TH11 EXPERIMENTAL MANUAL.pdf

SOLTEQ

EQUIPMENT FOR ENGINEERING EDUCATION

EXPERIMENTAL MANUAL

PERFECT GAS GAS EXPANSION EXPANSION APPARATUS APPARATUS MODEL: TH 11

SOLUTION ENGINEERING SDN. SDN. BHD. NO.3, JALAN TPK 2/4, TAMAN PERINDUSTRIAN KINRARA, 47100 PUCHONG, SELANGOR DARUL EHSAN, MALAYSIA. TEL: 603-8075800 603-807580000 FAX: 603-8075578 603-807557844 E-MAIL: [email protected] WEBSITE: www.solution.com.my 029-0210-TH

TABLE OF CONTENT

LIST LIST OF FIGURES

i

1.

INTRODUCTION INTRODUCTION

1

2.

GENERAL GENERAL DESCRIPTI DESCRIPTION ON 2.1 Descript Description ion 2.2 Experi Experim mental Capabili Capabilitities es 2.3 Specif Specificat ications ions 2.4 Opti Optional onal Item Items s 2.5 Requirements 2.6 Overal Overalll Dimensions Dimensions 2.7 Manual Manual 2.8 Assembly Assembly view view

2 2 3 3 3 3 3 4 4

3.

SUMMARY OF THEORY 3.1 The Perfect Gas 3.1.1 Boyle’ Boyle’s s Law 3.1.2 Charl Charles’s es’s Law 3.2 First First Law of Thermodynamics 3.3 Specif Specific ic Heat Heat 3.4 Internal Internal energy, enthalpy and specific specific heat of ideal gases 3.5 Specif Specific ic heat relati relations ons of ideal gas 3.6 Determinati Determination on of the Heat Heat Capacity Capacity Ratio 3.7 Determinati Determination on of Rati Ratio o of Volume Volume using an isotherm isothermal al process

5 5 5 6 7 8 8 9 9 11

4.

INSTALLATION AND COMMISSIONING 4.1 Installat Installation ion Procedures Procedures 4.2 Commissioning missioning Procedures

12 12 12

5.

EXPERIMENTAL PROCEDURES PROCEDURES 5.1 General General Operati Operating ng Procedures Procedures 5.1.1 General General Start-up Start-up Procedures Procedures 5.1.2 5.1.2 General Shut-down Procedures 5.2 Experimen Experimentt 1: Boyle’s Boyle’s Law Experime Experiment nt 5.3 Experime Experiment nt 2: Gay-Lussac Law Experimen Experimentt 5.4 Experi Experime ment nt 3: Isentropic Isentropic Expansion Expansion Process 5.5 Experi Experim ment 4: Stepwise Stepwise Depressurizati Depressurization on 5.6 Experi Experim ment 5: Brief Depressurizati Depressurization on 5.7 Experi Experim ment 6: Determinati Determination on of ratio ratio of volume 5.8 Experi Experim ment 7: Determinati Determination on of ratio ratio of heat capacit capacity y

13 13 13 13 14 15 16 17 18 19 20

6.

REFERENCE

21

AP APPENDICE ICES

TABLE OF CONTENT

LIST LIST OF FIGURES

i

1.

INTRODUCTION INTRODUCTION

1

2.

GENERAL GENERAL DESCRIPTI DESCRIPTION ON 2.1 Descript Description ion 2.2 Experi Experim mental Capabili Capabilitities es 2.3 Specif Specificat ications ions 2.4 Opti Optional onal Item Items s 2.5 Requirements 2.6 Overal Overalll Dimensions Dimensions 2.7 Manual Manual 2.8 Assembly Assembly view view

2 2 3 3 3 3 3 4 4

3.

SUMMARY OF THEORY 3.1 The Perfect Gas 3.1.1 Boyle’ Boyle’s s Law 3.1.2 Charl Charles’s es’s Law 3.2 First First Law of Thermodynamics 3.3 Specif Specific ic Heat Heat 3.4 Internal Internal energy, enthalpy and specific specific heat of ideal gases 3.5 Specif Specific ic heat relati relations ons of ideal gas 3.6 Determinati Determination on of the Heat Heat Capacity Capacity Ratio 3.7 Determinati Determination on of Rati Ratio o of Volume Volume using an isotherm isothermal al process

5 5 5 6 7 8 8 9 9 11

4.

INSTALLATION AND COMMISSIONING 4.1 Installat Installation ion Procedures Procedures 4.2 Commissioning missioning Procedures

12 12 12

5.

EXPERIMENTAL PROCEDURES PROCEDURES 5.1 General General Operati Operating ng Procedures Procedures 5.1.1 General General Start-up Start-up Procedures Procedures 5.1.2 5.1.2 General Shut-down Procedures 5.2 Experimen Experimentt 1: Boyle’s Boyle’s Law Experime Experiment nt 5.3 Experime Experiment nt 2: Gay-Lussac Law Experimen Experimentt 5.4 Experi Experime ment nt 3: Isentropic Isentropic Expansion Expansion Process 5.5 Experi Experim ment 4: Stepwise Stepwise Depressurizati Depressurization on 5.6 Experi Experim ment 5: Brief Depressurizati Depressurization on 5.7 Experi Experim ment 6: Determinati Determination on of ratio ratio of volume 5.8 Experi Experim ment 7: Determinati Determination on of ratio ratio of heat capacit capacity y

13 13 13 13 14 15 16 17 18 19 20

6.

REFERENCE

21

AP APPENDICE ICES

LIST OF FIGURES

Figure Figure 1

Assembly Assembly view of TH11 TH11

4

i

®PERFECT GAS EXPANSION APPARATUS EXPANSION APPARATUS (MODEL: TH 11) SOLTEQ ®PERFECT GAS

1.0

INTRODUCTION The Perfect Gas Expansion Apparatus (Model: TH 11) is a self-sufficient bench top unit designed to allow students familiarize with several fundamental thermodynamic processes. Demonstration of the thermodynamic processes is performed with air for safe and convenient operation.

1

SOLTEQ ®PERFECT GAS EXPANSION APPARATUS (MODEL: TH 11)

2.0

GENERAL DESCRIPTION 2.1 Description 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 the students to have a good understanding in energy conservation law and the 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 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.

2


2.2 Experimental Capabilities Demonstration of First Law of Thermodynamics Demonstration of Second Law of Thermodynamics and its corollaries Observation of P-V-T relationship and use it to determine other thermodynamic properties Observation of responses to different rate of changes in a process    

2.3 Specifications The Perfect Gas Expansion Apparatus comes complete with the followings: Test Section: Pressure vessel: 25 L and made of glass Vacuum vessel: 12.37 L and made of glass Temperature sensor with the range of 0-100 C mounted on the top of vessels Pressure sensor with the range of  160kPa mounted on the top of vessels ˚

Vacuum/Air p ump: Capacity: 1.1 CFM open flow Maximum vacuum: 24” HG Motor specification: 1/8 HP (230/50/1HP) Instrumentation: Digital indicator with bright LCD display 2.4 Optional Items - DAS SOLDAS Data Acquisition System i) ii) iii) iv)

A PC with latest Pentium Processor An electronic signal conditioning system Stand alone data acquisition modules Windows based software  Data Logging  Signal Analysis  Process Control  Real-Time Display  Tabulated Results  Graph of Experimental Results

2.5 Requirements Electrical: 230 VAC/1 phase/ 50 Hz Barometer (recommended) 2.6 Overall Dimension Height: 0.90 m Width: 0.75 m Depth: 0.60m 3


2.7 Manual The unit is supplied with Operating and Experiment Manuals in English giving full descriptions of the unit, summary of theory, experimental procedures and typical experimental results. 2.8 Assembly View

1 2 3

1

3

4

7 5 6

Figure 1: Assembly view of TH11 1

Pressure Transmitter

2

Pressure Relief Valve

3

Temperature Sensor

4

Big glass

5

Small glass

6

Vacuum pump

7

Electrode

4


3.0

SUMMARY OF THEORY 3.1 The 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 no intermolecular attractive forces. An ideal gas is also an imaginary substance that obeys the ideal gas equation of state. In 1662, Robert Boyle, an Englishman, discovered in his experiment that the pressure of gases is inversely proportional to their volume in a vacuum chamber. In 1802, J. Charles and J. GayLussac, Frenchman, determined that at low pressures the volume of a gas is proportional to its temperature. That is, T P  R ( ) V

(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 a fixed mass and simplifying, the properties of ideal gas at two different states are related to each other by: P1V 1 T 1



P2V 2 T 2

(3)

It has been experimentally observed that ideal gas relation closely approximate the P- v-T behavior 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. Besides of ideal gas equation of state, the ideal gas also obeys the following law: a. Boyle’s Law b. Charles’s Law c. Gay-Lussac’s Law 3.1.1 Boyle’s Law 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)

5


Where

P = pressure of the system V = volume of the gas k = constant value representative of the pressure and volume of the system

As long as the temperature remains constant at the same value the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will 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 is used to relate the volumes and pressure of the fixed amount of gas before and after expansion process, where the temperature before and after the process are the same. p1V1 = p2V2 (5) 3.1.2 Charles’s Law Charles’s law is 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: V T

 k

(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 increase. On the other hand, cooling the gas decreases the volume. 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. V 1 V 2 (7)  T 1 T 2 As a conclusion, when the temperature increases, the volume of the gas increase. 3.1.3

Gay-Lussac’s Law Gay-Lussac’s law states that the pressure of a fixed quantity of gas at constant temperature is directly proportional to its temperature in Kelvin. The formula is: P T

 k

Where

(8) P = pressure of the gas T = temperature of the gas (measured in Kelvin) k = constant 6


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 pressure. In order to compare the same substance under two different sets of condition, the law can be written as: P1 P2  (9) T 1 T 2 3.2 First Law of Thermodynamics The first law of thermodynamics, also known as the conservation of energy principle, states that the energy can be neither created nor destroyed; it can only change forms. The conservation of energy principle may be expressed as follows: The net change (increase or decrease) in the total energy of the system during a process is equal to the difference between the total energy entering and the total energy leaving the system during that process. Ein – Eout =  Esystem (10) This relation is often referred to as the energy balance and is applicable to any kind of system undergoing any kind of process. The determination of the energy change of a system during a process involves the evaluation of the energy of the system at the beginning and at the end of the process. That is, Energy change = energy at final state – energy at initial state Besides, the energy also can exist in numerous form such as internal (sensible, latent, chemical, and nuclear), kinetic, potential, electrical, and magnetic, and their sum constitutes the total energy of the system. For a simple compressible system, the change in the total energy of a system during a process is the sum of the changes in its internal, kinetic and potential energy can be expressed in the following form: (11)  E  U  KE  PE Where

U = m (u2 – u1) KE =

1 2

(12)

m(v 2  v1 ) 2

2

(13)

PE = mg (z2-z1)

(14)

Energy can be transferred to or from a system in three forms, which is heat, work and mass flow. Energy interactions are recognized at the boundary of system as they cross it and they represent the energy gained or lost by a system during a process. For a closed system, the energy involved is heat and work. Heat transfer to a system increases the energy of the molecules and thus the internal energy of the system, meanwhile the energy transfer from a system decreases it since the energy transferred out as heat comes from the energy of the molecules of the system. Work is an energy interaction that is not caused by a temperature difference between a system and its 7


surrounding system. The example of work interactions are rising piston and a rotating shaft. Work transfer to a system increases the energy of the system, and work transfer from a system decreases it as the energy transferred out as work comes from the energy contained in the system. The mass flow involved in the open system. When mass enters a system, the energy of the system increases because mass carries energy with it. Likewise, when the mass flows out from the system, the energy contained within the system decreases because the leaving mass takes out some energy with it. From the description above, it is known that the energy can be transferred in the forms of energy, work and mass flow, and the net transfer of a quantity is equal to the difference between the amounts transferred in and out. In conclusion, the energy balance can be written more explicitly as: Ein – Eout = (Qin – Qout) + (Win – Wout) + (Emass,in – Emass,out) =  Esystem (15) 3.3 Specific Heats The specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree. The energy depends on how the process is executed. Normally in thermodynamics, two kinds of specific heats are broadly used, which is specific heat at constant volume (Cv) and specific heat at constant pressure (C p). The specific heat capacity at constant volume is defined as the energy required to raise the temperature of the unit mass of a substance by one degree as the volume is maintained constant. The specific heat capacity at constant pressure is the energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant. The C p is always larger than Cv as at constant pressure the system is allowed to expand and the energy for expansion work must be supplied to the system. The defining equations for Cv and Cp are as follow: (16)  u  C v     T  v

 h    T  p

C p  

(17)

From the equation, it shows that the C v is a measure of the variation of internal energy of a substance with temperature, and Cp is a measure of the variation of enthalpy of a substance with temperature. 3.4 Internal energy, enthalpy and specifi c heats of ideal gases Joule has demonstrated in his classical experiment that the internal energy is a function of the temperature only. In his experiment, two tanks connected with a pipe and valve was submerged in a water bath. Initially, one tank contained air at high pressure and the other tank was evacuated. After thermal equilibrium was attained, he opened the valve to let air pass from one tank to the other until pressure equalized. From the observation, temperature of water bath remains constant and assumed no heat transfer. Since there is also no work done, he concluded that the internal energy of the air did not change even though the volume and the pressure changed. Internal

8


energy is a function of temperature only. By using the definition of enthalpy and the equation of state of an ideal gas, h = u +Pv and Pv = RT By combining both equations, h = u + RT (18) since R is a constant and u= u(T), the enthalpy of an ideal gas is also a function of temperature only, h = h (T) Therefore, at a given temperature for an ideal gas, u, h, C v and Cp will have fixed values regardless of the specific volume or pressure. Thus the differential changes in the internal energy and enthalpy of an ideal gas can be expressed as: du = Cv(T)dT (19) dh = Cp(T)dT (20) 3.5 Specific heat relati ons of i deal gas A special relationship between Cp and Cv for ideal gases can be obtained by differentiating the relation h = u +RT, which yields dh = du + RT

(21)

by replacing dh by CPdT and du by CvdT and dividing the resulting expression by dT, the equation becomes Cp = Cv + R (22) Another ideal gas property called the specific heat ratio k, defined as k 

C p C v

(23)

3.6 Determination of t he Heat Capacity Ratio The heat capacity ratio, k, given by equation (23) can be determined for air near standard pressure and temperature which is determined by a two step process: 1) 2)

An adiabatic reversible expansion from initial pressure, Pi, to an intermediate pressure Pm. A return of the temperature to its original value, To, at constant volume, attaining a final pressure, Pf k 

C p C v 9


Where Cp is the molar heat capacity at constant pressure and Cv is the molar heat capacity at constant volume. For a perfect gas, the following is true: Cp = Cv + R For a non-ideal gas, such as a reversible adiabatic expansion, dq = 0. According to first law of thermodynamics, dU = dq + dW During the expansion process: dU = dW dU = -PdV

(24)

The heat capacity related the change in temperature to the change in internal energy when the volume is held constant, shown as follow: dU = CvdT substituting CvdT into equation (24) and the equation becomes: CvdT = -PdV (25) Substituting into the ideal gas law, followed by integration yields equation (26) P V V C v (ln m  ln m )   R ln m Pi V i V i Rearranging and substituting from equation (22): ln

Pm Pi



C p C v

ln

V m V i

(26)

(27)

During the return of the temperature to its initial value, the following relationship is known: V m



V i

Pi P f

(28)

Substituting equation (28) into equation (27) and rearranging to obtain a heat capacity ratio (29), a comparison between theoretical and experimental heat capacity ratios can be easily conducted for a diatomic ideal gas. C p ln Pi  ln Pm C v



ln Pi  ln P f

10


3.7 Determination of Ratio o f vol umes using an isothermal process To determine the ratio of volumes using an isothermal process, one pressurized vessel is allowed to leak slowly into another vessel of different size. At the end of the process, the two vessels are equilibrated and the final pressure is constant in both vessels. The final equilibrium absolute pressure, Pabsf, can be determined using the ideal gas equation: Pabsf 

(m1  m2 ) RT (V 1  V 2 )

(29)

Where the subscript 1 and 2 represent vessels one and two respectively. Since both of the vessels are at room temperature before the valve is opened, and the entire process is isothermal, then the initial temperature will be equal to the final temperature. Taking the ideal gas equation into consideration, equations (30) and (31) are derived according to the initial mass contained within each vessel:

m1 

m2 

V 1 P1abs ,i RT

(30)

V 2 P2 abs ,i RT

(31)

using equations (30) and (31) and substituting the solutions for m1 and m2 respectively into equation (29), the equation becomes V 1 P1abs,i V 2 P2 abs,i ( ) RT  RT RT (32) P f  V 1 V 2 Cancelling RT and rearranging to provide the ratio of the two volumes, V 1 V 2



P2 abs ,i  P f P f  P1abs , i

(33)

11


4.0

INSTALLATION AND COMMISSIONING 4.1 Installation Procedures 1. 2. 3. 4.

Unpack the unit and place it on a table close to the single phase electrical supply. Place the equipment on top of a table and level the equipment with the adjustable feet. Inspect the all parts and instruments on the unit and make sure that it is in proper condition. Connect the pump to the nearest power supply.

4.2 Commissioning Procedures 1. Install the equipment according to 4.1. 2. Make sure that all valves are initially closed. 3. Fill up the sump tank with clean water until the water level is sufficient to cover the return flow pipe. 4. Then test the pump according to Section 5.1. 5. Check that pump, flow meter and the pressure gauges are working properly. Identify any leakage on the pipe line. Fix the leakage if there is any. 6. Turn off the pump after the commissioning. 7. The unit is now ready for use.

12


5.0

EXPERIMENTAL PROCEDURES 5.1 General Operating Procedur es 5.1.1 General Start-up Proc edures 1. Connect the equipment to single phase power supply and then switch on the unit. 2. Fully open all valves and check the pressure reading on the panel. This is to make sure that the chambers are under atmospheric pressure. 3. Then, close all the valves. 4. Connect the pipe from compressive port of the pump to pressurized chamber or connect the pipe from vacuum port of the pump to vacuum chamber. 5. Now, the unit is ready for use. 5.1.2 General Shut-down Procedures 1. Switch off the pump and remove both pipes from the chambers. 2. Fully open the valves to release the air inside the chambers. 3. Switch off the main switch and power supply.

13


5.2 Experiment 1: Boyle’s Law Experiment Objectives: To determine the relationship between pressure and volume of an ideal gas To compare the experimental results with theoretical results PRECAUTIONS: When carrying out the experiment, pump pressure level should not exceed 2 bar as excessive pressure may result in glass cylinder breaking. Experimental Procedures: 1. 2. 3. 4. 5. 6. 7. a) b) 8.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Switch on the compressive pump and allow the pressure inside chamber to increase up to about 150kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading for both chambers before expansion. Fully open V 02 and allow the pressurized air flows into the atmospheric chamber. Record the pressure reading for both chambers after expansion. The experimental procedures can be repeated for the following conditions: From atmospheric chamber to vacuum chamber From pressurized chamber to vacuum chamber Calculate the PV value and prove the Boyles’ Law.

14


5.3 Experiment 2: Gay-Lussac Law Experiment Objectives: To determine the relationship between pressure and temperature of an ideal gas Experimental procedures: 1. Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. 2. Connect the hose from compressive pump to pressurized chamber. 3. Switch on the compressive pump and records the temperature for every increment of 10kPa in the chamber. Stop the pump when the pressure PT 1 reaches about 160kPa. 4. Then, slightly open valve V 01 and allow the pressurized air to flow out. Records the temperature reading for every decrement of 10kPa. 5. Stop the experiment when the pressure reaches atmospheric pressure. 6. The experiment is repeated for three times to get the average value. 7. Plot graph of pressure versus temperature.

15


5.4 Experiment 3: Isentropic Expansion Process Objectives: To demonstrate the isentropic expansion process Experimental procedures: 1. 2. 3. 4. 5. 6. 7.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Connect the hose from compressive pump to pressurized chamber. Switch on the compressive pump and allow the pressure inside chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading PT 1 and temperature TT 1. Then, slightly open valve V 01 and allow the air flow out slowly until it reaches atmospheric pressure. Record the pressure reading and temperature reading after the expansion process. Discuss the isentropic expansion process.

16


5.5 Experiment 4: Stepwise Depressurization Objectives: To study the response of the pressurized vessel following stepwise depressurization Experimental procedures: 1. 2. 3. 4. 5. 6. 7.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Connect the hose from compressive pump to pressurized chamber. Switch on the compressive pump and allow the pressure inside chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading PT 1. Fully open valve V 01 and bring it back to the closed position instantly. Monitor and records the pressure reading PT 1 until it becomes stable. Repeat step 5 for at least four times. Display the pressure reading on a graph and discuss about it.

17


5.6 Experiment 5: Brief Depressurization Objectives: To study the response of the pressurized vessel following a brief depressurization Experimental procedures: 1. 2. 3. 4. 5. 6.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Connect the hose from compressive pump to pressurized chamber. Switch on the compressive pump and allow the pressure inside chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading PT 1. Fully open valve V 01 and bring it back to the closed position after few seconds. Monitor and records the pressure reading PT 1 until it becomes stable. Display the pressure reading on a graph and discuss about it.

18


5.7 Experiment 6: Determination of r atio of volume Objectives: To determine the ratio of volume and compares it to the theoretical value Experimental Procedures: 1. 2. 3. 4. 5. 6. 7. a) b) 8.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Switch on the compressive pump and allow the pressure inside chamber to increase up to about 150kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading for both chambers before expansion. Open V 02 and allow the pressurized air flows into the atmospheric chamber slowly. Record the pressure reading for both chambers after expansion. The experimental procedures can be repeated for the following conditions: From atmospheric chamber to vacuum chamber From pressurized chamber to vacuum chamber Calculate the ratio of volume and compares it with the theoretical value.

19


5.8 Experiment 7: Determination of ratio of heat capacity Objectives: To determine the ratio of heat capacity Experimental procedures: 1. 2. 3. 4. 5. 6.

Perform the general start up procedures in section 5.1. Make sure all valves are fully closed. Connect the hose from compressive pump to pressurized chamber. Switch on the compressive pump and allow the pressure inside chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber. Monitor the pressure reading inside the chamber until it stabilizes. Record the pressure reading PT 1 and temperature TT 1. Fully open valve V 01 and bring it back to the closed position after few seconds. Monitor and records the pressure reading PT 1 and TT1 until it becomes stable. Determine the ratio of heat capacity and compare with the theoretical value.

20


6.0

REFERENCES http://www.chemeng.queensu.ca/courses/CHEE218/projects/GasExpansion/ExpansionProcesses ofaPerfectGas.php

21

APPENDIX A SAMPLE DATA SHEET

EXPERIMENT 1: Boyle’s Law Experiment Before expansion

After expansion

PT 1 (kPa abs) PT 2 (kPa abs)

EXPERIMENT 2: Gay-Lussac Law Experiment

Pressure

Trial 1

Trial 2

Trial 3

Temperature (°C)

Temperature (°C)

Temperature (°C)

(kPa abs) Pressurise

Depressurise

Pressurise

Depressurise

Pressurise

Depressurise

vessel

vessel

vessel

vessel

vessel

vessel

110 120 130 140 150 160

EXPERIMENT 3: Isentropic Expansion Process Before expansion PT 1 (kPa abs) TT 1 (°C)

After expansion

EXPERIMENT 4: Stepwise Depressurization PT 1(kPa abs) initial

After first

After second

After third

After fourth

expansion

expansion

expansion

expansion

EXPERIMENT 5: Brief Depressurization PT 1(kPa abs) initial

After brief expansion

EXPERIMENT 6: Determination of ratio of volume PT 1 (kPa abs)

PT 2 (kPa abs)

Before expansion After expansion

EXPERIMENT 7: Determination of ratio of heat capacity initial PT 1 (kPa abs) TT 1 (°C)

intermediate

final

APPENDIX B TYPICAL EXPERIMENTAL RESULT

EXPERIMENT 1: Boyle’s Law Experiment Condition 1: from pressurised vessel to atmospheric vessel Before expansion

After expansion

PT 1 (kPa abs)

147.1

131.6

PT 2 (kPa abs)

101.5

131.7

Condition 2: from pressurised vessel to vacuum vessel Before expansion

After expansion

PT 1 (kPa abs)

157.1

123.7

PT 2 (kPa abs)

54.2

123.7

Condition 3: from atmospheric vessel to vacuum vessel Before expansion

After expansion

PT 1 (kPa abs)

103.9

92.9

PT 2 (kPa abs)

70.3

93.0

Sample calculation: For condition 1: from pressurised vessel to atmospheric vessel V1 = 0.025m3 V2 = 0.01237m3 By using Boyle’s Law, P1V1 = P2V2 (147.1 x 0.025)+(101.5 x 0.01237) = (131.6 x 0.025)+(131.7x 0.01237) 3.6775 + 1.255555 = 3.29 + 1.629129 4.933055 = 4.919129 The difference is only 0.013926, therefore the Boyle’s Law is verified.

EXPERIMENT 2: Gay-Lussac Law Experiment

Pressure

Trial 1

Trial 2

Trial 3

Temperature (°C)

Temperature (°C)

Temperature (°C)

(kPa abs) Pressurise

Depressurise

Pressurise

Depressurise

Pressurise

Depressurise

vessel

vessel

vessel

vessel

vessel

vessel

110

28.9

31.2

29.4

29.4

28.8

31.5

120

29.2

32.2

29.4

30.7

29.1

32.5

130

30.0

33.0

30.0

31.8

29.9

33.2

140

31.0

33.6

30.7

32.6

30.9

33.7

150

31.9

34.0

31.5

33.3

31.9

34.0

160

32.8

34.1

32.6

33.8

32.8

34.1

Pressure

Average

(kPa abs)

temperature (°C)

110

29.9

120

30.5

130

31.3

140

32.1

150

32.8

160

33.4

Graph of pressure against temperature The pressure is directly proportional to temperature. Hence, the Gay Lussac Law is verified.

EXPERIMENT 3: Isentropic Expansion Process Before expansion

After expansion

PT 1 (kPa abs)

157.0

101.4

TT 1 (°C)

31.4

28.4

Sample calculation:

For isentropic process,

T 2 T 1



P2

(

k 1 

k

)

P1

k = 1.4 (28.4/31.4) = (101.4/157.0)0.2857 0.9045 = 0.8826 The difference is 2.48%. The expansion process is proven as isentropic.

EXPERIMENT 4: Stepwise Depressurization Pressure (kPa abs) initial

156.6

After first

After second

After third

expansion

expansion

expansion

123.4

102.6

101.4

123.5

102.7

101.5

123.6

102.8

101.6

123.7

102.9

101.7

123.8

103.0

101.8

123.9

103.1

101.9

124.0

103.2

102.0

124.1

103.3

102.1

124.2

103.4

102.2

124.3

103.5

102.3

124.4

103.6

102.4

124.5

103.7

102.5

124.6

103.8

102.6

124.7

103.9

102.6

124.8

104.0

102.6

124.9

104.1

102.6

125.0

104.2

102.6

125.1

104.3

125.2

104.4

125.3

104.5

125.4

104.6

125.5

104.7

125.5

104.8

. 104.9 105.0 105.1 105.2 105.3 105.4 105.5 105.6 105.7 105.8 105.9 106.0 106.1 106.1 106.1 106.1

Graph of response of pressurised vessel following stepwise depressurisation

EXPERIMENT 5: Brief Depressurization PT 1(kPa abs) initial

After brief expansion

156.9

103.3 103.4 103.5 103.6 103.7 103.8 103.9 104.0 104.1 104.2 104.3 104.4 104.5 104.6 104.7 104.8 104.9 105.0 105.1 105.2 105.3 105.4 105.5

105.6 105.7 105.8 105.9 106.0 106.1 106.2 106.3 106.4 106.5 106.6 106.7 106.8 106.9 107.0 107.1 107.2 107.3 107.4 107.5 107.6 107.7 107.8 107.9 108.0 108.1

108.2 108.3 108.4

Graph of response of pressurised vessel following a brief depressurisation

EXPERIMENT 6: Determination of ratio of volume Condition 1: from pressurised vessel to atmospheric vessel PT 1 (kPa abs)

PT 2 (kPa abs)

Before expansion

147.1

101.4

After expansion

132.1

132.2

Condition 2: from pressurised vessel to vacuum vessel PT 1 (kPa abs)

PT 2 (kPa abs)

Before expansion

154.6

55.8

After expansion

122.5

122.5

Condition 3: from atmospheric vessel to vacuum vessel PT 1 (kPa abs)

PT 2 (kPa abs)

Before expansion

101.5

51.4

After expansion

85.1

85.1

sample calculation: condition 1: Volume 1/Volume 2 = (P2,initial – P2,final) / (P1,final – P1,initial) 0.025/0.01237 = (101.4-132.2) / (132.1-147.1) 2.02 = 2.05 Difference = 0.03

EXPERIMENT 7: Determination of heat capacity initial

intermediate

final

PT 1 (kPa abs)

191.8

109.8

120.0

TT 1 (°C)

31.8

29.0

29.3

C p C v



ln Pi



ln Pm

ln Pi



ln P f

ln 191.8 ln 109.8 



ln 191.8 ln 120.0 

= 1.189 The ideal k,

C p C v

= 1.4

deviation = (1.4-1.189) / 1.4 x 100% deviation = 15% The deviation is due to the measurement error. Theoretically, the intermediate pressure should be lower than the measured intermediate pressure. However, due to the heat loss and sensitivity of pressure sensor, the error occurs. The intermediate pressure should be taken as the lowest pressure which read at the moment the valve is closed. Note:

APPENDIX C ASSEMBLY OF TH11

Parts of TH11

Make sure the gasket is placed properly inside the groove.

Make sure the gasket is inside the groove of the PVC valve (V2).

Place the big glass on the flange on top of the gasket.

Screw in the electrodes into the support of the flange

TH11 EXPERIMENTAL MANUAL.pdf

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