ABSTRACT
The Perfect Gas Expansion Apparatus (Model: TH 11) is use in conducting this experiment. There are seven experiments which are Boyle’s Law experiment, Gay-Lussac Law experiment, Isentropic Expansion Process, Stepwise Depressurization, Brief Depressurization, Determination of ratio of volume, and Determination of the ratio of heat capacity. The purpose on carrying out these experiment are to make us more familiarize with several fundamental thermodynamic processes, to determine the relationship between pressure and volume of an ideal gas, to compare the experimental results with theoretical results , to determine the relationship between pressure and temperature of an ideal gas, to demonstrate the isentropic expansion process, to study the response of the pressurized vessel following stepwise depressurization, to study the response of the pressurized vessel following a brief depressurization, to determine the ratio of the heat capacity and to determine the ratio of volume and compares it to the theoretical value. The general start-up procedure was carried out in all of these seven experiments. Firstly, the equipment was connected to the single phase power supply and then switched on the unit. After that, all valves were fully opened and the pressure reading on the panel were checked to make sure that the chambers are under athmospheric pressure. Then, all the chamber were closed. The pipe were connected from compressive port of the pump to the pressurized chamber or connected from the pipe from vacuum port of the pump to vacuum chamber and the apparatus was ready to be used. Besides, the procedures for every experiment were carried out as follows from the manual. After that, the general shut-down procedures were also carried out after finishing all of the experiments. First of all, the pump was switched off and the both pipes were removed from the chambers. The valves were fully opened to release the air inside the chambers and the main switch and the power supply were switched off. The procedure must be done as follows as in the manual to prevent the repeating in doing the experiment for few times. For the Boyle’s Law experiment the PV must be calculated otherwise for the determination determination of ratio of volume experiment, the ratio of volume were calculate and the ratio of heat capacity also must be calculate in the determination of the ratio of heat capacity experiment.
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INTRODUCTION
The Perfect Gas Expansion Apparatus (Model: TH 11) is a self-sufficient bench top unit designed to allow us (students) familarize with several fundamental thermodynamics processes. Demonstration of the thermodynamics processes is performed with air forsafe and convenient operation. The Perfect Gas Law Apparatus is customarily designed and developed to provide students a comprehensive understanding of First Law of Thermodynamics, Second Law of Thermodynamics and relationship between P-V-T. The Perfect Gas Expansion Apparatus enable us to have a good understanding in energy conservation law and direction in which the processes proceed. The Perfect Gas Expansion Apparatus comes with one pressure vessel and one vacuum vessel. Both vessels are made of glass tube. The vessels are interconnected with a set of piping and valves. A large diameter pipe provides gradual or instant change. Air pump is provided to pressurize or evacuate air inside the vessels with the valves configured appropriately. The pressure and temperature inside the vessels v essels are monitored with pressure and temperature sensors and clearly displayed by digital indicator on the control panel. With an optional automatic data acquisition system, the modern version of a classic Clement and Desormes experiment can be conducted as pressure and temperature changes can be monitored continuously with the computer. The Perfect Gas Expansion Apparatus comes complete with the pressure vessel of 25L, vacuum vessel of 12.37L and bothe are made of glasses. The temperature sensor with the 0
range of 0-100 c and pressure sensor with the range of ± 160kPa that mounted on the top of vessels. There are seven experiment were conducted during this session which are Boyle’s Law experiment,
Gay-Lussac
Law
experiment,
Isentropic
Expansion
Process,
Stepwise
Depressurization, Brief Depressurization, Determination of ratio of volume, and Determination of the ratio of heat capacity. These experiments were carried out to make us more familiarize with several fundamental thermodynamic processes, to determine the relationship between pressure and volume of an ideal gas, to compare the experimental results with theoretical results , to determine the relationship between pressure and temperature of an ideal gas, to demonstrate the isentropic expansion process, to study the response of the pressurized vessel following stepwise depressurization, to study the response of the pressurized vessel following a brief depressurization, t o determine the ratio of the heat capacity and to determine the ratio of volume
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and compares it to the theoretical value. The reading of pressure and temperature were recorded shown on the panel. The perfect gas expansion apparatus (figure 1):
Figure 1. model: TH 11 OBJECTIVES
There are several objectives for carrying this experiment which are: 1. To make us more familiarize with several fundamental thermod ynamic processes. 2. To determine the relationship between pressure and volume of an ideal gas.(experiment1) 3. To compare the experimental results with theoretical results. (experiment 1) 4. To determine the relationship between pressure and temperature of an ideal gas.(experiment 2) 5. To demonstrate the isentropic expansion process.(experiment 3) 6. To study the response of the pressurized vessel following stepwise depressurization (experiment 4) 7. To study the response of the pressurized vessel following a brief depressurization. (experiment 5) 8. To determine the ratio of volume and compares it to the theoretical value. (experiment 6) 9. To determine the ratio of th eheat capacity. (experiment 7)
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THEORY
The perfect gas is also known as ideal gas. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and which there are no intermolecular attractive forces. An ideal gas is also an imaginary substance taht obeys the ideal gas equation of state. In 1662, Robert Boyle, an Englishman, discovered in the experiment taht the pressure of gases is inversely proportional to their volume in avacuum chamber. In 1802, J. Charles and J. Gay Lussac, Frenchman, determine that at low pressure the volume of a gas is proportional to its temperature. That is, P = R (
)
(1)
Where the constant of proportionality R is called the gas constant and is different for each gas. Equation (1) is called the ideal gas equation of state. Any gas that obeys this law is called an ideal gas. In ideal gas equation of state, P is the absolute pressure, T is the absolute temperature and V is the specific volume. The ideal gas equation of state can be written in other form: V = mv, thus PV = mRT
(2)
By writing equation (2) twice for fixed mass and simplifying, the properties of ideal gas at two different sataea are related toeach other by:
(3)
=
It has been experimentally observed that ideal gas relation closely approximately the P-v-T behaviour of real gases at low density. At low pressure and high temperature, the density of gas decreases, and the gas behaves as an ide4al gas under these conditions. Besides of ideal gas equation of state, the ideal gas also oneys the following law: a. Boyle’s Law b. Charles’s Law c. Gay-Lussac’s Law The Boyle’s Law is a special law that describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system. The mathematical equation for Boyle;s Law is: PV = k (4) Where
P = pressure of the system V = volume of the gas K = constant vlue representative of the pressure and volume of the system
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As long as the temperature remains constant at teh same value , the same amountof energy given to the system persists throughout its operation and therefore,theoretically, the value of k remain constant. By forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure p must decrease proportionally. On the contrary, reducing the volume of the gas will increase the pressure. The Boyle’s Law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The equation below and after expansion process, where the temperature before and after the process are the same. p1V1 = p2V2
(5)
Charles’s Lawis a gas law which states that: At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin) increases or decreases. The formula for this law is: (6)
Where V = volume of the gas T = temperature of the gas (measured in Kelvin) K = constant To maintain the constant, k, during the heating of gas at fixed pressure, the volume must icrease. On the other hand, cooling the gas decreases the vlume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure.
(7)
As a conclusion, when the temperature increases, the volume of the gas increases. Gay Lussac’s Law states that the pressure of a fixed quantity of gas at costant temperature is directly proportional to its temperature in Kelvin. The formula is: (8)
Where P = pressure of the gas T = temperature of the gas (measured in Kelvin) K = constant The temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particle collide with the container walls more rapidly, and therefore exerting increased presure. In order to coompare the same substance under two different sets of condition, the law can be written as:
5
(9)
APPARATUS
The Perfect gas Expansion Apparatus.
Valve (V02) Valve
Electrode Pressure Relief Valve Vacuum
Pressure
1. Perfect gas expansion apparatus (model: TH 11)
METHADOLOGY General start-up (apparatus model: TH 11) 1. The equipment was connected to the single phase power supply and then switched on the unit. 2. After that, all valves were fully opened and the pressure reading on the panel were checked to make sure that the chambers are under athmospheric pressure. 3. Then, all the chamber were closed. 4. Th e pipe were connected from compressive port of the pump to the pressurized chamber or connected from the pipe from vacuum port of the pump to vacuum chamber. 5. Next, the apparatus was ready to be used. General shut-down procedure 1. The pump was switched off and the both pipes were removed from the chambers. 2. The valves were fully opened to release the air inside the chambers.
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3. The main switch and the power suppl y were switched off. Experiment 1: Boyle’s Law Experiment 1. The general start up procedure were performed. Assured that all valves were fully closed. 2. The compressive pump was switched on and the pessure inside the chamber were allowed to increase up to about 150kPa. Then, the pump was switched off and the hose was removed from the chamber. 3. The pressure reading inside the chamber were mo nitored until it stabilized. 4. The pressure reading before expansion for both chambers were recorded. 5. The valve 02 was fully opened and the pressurized air were allowed to flows into the atmospheric chamber. 6. The pressure reading after expansion for both chambers were recorded. 7. The experimental procedure were repeated for the following conditions: a) From atmospheric chamber to vacuum chamber. (on pump to release preeure until 5060kpa at vacuum chamber) b) From pressurized chamber to vacuum chamber. (on pump to release preeure until 5060kpa at vacuum chamber) 8. The PV value were calculated and the Boyle’s Law was proved. Experiment 2: Gay-Lussac Law experiment 1. The general start-up procedure were performed and assured that all valves were fully closed. 2. The hose were connected from the compressive pump to pressurized chamber. 3. The compressive pump was switch on and the temperature were recorded for every increment of 10kPa in the chamber. The pump was stopped when the pressure PT reached about 160kPa. 4. Then, the valve 01 was slightly opened and the pressurized air were allowed to flows out. The temperature reding were recorded for every decrement of 10kPa. 5. The experiment was stopped when the pressure reached atmospheric pressure. 6. Te experiment were repeated for three times to get the average value. 7. The graph of pressure versus temperature was plotted. Experiment 3: Isentropic Expansion Process 1. The general start up procedure was performed. 2. The hose was connected from compressive pump to the pressurized chamber.
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3. The compressive pump was switched on and the pressure inside the chamber were allowed to increased until about 160kPa. Then, the pump was switch off and the hose from the chamber was removed as well. 4. The pressyre reading inside the chamber were monitored until it stabilize. The pressure reading PT1 and the temperature TT1 were recorded. 5. Then, the valve 02 was slightly opened and the air were allowwd to flow out slowly until it reached atmospheric pressure. 6. The pressure reading and the temperature reading after the expansion process were recorded. 7. The isentropic expansion process were discussed.
Experiment 4:Stepwise Depressurization 1. The general start-up procedure were performed and all valves were assured to be fully closed. 2. The hose was conected from compressive pump to pressurized chamber. 3. The compressive pump was switched on and the pressure inside chamber were allowed to increased until about 160kPa. Then, the pump was switched off and the hose was removed from the chamber. 4. The pressure reading inside the chamber were monitored until it stabilized. The pressure reading PT 1 were recorded. 5. The valve 01 was fully opened and the it was bringing back to the close position instantly. The pressure reading PT 1 were monitored and recorded until it became stabled. 6. The step 5 was repeated fo at least four times. 7. The pressure reading were displayed on a graph and discussed about it. Experiment 5: Brief Depresurization 1. The general start-up were performed as well. All valves were assured to be fully closed. 2. The host was connected from compressive pump t o pressurized pump. 3. The compressive pump was switched on and the pressure inside the chamber were allowed to increase until about 160kPa. 4. The pressure reading inside the chamber were monitored until it stabilized. The presusre reading PT 1 were recorded. 5. The valve 01 was fully opened and brought it back to the closed position after seconds. The pressure reading PT 1 were recorded and monitored until it became stabled. 6. The pressure reading were displayed on a graph and discussed about it.
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Experiment 6 : Determination of ratio of volume 1. The general start-up were performed as well. All valves were assured to be fully closed. 2. The compressive pump was switched on and the pressure inside the chamber were allowed to increase until about 150kPa. Then, the pump was switched off and the hose was removed from the chamber. 3. The pressure reading inside the chamber were mo nitored until it stabilized. 4. The pressure reading before expansion for both chambers were recorded. 5. The valve 02 was opened and the pressurized air were allowed to flows into the atmospheric chamber slowly. 6. The pressure reading for both chambers were recorded after the expansion. 7. The experimental procedures were repeated for th e following conditions: a) From atmospheric chamber to vacum chamber b) From pressurized chamber to vacuum chamber 8. The ratio of the volume were calculated and compared with the theoretical value. Experiment 7: Determination of the ratio of heat c apacity 1. The general start-up were performed as well. All valves were assured to be fully closed. 2. The host was connected from compressive chamber to pressurized chamber. 3. The compressive pump was switched on and the pressure inside the chamber were allowed to increase until about 160kPa. Then, the pump was switched off and the hose was removed from the chamber. 4. The pressure reading inside the chamber were monitored until it stabilized. Then, the pressure reading PT 1 and the temperature reading TT 1. 5. The valve 01 was fully opened and brought it back to the closed position after seconds. The pressure reading PT 1 and temperature TT 1 were recorded and monitored until it became stabled. 6. The ratio of heat capacity were determined and compared with the theoretical value.
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RESULT
Experiment 1: Boyle’s Law Experiment Before Expansion Pressure chamber Vacuum chamber PT1 150.3 kPa PT2 101.2 kPa TT1 25.5 ºC TT2 24.0 ºC
Increment, P(kPa) 101.6 111.8 121.4 131.2 141.3 151.3 161.7
After Expansion Pressure chamber Vacuum chamber PT1 134.1 kPa PT2 133.7 kPa TT1 24.1 ºC TT2 26.0 ºC
Experiment 2: Gay-Lussac Law Experiment T1 (ºC) T2 (ºC) T3 (ºC) Decrement, T1 (ºC) P(kPa) 23.7 24.3 26.1 26.5 27.1 27.7 28.8
24.1 25.0 25.5 26.5 27.5 28.2 28.7
24.4 25.2 25.6 26.3 27.1 27.0 28.6
151.7 141.7 131.2 121.7 111.7 101.7
26.0 25.5 25.0 24.0 23.6 23.2
increment 180 160 140 a P k e r u s s e r p
120 100
temperature 1
80
temperature 2
60
temperature 3
40 20 0 23.7
24.3
26.1
26.5
27.1
27.7
28.8
10
T2 (ºC)
T3 (ºC)
28.8 28.1 26.9 26.2 25.3 25.0
29.0 28.3 27.6 27.0 26.2 25.9
decrement 160 140 120 a P k e r u s s e r p
100
temperature 1
80
temperature 2
60
temperature 3
40 20 0 29
Before Expansion After Expansion
P1 (initial) kPa 161.1 128.3 108.9 103.5
28.3
27.6
27
26.2
25.9
Experiment 3: Isentropic Expansion Process PT 1 (kPa)
TT 1 ( C)
161.3 101.5
29.2 26.4
Experiment 4: Stepwise Depressurization (Pressurized Chamber) P2 ( open and close instantly) kPa 123.8 106.8
P3 (stable) kPa 127.6 108.7
102.4 101.6
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103.2 102.1
stepwise depressurization 180 160 140 a P k , e r u s s e r p
120
Series1
100
Series2
80
Series3
60 40
Series4
20 0 1
PT1 (initial) 161.3
2
3
Experiment 5: Brief Depressurization Pressure Chamber PT1 (after opened a few second) 102.7
PT1 (stable) 108.5
brief depressurization 200 a P k , e r u s s e r p
150 100 50 0 PT1 (initial)
PT1 (after opened a few second)
PT1 (stable)
Experiment 6: Determination of Ratio of Volume Pressure chamber Vacuum chamber Before expansion After expansion
PT1 (kPa) 151.1 133.9
TT1 (ºC) 29.5 27.3
PT1 (kPa) 101.1 131.6
TT1 (ºC) 24.9 27.1
Experiment 7: Determination of Ratio of Heat Capacity Pressure chamber PT1 (kPa) TT1 (ºC) Before expansion 160.3 30.2 After expansion 104.1 28.1
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SAMPLE OF CALCULATION CALCULATION
Experiment 1: Boyle’s Law PV= k
T= Constant in closed system
Properties of ideal gas at two different states; P1V1= P2V2 T1 T2 P1V1 = P2V2
(when T= Constant)
PV= RT V= RT/P Before expansion in pressurized chamber P1 = 150.3 Kpa
in vacuum chamber P1 = 101.2 Kpa
0
T1= 25.5 C/ 298.65 K V1 = (8.314)(298.65) 150.3 3 = 16.52 m
P1V1= (150.3)(16.52) 3
= 2483 Kpa.m
0
T2= 24.0 C/ 297.15 K V2= (8.314)(297.15) 101.2 3 = 24.4 m
P2V2 = (101.2)(24.41) 3
= 2470.3 Kpa.m
After expansion In the pressurized chamber
in vacuum chamber
P1 = 134.1 Kpa
P2 = 133.7 Kpa
0
T1= 24.1 C/ 297.25 K V1 = (8.314)(297.25) 134.1
0
T2= 26.0 C/ 299.15 K V2= (8.314)(297.15) 133.7
13
3
3
= 18.43 m P1V1= (134.1)(18.43)
= 18.60 m P2V2 = (133.7)(18.60)
3
3
= 2471.5 Kpa.m
= 2486.8 Kpa.m
The Boyle’s Law is used to predict before and after expansion process; P1V1 = P2V2
(T1 = T2)
P1V1 = P2V2 3
3
3
(2483.0 Kpa.m ) = (2486.8 Kpa.m )
Sample error calculation: 2486.8 – 2483.0 x 100 % 2483.0
2471.5 - 2470.3 x 100% 2470.3
= 0.15%
= 0.05%
EXPERIMENT 1 : BOYLE’S LAW EXPERIMENT
PV = k P1V1 = k
T = constant ;
P2V2 = k
P1V1 = P2V2
Before Expansion = after expansion ( P pressurized + P atmospheric) (25 L + 12.5L) = ( P pressurized + P atmospheric) V2 (157.5 kPa + 101.1 kPa)(37.5L) = (139.2 kPa + 138.6 kPa) V2 258.6 (37.5) = 277.8V2 V2= 34.9 L
3
(2470.3 Kpa.m ) = (2471.5 Kpa.m )
P1V1 = P2V2
Before Expansion = after expansion ( P vacuum+ P atmospheric) (25 L + 12.5L) = ( P vacuum + P atmospheric) V2 (54.4 kPa + 101.9 kPa)(37.5L) = (85.8 kPa + 86.5 kPa) V2 156.3 (37.5) = 172.3V2 V2= 34.02 L
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It is proved that for Boyles’s law it means that when pressure increase the volume decrease.
EXPERIMENT 2: GAY-LUSSAC LAW EXPERIMENT. Average temperature :
Tavg=
Ex:
Tavg
=
Tavg
= 24.3 °C
EXPERIMENT 6: DETERMINATION OF RATIO VOLUME. From pressurized chamber to atmospheric chamber :
) ( = Pf =
Pf = 125.6 kPa
= 1.0
From atmospheric chamber to vacuum chamber :
Pf =
) ( Pf = 89.97 kPa
15
=
2.77
Theoretical value :
m1 = 28.966 (air) m2 = 0 (vacuum)
) ( =
Pf =
Pf = 67.8kPa
2
From pressurized chamber to vacuum chamber:
Pf =
) ( Pf = 125.17 kPa
2.0
Theoretical value :
m1 = 28.966 (air) m2 = 0 (vacuum)
( ) =
Pf =
Pf = 106.67kPa
2.0
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EXPERIMENT 7: DETERMINATION OF RATIO OF HEAT CAPACITY.
=
= 0.446
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DISCUSSION
The purpose of this experiment is to demonstare or familiarize the students with several fundamental thermodynamic processes and alsom to relate it. The first experiment (Boyle’s Law Experiment) are to determine the relationship between pressure and volume of an ideal gas and to compare the experimental results with theoretical results. For the first experiment the PV value were calculated which are 142.2. The Boyle’s Law is approved as the value of PV is calculated.
Thus, the absolute pressure is inversely proportional with volume of gas if the
temperature is kept constant within a closed s ystem. For the second exper iment which related with the Gay Lussac’s experiment, the purpose of this experiment is to determine the relationship between pressure and temperature of an ideal gas. The graph of pressure versus temperature was plotted which are the graph of increment and also graph of decrement. Meanwhile, the purpose of carrying out the experiment 3 (isentropic expansion process) is to demonstrate the isentropic expansion process and the (pressure) PT 1 and (temperature) TT1 after and before expansion which are recorded in the table of experiment 3. After that, the purpose of carrying out the experiment 4 (stepwise depressurization) is to study the response of the pressurized vessel following stepwise depressurization. Besides that, the pressure reading that is displayed on a graph. In this experiment, as the valve is open and closed instantly, the pressure will decrease abruptly before it increasing back as it becomes stables. The next is experiment 5 is brief depressurization where the point of carrying out this experiment is to study the response of the pressurized vessel following a brief depressurization. All the pressure reading is displayed on the graph after undergo all the experiments. The objective for the experiment 6 (determination of ratio) is to determine the ratio of volume and compares it to the theoretical value. The ratio of the volume for pressurized chamber is -0.0886. Lastly, the experiment 7 (determination of ratio of heat capacity), in this experiment the ratio of heat capacity is determined. The result which is the ratio of heat capacity is 0.446. The initial values of PT 1 before expansion and PT 1 after expansion are 160.3 and 104.1 respectively. As the graph pressure versus temperature plotted at the experiment 2, it proves that the as the temperature rising the pressure also rising and like wise. This obeyed the equation of an ideal gas which the pressure is inversely proportional with temperature. For the experiment 3 which is related to the isentropic expansion, the temperature is decrease as the pressure also
18
decrease. The results that have been taken during carrying out the experiment is not too accurate due to some parallax error.
CONCLUSION
As the conclusion, the purpose of this experiment is to demonstrate the students with several fundamental thermodynamic processes. The purpose of the first experiment is to determine the relationship between pressure and volume of an ideal gas and to compare the experimental results with theoretical results which have been calculated and the Boyle’s Law calculation also is proven throughout this experiment. For the first experiment the PV value were calculated which are 142.2 for pressurized chamber. For the experiment 6 which related to the determination of ratio pressurized chamber ratio is calculated which is-0.886. Meanwhile, as for the experiment 7 that related to the determination of ratio of heat capacity which is the ratio of heat capacity result was calculated and the result is 0.446 with the initial value of PT 1 before expansion and PT 1 after expansion are 160.3 and 104.1 respectively. As the graph pressure versus temperature plotted at the experiment 2, it proves that the as the temperature rising the pressure also rising and like wise. This obeyed the equation of an ideal gas which the pressure is inversely proportional with temperature. For the experiment 3 which is related to the isentropic expansion, the temperature is decrease as the pressure also decrease. Meanwhile, experiment 4 for is to study the response of the pressurized vessel following stepwise depressurization. In this experiment, as the valve is open and closed instantly, the pressure will decrease abruptly before it increasing back as it becomes stables.
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RECOMMENDATIONS
There are a few recommendations that are necessary in these experiment in order to get a more accurate results. Ensure that the Perfect gas expansion apparatus (model: TH 11) is in good conditions before and after perform experiment. The lab manual given should be followed respectively and sequencly while carrying out the experiment. The general start-up and general shut-down procedure must be performed before and after use the apparatus. During releasing all the pressure inside the pressurize chamber, the valve should be opened slowly otherwise it will cause us becoming deaf due to the pressure that released is higher. Make sure that the pump is switched off after reload the pressure inside the pressurize chamber. REFFRENCES 1) Thermodynamics and engineering approach, Yunus Cengel, Michael Boles, 4th Ed. 2) http://www.google.com.my/url?sa=t&rct=j&q=perfect+gas+expan sion+apparatus&source 3) http://www.discoverarmfield.co.uk/data/th5/?js=enabled 4) http://vohweb.chem.ucla.edu/voh/classes%5Cspring12%5C114ID2 6%5CT9-GNS.pdf 5) http://www.pete.metu.edu.tr/files/216labmanual.pdf 6) http://www.chemeng.queensu.ca/courses/CHEE218/projects/GasE xpansion/ExpansionProcessesofPerfectGas.php (lab manual)
APPENDICES
20
