UNIVERSITI TEKNOLOGI MARA FAKULTI KEJURUTERAAN KIMIA PROCESS ENGINEERING LABORATORY 1 (CPE435)
NAME : STUDENT ID. : GROUP : EXPERIMENT : DATE SUBMITTED SEMESTER PROGRAMME / CODE SUBMIT TO
Abstract/Summary Introduction Aims Theory Apparatus Methodology/Procedure Results Calculations Discussion Conclusion Recommendations Reference / Appendix Supervisor’s grading
Allocated Marks (%) 5 5 5 5 5 10 10 10 20 5 5 5 10
TOTAL MARKS
100
No. 1 2 3 4 5 6 7 8 9 10 11 12 13
MUHAMMAD SOLAHUDIN BIN MUSA 2014342085 EH2202 PVT : 2ND DECEMBER 2015 :2 : EH220 : DR ZULKIFLI ABDUL RASHID
Title
Remarks: Checked by:
--------------------------Date: ABTRACTS
Marks
This experiment involving a perfect gas or ideal gas has seven experiment. An equipment has been used which called Perfect gas expansion apparatus in order to determine the properties of measurement and study the relationship between ideal gas and various factor that can propose an understanding of First and second law of thermodynamics. For Boyle’s Law experiment and determination of ratio of volume are to determine the relationship between pressure and volume of an ideal gas, to compare the experimental results with theoretical results and to determine the ratio of volume and compares it to the theoretical value. For Gay-Lussac Law experiment is to determine the relationship between pressure and temperature of an ideal gas. For determination of ratio of heat capacity is to determine the ratio of heat capacity. Lastly, for Isentropic expansion process is to demonstrate the isentropic expansion process. The objectives of this experiment successfully achieved. Boyle’s and Gay-Lussac’s law was proven in this experiment when the ideal gas was obey the law. The volume ratio and heat capacity were also determined. The experiment was successful.
INTRODUCTION
The Perfect Gas Expansion Apparatus is a sufficient bench top unit designed in order to expose the student and familiar with the fundamental thermodynamic processes. This experiment is likely safe and more convenient to demonstrate thermodynamic properties. The apparatus have two vessels, one is for pressurized chamber and the other one is for vacuum chamber. This apparatus also equip with pressurized pump and vacuum pump and several valve which can connect between chambers and also to the surrounding. The chamber is made from glass that can withstand maximum pressure of apparatus can operate. The apparatus also equipped with temperature and pressure sensors for both tanks which can be read on the board. These sensors used to monitor and manipulate the pressure and temperature. The board displays the temperature and pressure in a digital indicator that dealt with the PVT laws. Gas particles in the chamber collide with each other and the walls which transfer momentum in each collision. The gas pressure is equal to the momentum delivered to the wall per unit time. A single particles moves arbitrarily along some direction until it strikes back and forth with wall and change direction and speeds. Equations are derived directly from the law of conservation of linear motion of conservation of energy.
OBJECTIVES Experiment 1: Boyle’s Law Experiment To determine the relationship between pressure and volume of an ideal gas. To compare the experimental result with theoretical result.
Experiment 2: Gay-Lussac Law Experiment To determine the relationship between pressure and temperature of an ideal gas.
Experiment 3: Isentropic Expansion Process To demonstrate the isentropic expansion process.
Experiment 4: Stepwise Depressurization To study the response depressurization.
of
pressurized
vessel
following
stepwise
of
pressurized
vessel
following
a
Experiment 5: Brief Depressurization To study the response depressurization.
Experiment 6: Determination of Ration Volume To determine the ratio of volume and compares it to the theoretical value.
Experiment 7: Determination of Ratio of Heat Capacity To determine the ratio of heat capacity.
brief
THEORY
Perfect Gas 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 in which there are ni intermolecular attractive forces. An ideal gas is also an imaginary substance tht obeys the ideal equation state. An equation had been introduced in 1662 where it has been named as ideal gas equation of state:
T V ) P=R ¿
(1)
Where the constant of proportionally R is called the gas constant and is different for each gas. Any gas that obeys this law is called an ideal gas. The equation also can be written as:
PV =mRT
(2)
By writing equation (2) twice for fixed mass and simplifying, the properties of ideal gas at two different states are related to each other by:
(3) It has been experimentally observed that ideal gas relation closely approximate 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 ideal gas under these conditions.
Boyle’s Law Boyle’s law describe the relationship between the pressure and the volume of a gas. This law works when the pressure increase inversely with the volume of gas where the temperature held constant along the process. The gas inside a system loosely packed and move randomly. If the volume is reduce, then the pressure become high as the molecules having less space to move, to hit the wall of container more frequently.
Figure 1: Graph of Boyle's Law
Charles’s Law Second law is Charles’s Law which involves with the effect of heat on the expansion of gases. The pressure will remain constant throughout the process and the volume of gas will go directly proportional to the absolute temperature. The moving molecules increase their speed and hit the wall more frequently as the temperature getting higher because the temperature transfer the heat of energy into the molecule. Thus, as the speed increase and the frequency of collision increases, the volume of the container increases. Therefore the equation of Charles’s law simply shows below where the k is a constant. The temperature must be calculated in Kelvin unit. If the constant value of k is not known then, the equation is derived as follow:
The relationship of volume and temperature of Charles’s law describe in a graph as follow :
Figure 2 : The graph of Charles's Law
Gay-Lussac’s Law The third law involving ideal gas is Gay-Lussac’s law where the volume of the system becomes constant throughout the process. This law stated that the pressure and temperature are in direct relation. That means as the pressure increase, the temperature also increase. Temperature is a parameter for kinetic energy, as the temperature increase, the kinetic energy also increase, therefore the frequency of collision also increase which causing the pressure to be increase with the constant volume. The equation below can prove the relationship between pressure
and
temperature
in
a
particular
system
with
constant
volume.
Graph below show the relationship of temperature and pressure in the Gay-Lussac’s law with constant volume. The conclusion is that the pressure directly proportional to the temperature.
Figure 1: Graph of Gay-Lussac's Law
Heat capacity The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). To determine the ratio of heat capacity,
For an ideal gas the internal energy - u - is a function of temperature and the change in internal energy can be expressed as du = Cv dT
(1)
where du = change in internal energy Cv = specific heat capacity for the gas in a constant volume process dT = change in temperature Cv varies with temperature, but within a moderate temperature change the heat capacity - Cv can be regarded as constant. Now, let talk about enthalpy. For an ideal gas the enthalpy - h - is function of temperature and the change in enthalpy can be expressed as dh = Cp dT
(2)
where dh = change in enthalpy Cp= specific heat capacity for the gas in a constant pressure process Cp can within a moderate temperature change be regarded as constant.
APPARATUS
V1
1. 2. 3. 4. 5. 6. 7.
Pressure transmitter Pressure relief valve Temperature sensor Pressurized chamber Vacuum chamber Vacuum pump Electrode
V2
V3
PROCEDURE
General Start-up Procedures 1. The equipment was connecting to single phase power supply and then the unit was switch off. 2. All valves were fully open and the pressure reading was checked on the panel. This was to make sure that the chambers were under atmospheric pressure. 3. Then, all valves were closed. 4. The pipe was connecting from compressive port of the pump to pressurized chamber or the pipe was connecting from vacuum port of the pump to vacuum chamber. 5. Now, the unit was ready for used.
General Shut-Down Procedures 1. The pump was switch off and both pipes were removed from the chambers. 2. The valves were fully open to release the air inside the chambers. 3. The main switch and power supply were switch off.
EXPERIMENT 1: Boyle’s Law Experiment 1. The general start up method as previously mentioned was performed and the valves were once again made sure to be fully closed. 2. The compressive pump was switched on and the pressure inside the chamber was 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 was monitored until it stabilized. 4. The pressure reading for both chambers before expansion was recorded. 5. The V 02 was fully opened and the pressurized air flows were allowed into the atmospheric chamber. 6. The pressure reading for both chambers after expansion was recorded. 7. The experimental methodology was repeated for the following conditions: i. From atmospheric chamber to vacuum chamber; ii. From pressurized chamber to vacuum chamber. 8. The PV value was calculated and Boyle’s Law was proven in further sections
EXPERIMENT 2: Gay-Lussac Law Experiment 1. The general start up method was performed again. 2. The hose was connected from the compressive pump to pressurized chamber. 3. The compressive pump was switched on and the temperature for every increment of 10kPa in the chamber was recorded. The pump was stopped when the pressure PT 1 reaches about 160kPa. 4. Then, the valve V 01 was slightly opened and the pressurized air was allowed to flow out. The temperature reading for every decrement of 10kPa was recorded. 5. The experiment was stopped when the pressure reached atmospheric pressure. 6. The experiment was repeated for three times to get the average value. 7. A graph was plotted to represent the pressure versus temperature.
EXPERIMENT 3: Isentropic Expansion Process 1. The general start up procedures was performed. 2. The hose was connected from compressive pump to pressurized chamber 3. The compressive pump was switched on and the pressure inside the chamber was 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 was monitored until it stabilized. The pressure reading PT 1 and temperature TT 1 were recorded. 5. Valve V 01 was slightly opened and air was allowed 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 was discussed in further section.
EXPERIMENT 4: Stepwise Depressurization 1. The general start up procedure was performed. 2. The hose from the compressive pump was connected to the pressurized chamber. 3. The compressive pump was switched on and the pressure inside the chamber was allowed to increase until about 160kPa. The pump was then switched off and the hose was removed from its chamber. 4. The pressure reading inside the chamber was monitored until it stabilized. The pressure reading PT 1 was recorded. 5. The valve V 01 was fully opened and brought back to closed position instantly. The pressure reading PT 1 was monitored and recorded until it became stable. 6. Step 5 was repeated at least four times.
EXPERIMENT 5: Brief Depressurization 1. General start up procedure was performed. 2. The hose was connected from the compressive pump to the pressurized chamber. 3. The compressive pump was switched on and allowed to increase the pressure inside the chamber until about 160kPa. Then it was switched off and the hose was removed. 4. The pressure reading inside the chamber was monitored until it stabilized. The pressure reading was recorded as PT 1. 5. The valve V 01 was fully opened and brought back to closed position after a few seconds. The pressure reading after expansion was monitored and recorded as PT 1 until it became stable. 6. The result was displayed on graph and further discussed.
EXPERIMENT 6: Determination of Ratio of Volume 1. General start up procedure was performed and valves were made sure to be closed. 2. Compressive pump was switched on and the pressure inside the chamber was 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 was monitored until it stabilized. 4. The pressure reading for both chambers was recorded before expansion. 5. Valve V 02 was opened and the pressurized air was allowed to flow into the atmospheric chamber slowly. 6. The pressure reading for both chambers after expansion was recorded. 7. The experimental procedures were repeated for the following conditions: i. From atmospheric chamber to vacuum chamber. ii. From pressurized chamber to vacuum chamber. 8. The ratio of volume was calculated and compared with the theoretical value
EXPERIMENT 7: Determination of Ratio of Heat Capacity 1. The general start up method was performed. 2. The compressive pump was connected to pressurized chamber. 3. The compressive pump was switched on and the pressure inside the chamber was 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 was monitored until is stabilized. The pressure reading PT1 and temperature TT1were recorded. 5. The valve V 01 was fully opened and brought back to closed until after a few seconds. The reading PT1 and temperature TT1 were monitored and recorded until they became stable. 6. The ratio of the heat capacity was determined and then compared with the theoretical value.
RESULTS Experiment 1: Boyle’s Law Experiment A. EXPERIMENT 1.1 PT 1 (kPa abs) PT 2 (kPa abs)
Before expansion 156.5 102.3
After expansion 137.9 137.4
Before expansion 103.2 53.3
After expansion 88.8 88.2
Before expansion 155.9 54.0
After expansion 122.4 121.4
B. EXPERIMENT 1.2 PT 1 (kPa abs) PT 2 (kPa abs) C. EXPERIMENT 1.3 PT 1 (kPa abs) PT 2 (kPa abs)
Experiment 2: Gay-Lussac Law Experiment
Pressure (kPa abs)
Trial 1
Trial 2
Trial 3
Temperature (˚C)
Temperature (˚C)
Temperature (˚C)
Depressure rise vessel
110
Pressure rise vessel 22.6
Depressure rise vessel
22.3
Pressure rise vessel 22.1
Depressure rise vessel
22.6
Pressure rise vessel 22.2
120
22.9
22.8
22.3
23.3
22.4
24.1
130
23.5
23.6
22.8
24.5
23.0
25.3
140
24.5
24.8
23.9
25.7
23.8
26.6
150
25.4
26.6
24.8
26.8
24.8
26.9
160
26.3
27.9
25.9
27.3
25.6
27.0
Experiment 3: Isentropic Expansion Process
23.1
PT 1 ( kPa abs)
Before expansion 163.0
After expansion 103.5
PT 2 ( kPa abs)
25.2
21.7
Experiment 4: Stepwise Depressurization PT 1 (kPa abs) AFTER FIRST EXPANSION 120.2
INITIAL 160.0
AFTER SECOND EXPANSION 102.3
Experiment 5: Brief Depressurization
INITIAL 159.1
PT 1 (kPa abs) AFTER BRIEF EXPANSION 147.5
Experiment 6: Determination of Ratio of Volume A. PRESSURIZED AIR FLOW FROM TANK 1 TO TANK 2 PT 1 (kPa abs) 160.0 140.4
BEFORE EXPANSION AFTER EXPANSION
PT 2 (kPa abs) 102.2 140.5
B. PRESSURIZED AIR FLOW FROM TANK 2 TO TANK 1 PT 1 (kPa abs) 103.2 88.3
BEFORE EXPANSION AFTER EXPANSION
PT 2 (kPa abs) 55.0 87.7
C. BOTH TANK 1 AND 2 WAS PRESSURIZED PT 1 (kPa abs) 158.8 54.7
BEFORE EXPANSION AFTER EXPANSION
PT 2 (kPa abs) 123.9 123.6
Experiment 7: Determination of Ratio of Heat Capacity
PT 1 (kPa abs) TT 1 (°C)
INITIAL
INTERMEDIATE
FINAL
160.2 31.0
143.1 30.4
144.6 29.0
CALCULATIONS Experiment 1: A. CONDITION 1 V1 = 0.025m3 V2 = 0.01237m3 By using Boyle’s law P1V1 = P2V2 (P1V1 + P2V2)before = (P1V1 + P2V2)after (156.5×0.025) + (102.3×0.01237) = (137.9×0.025) + (137.4×0.01237) 5.178 = 5.147 The difference is only 0.030862, therefore the Boyle’s Law is verified. B. CONDITION 2 V1 = 0.025m3 V2 = 0.01237m3 By using Boyle’s law P1V1 = P2V2 (P1V1 + P2V2)before = (P1V1 + P2V2)after (103.2×0.025) + (53.3×0.01237) = (88.8×0.025) + (88.2×0.01237) 3.239 = 3.311 The difference is only 0.0720, therefore the Boyle’s Law is verified. C. CONDITION 3 V1 = 0.025m3 V2 = 0.01237m3 By using Boyle’s law P1V1 = P2V2 (P1V1 + P2V2)before = (P1V1 + P2V2)after (155.9×0.025) + (54×0.01237) = (122.4×0.025) + (121.4×0.01237) 4.565 = 4.562 The difference is only 0.003, therefore the Boyle’s Law is verified.
Experiment 2: In every increment of 10kPa PRESSURE (kPa) (y-axis)
AVERAGE TEMPERATURE (x-axis)
110
22.30
120
22.53
130
23.10
140
24.07
150
25.00
160
25.93
Pressure versus Temperature 180 160 140 120 100
Pressure (kPa)
80 60 40 20 0 22.3
22.53
23.1
24.07
Temperature (˚C)
25
25.93
In every decrement of 10kPa PRESSURE (kPa) (y-axis)
AVERAGE TEMPERATURE (x-axis)
110
22.67
120
23.40
130
24.47
140
25.70
150
26.77
160
27.40
Pressure versus Temperature 180 160 140 120 100
Pressure (kPa)
80 60 40 20 0 22.67
23.4
24.47
25.7
Temperature (˚C)
26.77
27.4
Experiment 3: For isentropic process,
(21.7/25.2) = (103.5/163.0) ^( 0.8611 = 0.6350^( ln 0.8611 =(
k−1 ¿ k
k−1 ¿ k
k−1 ¿ ln 0.6350 k
(
k−1 ¿ = ln 0.8611/ ln 0.6350 k
(
k−1 ¿ = 0.3293 k
K = 1.4910
Experiment 4:
Response of pressurized vessel following stepwise depressurization 180 160 140 120 100
Pressure (kPa)
80 60 40 20 0
1
2
Graph of response of pressurized vessel following stepwise depressurization
3
Experiment 5: Responses of pressurization vessel following of brief depressurization 165
160
155
Pressure (kPa) 150
145
140
Graph of responses of pressurization vessel following of brief depressurization
Experiment 6: A. CONDITION 1 V1/V2 = (P2,initial - P2,final) / (P1,final - P1,initial) 0.025/0.01237 = (102.2-140.5)/(140.4-160) 2.021 = 1.954 Difference = -0.067 Percentage difference : -3.32% B. CONDITION 2 V1/V2 = (P2,initial - P2,final) / (P1,final - P1,initial) 0.025/0.01237 = (55-87.7)/(88.3-103.2) 2.021 = 2.194 Difference = 0.173 Percentage difference : 8.56% C. CONDITION 3 V1/V2 = (P2,initial- P2,final) / (P1,final - P1,initial) 0.025/0.01237 = (54.7-123.6)/(123.9-158.8) 2.021 = 1.974 Difference = -0.046 Percentage difference : -2.28%
Experiment 7:
ln 160.2−ln 143.1 = ln160.2−ln 144.6 = 1.102 The ideal k, Cp/Cv = 1.4 Deviation = (1.4 - 1.102) / 1.4 × 100% =21.28%
DISCUSSION Boyle’s law stated that the pressure of gas inversely proportional to the volume of a container. From the results recorded, some calculation have been made in order to know the difference value between before and after of the experiment one. For conditions 1, 2 and 3 the value are 0.030862, 0.0720 and 0.003. These values are very small and close with the theoretical value, therefore the Boyles’s Law is verified. According to the data tabulated, it can been said that the pressure and volume inversely proportional. When the pressure increase, the volume start to decrease. This is happen because if the gas of the same pressure with constant temperature injected into small and big container which means have different volume. The gas molecule in small container have less spacious room and will collide to the wall and with each other more often which exert more pressure. Gay-Lussac’s Law stated that pressure is directly proportional to the temperature which means when the pressure increase, the temperature increase with constant volume. From the data tabulated and graph plotted, it can be said that the Gay-Lussac’s Law is verified. The same concept applied here, if the temperature of a gas in a container increase, the heat energy of the system transfer its energy into the molecule of gas which actually increase the frequency of collision in that container which exert more pressure. The heat capacity ratio is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). Based on calculated value, the value of heat capacity ratio is 1.059 whereas the theoretical value is 1.4.The percentage error 24.36%. The actual intermediate pressure supposed to be lowered that the measured one. Unfortunately the error could be occurs due to heat loss and sensitivity of pressure sensors. Supposed, the intermediate pressure taken as the lowest pressure at the moment the valve is closed. Since the percentage difference is more than 10%, the experiment can be declared as failed.
Isentropic expansion process is occurred when the system is reversible and adiabatic where no heat will be transferred in or out and no energy transformation occurs. From the data recorded, a constant k is now known which is equal to 1.4910. It was obtained that both temperature and pressure of the gas before expansion were higher compared to after the expansion. The process is said to be isentropic since there was no change in the entropy throughout the process. Stepwise depressurization is
a
strategy
to
adopt
an
equal
time-stepwise
depressurization approach in this study yield a more reliable result for an example in the production sector in industries. The molecule in the container affected when the number of them decreasing slowly as they do not have to collide between them more often. The depressurization shown that pressure decrease with time and also affecting the temperature. As the pressure decrease, the temperature also decrease in the system. Brief depressurization shown in the graph plotted in result section which is decrease more linear compared to stepwise. The expansion occur when the pressure of gas increase. Expansion of gas decrease as the gas is free to flow out time by time. Ratio volume can be determine by manipulating the equation of Boyle’s law. Boyle’s law proposed an equation P1V1=P2V2 and after manipulate the equation ratio volume can be determine byV2/V1=P1P2. This experiment test in three different condition where first condition the gas is flow from tank 1 to tank 2, while gas flow from tank 2 to tank 1 in second condition and both were filled with gas in third condition. The theoretical value is 2.021 in this experiment where the error or percentage difference are between 10 and -10. There must be environmental factors that affect the stability of pressure and temperature or random mistake during experiment. Since the percentage error is less than10%, it can be said that the experiment is successful.
Determination of ratio of heat capacity using the expression of the heat capacity ratio and it gives the 1.102. The theoretical value of this experiment is 1.4. The deviation which now is equal to 21.28%.The deviation is due to measurement error. The actual intermediate pressure supposed to be lowered that the measured one. Unfortunately the error occur due to heat loss and sensitivity of pressure sensors. Supposed, the intermediate pressure taken as the lowest pressure at the moment the valve is closed. Since the percentage difference is more than 10%, the experiment can be declared as failed.
CONCLUSION In a nutshell, the experiment was to determine the properties of measurement/PVT according to Boyle’s law, Gay-Lussac’s law, isentropic expansion, and heat capacity equation. We managed to prove the Boyle’s law and Gay-Lussac’s law which is based on their law. The volume ratio of gas indicates and expresses the dynamics of compression and expansion of gases. Although there is fail experiment but we managed to find the reason behind the failure. For example experiment 7, related to heat capacity ratio, the experiment fail maybe because of the intermediate pressure not taken after the valve is closed. In conclusion, the experiment is successfully done and the objective of the experiment is achieved.
RECOMMENDATION Before starts the experiment, each of the experiment must do the start-up and shutdown step in order to make sure there is no gas left in the chamber. Most important during recording data, keep eye on the sensor while monitoring the board because the parameter can increase and decrease really fast and read the procedure carefully. Get an average reading by repeating the experiment normally three times in order to reduce amount of deviation. Handle the valve carefully and do not make mistake by choosing the valve because it will affect the data. The place where the experiment is conducted also must be at stable and no vibration. All the equipment must be handle carefully in order to avoid explosion because over-pressure in the tank would cause an explosion.
REFERENCE 1. Charles's Law. (n.d.). Retrieved from how stuff works: http://science.howstuffworks.com/dictionary/physics-terms/charles-law-info.htm 2. Charles's Law. (2010). Retrieved from Sparknotes http://www.sparknotes.com/testprep/books/sat2/chemistry/chapter5section8.rhtml3. 3. Irfan,M.H. (2013). The Perfect Gas Expansion Experiment (TH11). Muhammad Haidharul Irfan. 4. Ngagiman, S. F. (2013). Perfect Gas Expansion. Siti Fatimah Ngagiman.
APPENDIX