and cause the

apparatus to become hot or produce smoke then immediately turn off the apparatus.


[48]

Theory:

Referring to Figure (1a,b,c), let’s imagine we have a cold environment at an

absolute temperature and a hot environment at an absolute temperature . Cold

and hot are relative terms here: the “hot” environment could be uncomfortably cool

, it just needs to be hotter than the “cold” environment.

Inevitably, we have to run some machinery to affect this flow of heat against the

natural gradient (pushing heat uphill). Let’s call the amount of work (energy)

needed to force this thermal extraction, . That mechanical/electrical/whatever

energy also ultimately turns to heat, and if we cleverly send this additional energy

to the hot place, we end up pumping an amount of heat into the hot environment is

just the sum of two arrows indicated in Figure (1) as:

) + = + …………….....…...(1)

Where,

= ( ) = ( ) = ( )

……………………….…..(2)

and

= ( ) = ( ) = ( )

…………………………..(3)

However, the work used to pump heat from low temperature region to a high

temperate one is ,W, which is less than that produced electrically, . This is


[49]

mainly because the process is not a reversible due to friction between movable

parts of the compressor. Thus,

= ……………………………………………...(4)

Now, for a heat pump [Figure (1a and b)], the maximum value of the is

given by:

( ) = …………………….………..………....(5)

If, instead, you want to cool something down [refrigeration shown in Figure (1c)],

the maximum COP for a refrigerator is how much heat is removed from the cold

zone divided by the input work as:

( ) = = ……………………..….…...(6)

Since, is taken out of the system, thus is should be negative.

While the electrical work input is determined by recording the watt meter reading

(if it is integrated) or else by measuring the time in second and the electric voltage

and current as,

= , ……………………….…(7)

Now, since the electrical work is greater than the work needed to push the heat

from the cold sink to the hot one, therefore, there should be a certain value of

mechanical efficiency for the compressor which may be given by:

% = ………….…………………………...(8)


[50]

Figure (1): Schematic diagram of a heat pump, which takes in

energy from a cold reservoir and expels energy to a hot

reservoir. Work W is done on the heat pump. A refrigerator

works the same way.


[51]

Apparatus overview:

The apparatus is delivered complete, Figure (2), charged with refrigerant,

ready to operate with the minimum of preparatory work. A single phase electricity

supply, a water and thermometers [Figure (3)] are the only external facilities

required.

It consists of two water/refrigerant heat exchangers (left water and

refrigerant and right water & refrigerant heat exchangers). Either of the two heat

exchangers (left and right) can operate as an evaporator while the other operates as

a condenser. The component that switches the left and right heat exchangers as an

evaporator/condenser is called metering/expansion device [Figure (4)].

The apparatus also consists of a compressor. The compressor is connected with an

accumulator (suction line accumulator)to prevent the compressor from taking in

liquid refrigerant.

Figure (5) shows different types of mechanical heat pumps. Most of them

can be used to study the coefficient of performance of heat pump.


[52]

Figure (2): Picture of mechanical heat pump used in the experiment.


[53]

Figure (4): Metering or expansion device/capillary tube.

Figure (3): Types of thermometers that can be used in the experiment.


[54]

Figure (5): Different types of heat pumps.


[55]

Cycle of operation:

The method of operation of the heat pump can be explained by refereeing to

the schematic diagram in Fig.(6). The working fluid or heat transfer medium is the

refrigerant Dichlorodifluoromethane (Freon 12 or R-12) and the heat source and

heat sink is water.

The sealed compressor is operating on 220V- 50Hz acts as an external

energy source. The super-heated refrigerant is compressed and pumped through

insulated copper pipes to the nickel-plated copper condensing coil at pressure P1 and temperature T1. The coil is immersed in cold water in the transparent plastic

condensing tank. The refrigerant pressure remains substantially constant at P1 while

passing through the coil, but falls in temperature from T1 to T2, losing its super-

heat and all of its latent heat or heat of change of phase to the water. It reaches the

expansion device as a sub-cooled liquid still at pressure P1 and temperature T2. The

function of the silica gel drier is to eliminate water, not liquid refrigerant. The pipe

work here is nickel plated copper with brass fittings. The refrigerant now expands

through the expansion device/ valve/ capillary tube [Figure (4)] where it expands

to a lower pressure P2 and commences to boil. The boiling temperature or wet

vapour temperature T3is measured before the refrigerant passes through the nickel-

plated copper evaporator coil. This coil is also immersed in cold water in the

transparent plastic evaporating tank. During its passage through the coil the

refrigerant absorbs from the water the latent heat of evaporation or heat of change

of phase, and in addition may receive some further heat to superheat the refrigerant

to temperature T4. The boiling or evaporation process occurs at constant pressure

P2. The super-heated vapor refrigerant leaves the evaporator to return to the

compressor through insulated copper pipes to begin the cycle again.


[56]

Water temperatures are measured by standard digital/mercury thermometers

[Figure (3)] in both evaporator and condenser reservoirs. While pressures are

measured by refrigeration quality pressure gauges. Their values are not need to be

measured in this experiment because they are not used in the calculations.

Electrical power input to the heat pump compressor is measured by an integrating a

watt/volt and ampere meters where power expended is a direct function of volts ,

amperes and time.

Figure (6): Apparatus schematic diagram.


[57]

Set up and instruction/Procedure:

The following order of instructions should be followed:

1. Stand the unit on a firm even surface higher than the water drain which is to be used using siphoned method.

2. Fill both the evaporator and condenser reservoirs with the necessary

amount of distiller water (= . = = . ) or

to the marked level, such that the evaporator and condenser coils are

completely submerged. Carefully stir the water in the reservoirs.

3. Position digital/mercury thermometers in the right position in accordance with the range.

4. Read and record the initial temperatures of water in both tanks. 5. Plug the lead from the unit into the laboratory socket. Do not switch

on at this stage.

6. Switch on the mains electricity supply and switch on the compressor. 7. Wait for at least ten minutes, before taking the second reading of the

water temperature at both reservoirs. At the same time record also the

watt-hour meter/volt and ampere meter reading and the time.

8. Substantial change of conditions will require approximately 15-20

minutes to obtain equilibrium. Thus, the last step should be repeated

at least three times to get an average values of the results with an

interval time of 15 minutes.

9. When the experiments have been completed, the electricity should be first switched off and then empty the water tanks with any suitable

method .


[58]

Readings and calculations:

The terms that should be read or measured and recorded are:

1. Mass of distiller water in both evaporator , , and condenser reservoir,

, .

2. Initial evaporator and condenser tanks water temperature ( ) in

Kelvin for each trail.

3. Final evaporator and condenser tanks water temperature( ) in

Kelvin for each trial.

4. Time, in second.

5. Take specific heat capacity value of water constant of ..

.

6. Record the reading of the volt and ampere/watt-hour meters for each trial.

7. Determine the ( ) ( ) using Eq.(5) and Eq.(6) respectively.

8. Determine the efficiency of the compressor of the heat pump using Eq.(7).

9. Collect data as shown in Tables (1) and (2).


[59]

Table (1): Readings data.

Trial 1 Trial 2 Trial 3 = ,

, , , ,

voltage, V current, A

Time, ,

,.

Table (2): Results .

Trial 1 Trial 2 Trial 3 Average value

, kJ

, kJ

,

,

( )

( )

%


[60]

Discussion:

1. Discuss the effect of temperature difference between the cold source and

the hot sink on the coefficient of performance of the heat pump on both

heating and cooling modes.

2. Analyze the results, indicating all factors which may affect the efficiencies

or COP of each device. Then show that: = + 1.

3. Discuss the differences between heating and cooling modes of the heat pump.

4. Discuss the benefits of using heat pumps in heating compared with using other electric heating devices.

5. Discuss the results shown in this Figure:

Figure (7): Relationship between COP and the temperature of hot reservoir.


[61]

Objective:

1. To find out the heat of combustion (Calorific Value) of an organic compound

using an adiabatic bomb calorimeter.

2. To demonstrates the First Law of Thermodynamics for a control mass.

3. To gain a better understanding of the working principles of the bomb

calorimeter

Introduction:

The bomb calorimeter which represents the bomb and the water bath is a

classic adiabatic device used for the measurement of calorific value at constant

volume of fuel oils, gasoline or petrol, coke, coal, combustion waste, foodstuffs

and building materials etc. Bomb calorimeter is also used for energy balance study

in ecology and study of a non-material such as ceramics. Bomb calorimeter is

helpful to study thermodynamics of common combustible materials. Basically, this

device burns a fuel sample and transfers the heat released in a chemical reaction


[62]

into a known mass of water. Continuous stirring ensures that heat is distributed

evenly in the calorimeter. The bomb is immersed in a weighted quantity of water

and surrounded by an adiabatic shield that serves as a heat insulator. From the

weight of the fuel sample and temperature rise of theater, the calorific value can be

calculated. The calorific value obtained in a bomb calorimeter test represents the

gross heat of combustion per unit mass of fuel sample. This is the heat produced

when the sample burns, plus the heat given up when the newly formed water

vapour condenses and cools to the temperature of the bomb. Determining calorific

values is profoundly important; fuels are one of the biggest commodities in the

world, and their price depends primarily on their heating/calorific value.

General description of the bomb calorimeter:

Referring to Figures (1) and (2) the unit comprises the calorimeter, a

calorimeter vessel, an outer double walled water jacket, control unit to switch

on/off the stirrer and the ignition device, a Liquid-in-Glass thermometers or a

Beckman differential thermometer or digital thermometer, a magnifying glass is

required for reading liquid-in-glass thermometers to one tenth of the smallest scale

division. This shall have a lens and holder designed so as to introduce no

significant errors due to parallax.

Continuous stirring for 10 min shall not raise the calorimeter temperature more

than 0.01°C starting with identical temperatures in the calorimeter, room, and


[63]

jacket. The immersed portion of the stirrer shall be coupled to the outside through a

material of low-heat conductivity. The apparatus has also charging unit with

pressure gauges to facilitate the charging of the calorimeter with oxygen. The

particular features of the calorimeter bomb are the method of sealing and the

method of ensuring ignition.

The calorimeter vessel and outer jacket wall are manufactured in stainless

steel, and with all outer surfaces highly polished (its size shall be such that the

bomb will be completely immersed in water when the calorimeter is assembled).

The sides, top, and bottom of the calorimeter vessel shall be approximately 10 mm

from the inner wall of the jacket to minimize convection currents. Mechanical

supports for the calorimeter vessel shall provide as little thermal conduction as

possible.

The calorimeter bomb is a container made of stainless steel that must be

capable of withstanding a hydrostatic pressure test of 25-30 MPa at room

temperature without stressing any part beyond its elastic limit. It is sealed by a

screw top. The bomb is charged with oxygen through the filling valve. This bomb

is introduced inside a calorimeter vessel made of stainless steel that is filled with

water, and at the same time it is introduced inside a double walled water jacket. The

rod of the calorimeter supports a metallic crucible. The calorimeter bomb, Figure

(3), is a 342 ml pressure vessel with a removable head and a closure that can be


[64]

sealed by simply turning a knurled cap until it is hand tight. Sealing forces develop

internally when the bomb is pressurized, but after the pressure has been released

the cover can be unscrewed and the head lifted from the cylinder. Two valves with

replaceable stainless steel bodies are installed in the bomb head. On the inlet side,

there is a check valve that opens when pressure is applied and closes automatically

when the supply is shut off. On the outlet side, gases are released through an

adjustable needle valve passing through a longitudinal hole in the valve stem and

discharging from a short hose nipple at the top. Gas flow through the outlet valve is

controlled by turning a knurled adjusting knob. A deflector nut on the inlet passage

diverts the incoming gas so that it will not disturb the sample. A similar nut on the

outlet side reduces liquid entrainment when gases are released.

The bomb contains the fuel sample to be burned, is hermetic to the gas by

closing the filling valve and its cover. Combustion is started through a thin wire

that is red hot-heated up momentarily due to the passing of an electrical current that

flows through an isolated terminal and the rod, which is electrically connected to

the cover. The water in the calorimeter vessel is agitated automatically with a

stirrer driven by a small motor with one rod and two blades (330 rpm). The top of

the double walled jacket is closed with a cover that has some orifices. A Beckman

thermometer to measure the temperature of the calorimeter vessel passes through

one of these orifices. Other orifices are used to fasten the jacket to the cover. Also,


[65]

one of these holes is used to insert the wire that supplies the electric current to the

rod. The unit includes a control unit that switches on/off the stirrer and the ignition

device through the heating up of the thin wire, a load unit with pressure gauges to

make the filling with oxygen of the calorimeter easier and a magnifying glass to

magnify the Beckman’s thermometer reading accuracy.

To perform the experiment, it is also needs a balance capable to weigh the

sample to the nearest 0.0001 g. It should be checked periodically to determine its

accuracy. Sample Holder, shall be an open crucible of platinum, quartz, or

acceptable base-metal alloy. Base-metal alloy crucibles are acceptable, if after a

few preliminary firings, the weight does not change significantly between tests.

Ignition Wire, shall be 100 mm length and 0.16 mm diameter nickel-chromium

alloy or iron wire. Platinum or palladium wire, 0.10 mm diameter, may be used,

provided constant ignition energy is supplied. The length, or mass, of the ignition

wire shall remain constant for all calibrations and calorific value determinations.

Ignition Circuit, for ignition purposes shall provide 6 to 16 V alternating or direct

current to the ignition wire. An ammeter or pilot light is required in the circuit to

indicate something when current is flowing. A step-down transformer, connected to

an alternating current lighting circuit or batteries, may be used.


[66]

Figure (1): The apparatus used in the experiment.


[67]

Figure (2): Different types of bomb calorimeter.


[68]

Figure (3): Different parts of the bomb and its sections.


[69]

Theory:

Consider a system that consists of the sample (s), the bomb (b), and the

calorimeter water (w) and bucket. The sample is contained within the bomb, which

is immersed within the water inside the bucket. Applying the First Law of

Thermodynamics to this system gives,

= ………………………………….……..(1)

Where, = the change in internal energy of the system , = the heat

transfer at constant volume and = work performed on or by the system

Since there is no work crossing the system boundary, = .and if the entire

system is adiabatic, the heatof combustion is used to change the temperature of the

water and the bomb, thus:

= = [( ) + ( ) ] …..…(2)

Here, m denotes mass quoted in kg.

Since, the temperature range is not high, therefore, specific heats of the bomb and

water may be assumed constant. Hence,

= [( ) + ( ) ] ………………………..(3)

Where, represents the total temperature difference between the final and

initial temperatures of the system.


[70]

Water equivalent of bomb calorimeter, ( ) , can be found out for

particular bomb calorimeter by first doing an experiment based on known fuel

sample whose calorific value is already known.

The heat transfer, ,is also equal to the heat of combustion of the sample

= ( ) .

Here, subscript f denotes fuel sample and CV means calorific value of fuel/energy

release by a unit quantity of fuel when it is burnt.

The wire used as a fuse for igniting the sample is partly consumed in the

combustion. Thus the fuse generates heat both by the resistance it offers to the

electric firing current, and by the heat of combustion of that portion of the wire

which is burned. It can be assumed that the heat input from the electric firing

current will be the same when standardizing the calorimeter as when testing an

unknown sample, and this small amount of energy therefore requires no correction.

However, it will be found that the amount of wire consumed will vary from test to

test, therefore a correction must be made to account for the heat of combustion of

the metal. The amount of wire taking part in the combustion is determined by

subtracting the length of the recovered unburned portion from the original length of

10 cm. The correction is then computed for the burned portion by assuming a heat

of combustion of . or . (=2.3 calories per cm). for Parr 45C10


[71]

(No. 34 B & S gauge “Chromel C”) wire, or . (=2.7 calories per cm)

for No. 34B & S gauge iron wire. Thus,

( ) + ( ) = [( ) + ( ) ] ……….….(4)

Where, the subscript “ fw “ means fused wire.

From Eq.(4), we can get:

= ( ) =[( ) ( ) ] ( )

…………...…(5)

Here, m quoted in kg, CV in . which represents the difference

between the maximum temperature, , and the ignition temperature, , CV

denotes the calorific value of fuel is quoted in , while HCV represents higher

/gross calorific value which is quoted in .

Gross and net heats of combustion:

If, after combustion, the water originally contained in the fuel and the water

formed from the burning of the hydrogen in the fuel are present in liquid form, the

quantity of heat liberated is characterized by the high/gross, heat value .

However, if the water is in the form of vapor, the heat liberated is characterized by

the low, or net, heat value . The relation between the high and low heat values

is given by the equation,

= ( + ) …………………………(6)


[72]

Here, denotes summation of water originally contained in the fuel

and condensed water vapour inside the bomb during the experiment, in

percent of the total weight; H is the amount of hydrogen in the fuel, in

percent of the total weight; and k is a constant equal to 25 kJ/kg. It is

obvious that the above equation requires a knowledge of the hydrogen

content of the sample. If the hydrogen content is known, the net heat of

combustion can be calculated from Eq.(6). An alternative and easy relation

between the higher/gross and lower calorific value of fuel combustion can be

adopted. Again if, after combustion, the water originally contained in the fuel

and the water formed from the burning of the hydrogen in the fuel are present

in liquid form as:

= …………………………....(7)

Where, the number 2442 represents the heat of vaporization (enthalpy of

evaporation) given up when the newly formed water vapor produced by oxidation

of hydrogen is condensed and cooled to the temperature of the bomb.


[73]

The reading:

The reading data should be tabulated as:

Time, sec , T, , , , , , 0

15 30 45 60 75 90

105 120 180 240 300

= = , where , denotes the maximum temperature in Table (1): Experimental data with calculated values for temp. difference.


[74]

Calculation of standard deviation and percentage error:

To see how accurate you are in your measurements during the laboratory ,an

average value for the calorific value of fuel sample was determined using the

results from several trials and the standard deviation and percentage error analyzed

to verify the reliability of the experiment as follow:

= =

Standard deviation of the mean of = = [ ]( )

…………………………………..……...(8)

Where, are the values of from different trial and N is the number of trial.

Table (2): Working for calculation of .

Trial (N) , ( ), ( ) ,

7 8 9 10

Total


[75]

Table (2) shows the values for the square of the differences and their sum.

The value of standard deviation , , can therefore be easily evaluated using Eq.

(8).

Then the % error can be calculated using the standard deviation and the

mean value of obtained as;

% = ………………………..………(9)

Note that in this experiment the number of trial is quite small and thus the

error estimate may not be very accurate. However, the general laboratory manual of

the apparatus may give more and better information about the acceptable value of

error.


[76]

Procedure of bomb calorimeter experiment:

( Please follow strictly the procedure listed below and observe the

safety precautions highlighted ).

1. Prepare the fuel sample by placing it in a capsule and weighing on a balance

(sensitivity of the balance: ±0.0001g). Ensure that the weight of the fuel does

not exceed 1.1 g. Note down the weight of the fuel sample, . Figure (4)

shows typical shapes of fuel samples that can be used with the bomb

calorimeter.

2. Remove the lid and place it on the ring stand. Check to see that the bucket is

resting properly in the jacket, noting the four pegs on the bottom of the jacket,

which hold the bucket in place.

3. To absorb the combustion products of sulphur and nitrogen from their

present in the oxygen mixture2 ml of water is poured in the bomb.

4. Carefully place the charged bomb in the bucket, noting that it rests on the

raised circular area on the bottom of the bucket.

5. Set the bomb head on a suitable support stand and attach a 10 cm long 0.16

mm diameter Nickel-Chrome fuse wire and weight it, as shown in Figure

(3). Bend the loop of fuse wire down just above the fuel sample. Position the

wire so that it almost touches the surface of the pellet (about 1 mm

separation) and it does not touch the cup. It will also be necessary to weigh


[77]

any unburned wire after combustion since this is an important factor in the

calculations.

6. Connect the ignition wire to the terminal socket on the bomb head. Prepare 2

L of water that is between . To obtain this, start with deionized

water and add warm tap water or ice chips, as needed. Fill the bucket with the

. of water. Be careful not to spill it. Make sure that the

thermometer can measure the initial temperature. Note that if the initial

temperature of the water bath is too high, you may not be able to measure the

temperature increase because the final temperature might over the scale of the

thermometer. Atypical temperature increase is around 4 C.

7. Care must be taken not to disturb the sample when moving the bomb head

from the support stand to the bomb cylinder. Be sure that the contact ring is in

place above the sealing ring and that the sealing ring is in good condition; then

slide the head into the cylinder and push it all the way down. Set the screw cap

on the cylinder and turn it down firmly by hand. Do not use a wrench or

spanner on the cap. Tightening with hand should be sufficient to secure a

tight seal.

8. Press the fitting on the end of the oxygen hose into the inlet valve socket and

turn the union nut finger tight. Close the valve on the filling connection; then

open the oxygen tank valve not more than one-quarter turn. Open the filling


[78]

connection control valve slowly and watch the gauge as the bomb pressure

rises to the desired filling pressure (25-30 atmospheres); then close the

control valve. If the bomb is filled too quickly you can blow your sample out

of the sample cup. Warning: Do not exceed the specified pressure! Release

the residual pressure in the filling hose by pushing downward on the lever

attached to the relief valve. The gauge should now return to zero. If too much

oxygen should accidentally be introduced into the bomb, do not proceed with

the combustion. Detach the filling connection; exhaust the bomb; remove the

head and reweigh the sample before repeating the filling operation.

9. Set the bucket in the calorimeter; attach the lifting handle to the two holes in

the side of the screw cap and lower the bomb into the water with its feet

spanning the circular boss in the bottom of the bucket. Handle the bomb

carefully during this operation so that the sample will not be disturbed.

Remove the handle and shake any drops of water back into the bucket; then

push the two ignition lead wires into the terminal sockets on the bomb head

using a tweezers as shown in Figure (3), being careful not to remove any

water from the bucket with the fingers.

10. Set the cover on the jacket with the thermometer facing toward the front. Turn

the stirrer by hand to make sure that it runs freely; then slip the drive belt onto

the pulleys and start the motor.


[79]

11. Let the stirrer run for at least 5 minutes to reach equilibrium before starting a

measured run. At the end of this period start the timer, and read and record the

temperature at one-minute intervals for 5 min. At the start of the 6th minute,

stand back from the calorimeter and fire the bomb when prompted by

pressing the ignition button and holding for 5 seconds to ensure complete

burning of the fuel (until the light goes out if there is a signal light). Normally

the light will glow for only about half a second, but release the button within 5

seconds. Take note of the value that can be found on the calorimeter jacket.

Caution: Do not have the head, hands or any parts of the body over

the calorimeter when firing the bomb; and continue to stand clear for 30

seconds after firing.

12. The bucket temperature will start to rise within 20 seconds after firing. This

rise will be rapid during the first few minutes; then it will become slower as

the temperature approaches a stable maximum as shown by the typical

temperature rise curve shown in Figures(5) and (6). Take the first

temperature reading at and continue to do so every for a period of 2

min. The temperature should be read to the nearest . . The reading lens

is not required at this point.

13. After this two-minute period record the temperature to the nearest tenth

( . ) with the aid of the reading lens at one-minute intervals


[80]

until the difference between successive readings is zero (or perhaps becomes

negative). This will take approximately five minutes. Accurate time and

temperature observations must be recorded to identify certain points needed to

calculate the calorific value of the sample. Usually the temperature will reach

a maximum and then drops very slowly as shown in the typical Figure (Figure

(5) or (6)).

14. The last part of the previous step is not always true since a low starting temperature may result in a slow continuous rise without reaching a

maximum. As stated above, the difference between successive readings must

be noted and the readings continued until the rate of the temperature change

becomes constant over a period of 5 minutes.

15. After the last temperature reading, stop the motor, remove the belt and lift the cover from the calorimeter. Wipe the stirrer with a clean cloth and set the

cover on a support stand. Lift the bomb out of the bucket; remove the ignition

leads and wipe the bomb with a clean towel.

16. Open the knurled knob on the bomb head to release the gas pressure before attempting to remove the cap. This release should proceed slowly over a

period of not less than one minute to avoid entrainment losses. After all

pressure has been released, unscrew the cap; lift the head out of the cylinder

and place it in the support stand. Examine the interior of the bomb for soot or

other evidence of incomplete combustion. If such evidence is found, the test

will have to be discarded.

17. Remove all unburned pieces of fuse wire from the bomb electrodes; straighten them and measure their combined length in centimeters or weigh them.


[81]

fuel sample fuel sample fuel sample

Subtract this length or weight from the initial length of 10 centimeters or

weight and enter this quantity on the data as the net amount of wire burnt.

18. On completion of the experiments, students are required to wash the bomb set thoroughly with soap and water. Keep the bomb set dry and clean with the

provided wiping tissue.

Figure (4): Fuel samples used with the bomb calorimeters..


[82]

Possible problems:

1. If there is a continuous escape of gas from the bomb head connections once the

oxygen tank valve is unscrewed the bomb is defective and should not be used.

2. If the bomb will not hold pressure and you can hear oxygen escaping around

the vent cap, then the cap is not sealed tightly enough. Tighten down the screw

cap by hand again and try to pressurize the bomb. If you are not successful after

one or two attempts check the bomb thoroughly – do not fire a leaking bomb!

3. If too much oxygen should accidentally be introduced into the bomb, do not

proceed. Unscrew the oxygen tank connection and exhaust the bomb in the

hood. This can be done by opening the vent cap. Reweigh the sample before

repeating the filling procedure.

4. If there is no significant temperature rise ( ). Check to see

that the ignition unit is plugged in and all electrical connections are tight. Ignite

the bomb again.

5. If this does not solve the problem it will be necessary to turn off all electrical

connections. Then place the bomb in the hood and open the valve to release the

pressure. If the pellet is still intact but fuse wire is partially burned re-wire the

bomb, weigh the pellet again, charge the bomb and ignite it again. If the pellet

is only partially burned replace it and start again.


[83]

Plotting the data:

Plot the (temperature, , vs time, ) data for each run as illustrated in a typical

Figure (5) or (6). Note the important points in the Figure (5) denoted by ’ i ’, ’ a ’,

’ b ’, ’ c ’, and ’ f ’. The point ’ a ’ denotes the time of firing of the bomb, ’ b’ the

position where the temperature reaches 60 % of the total change, and ’c’ the time

of maximum temperature (i.e. end of the reaction).While points ’ i ’ and ’ f ’

denote the initial and final points of measurement, respectively. The accuracy for

reading the points should be to nearest 0.1 min. A simple approach for obtaining

the temperature rise would consist of subtracting the maximum temperature, ,

and the ignition temperature, as shown in Table (1).


[84]

Figure (5): A typical relation between temperature and time of the calorimetric process with all important points.

Figure (6): A typical relation between temperature and time of the calorimetric process.

1435 - الجامعة التكنولوجية · 2018-01-19 · observed and boyle’s law is...

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