Pvt Lab Report

ABSTRACT

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. The objectives of this experiment successfully achieved. Boyle’s and

Gay-Lussac’s law was proven in this experiment when the ideal gas obey the law. The

volume ratio and heat capacity were also determined. . In first experiment, we are

investigating about boyle’s law. We will compare the results with boyle’s law. The

experiment is run from pressurize chamber to atmospheric atmospheric to vacuum,

pressurized to vacuum chamber. Then take the pressure reading. For second experiment,

we are investigating about the relationship between pressure and ideal gas. For every

increment of 10 kPa from atmospheric pressure, and every decrement of 10kPa, the

temperature reading is taken and the graph is plotted. For experiment 3, we set the

temperature to 160kPa then slightly open the valve for 3 seconds, then take the pressure

and temperature reading. This is to determine the ratio of heat capacity. For last

experiment, we are investigating about isentropic expansion process, by releasing the gas

inside chamber bit by bit for 3 seconds. The pressure and temperature reading is taken.

The experiment was successful.

INTRODUCTION

The Perfect Gas Expansion Apparatus from model TH11 is a sufficient bench top unit

designed in order to expose the student and familiar with the fundamental thermodynamic

processes.

This experiment likely safe and more convenient to demonstrate thermodynamic

properties. The apparatus have two vessel, 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.

An “ideal” gas exhibits certain theoretical properties. Specifically, an ideal gas …

•Obeys all of the gas laws under all conditions.

•Does not condense into a liquid when cooled.

•Shows perfectly straight lines when its V and T & P and T relationships are plotted on a

graph.

The ideal gas law :

PV = nRT

P = Pressure (in kPa)

V = Volume (in L)

T = Temperature (in K)

n = moles

Isentropic (reversible adiabatic) processes are often desired and are often the

processes on which device efficiencies are based. An isentropic process is an idealization

of an actual process, and serves as a limiting case for an actual process.

In this experiment, we are going to demonstrate boyle’s law , isentropic process, and

determination of heat capacity.

OBJECTIVES

i.EXPERIMENT 1

The objectives of this experiment is to determine the relationship between pressure and

volume of an ideal gas and to compare the experimental results with theoretical results.

ii.EXPERIMENT 2

The objectives of this experiment is to determine the relationship between pressure and

the temperature of an ideal gas.

iii.EXPERIMENT 3

The experiment is to demonstrate the isentropic expansion process.

iv.EXPERIMENT 4

The experiment is to study the response of the pressurized vessel following stepwise

depressurization.

v.EXPERIMENT 5

The objectives of this experiment is to study the response of the pressurized vessel

following a brief depressurization.

vi.EXPERIMENT 6

The experiment is to determine the ratio of volume and compares it to the theoretical

value.

vii.EXPERIMENT 7

This experiment is to determine the ratio heat capacity.

THEORY

Perfect Gas

Theories of perfect gas can be divided into three which is Charles’s law, Boyle’s law and Gay-Lussac’s law. Perfect gas is same with ideal gas where there is none attractive forces exist in the ideal gas. Since perfect gas is an ideal gas, they collide between atoms or molecules elastically with no intermolecular attractive forces. Some assumption has been respect to kinetic theory of ideal gas which is the gasses are made up of molecules that always move in a constant straight line. An equation had been introduced in 1662 where it has been named as ideal gas equation of state:

P=R ¿)

The subscript R refer to gas constant where different gas would have different value of R. Any gas that obeys this law is called an ideal gas. The equation also can be written as:

PV=mRT

The properties of ideal gas at two different state is related to each other as long as they has one constant property throughout the experiment where:

Boyle’s Law

The behavior real gas using parameter of pressure, temperature and volume is considered at low density. Ideal gas also obeys the law of Boyle’s, Charles’s and Gay-Lussac’s. Boyle’s lawdescribe 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 increase, the volume of the container also increase. Therefore the equation of Charles’s law simply show 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 become 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 3: Graph of Gay-Lussac's Law

First law of thermodynamics

Based on first law of thermodynamics statement, energy can be neither created nor destroyed but it can only change in the form of energy. For example the change of energy of lamp, from electric energy convert to light and heat energy. Therefore, the conservation of energy principle introduced as the net change in the total energy of the system equivalent to the difference in the total energy enter the system and total energy leaving the system.

That equation also referred as energy balance equation that applicable to any kind system any kind of process. Since the energy has numerous form such as internal, kinetic, potential, electrical and magnetic and their sum constitutes the total energy of the system. Simple compressible system has the following equation which the change in the total energy of a system is the sum of the changes in its internal, kinetic, potential energy can be expressed as:

Where internal energy, U

Where kinetic energy, KE

Where the potential energy, PE

Energy can be transfer in or out of a system in three forms such as heat, work and mass flow. As there is one of any three form cross the boundary of an open system, it can be concluded as energy gained or lost during a process. In a closed system, there is only two form can pass through the boundary which can change the energy which are heat and work. Temperature difference in a system with its surrounding is not an energy interaction. Work interactions refer as rising piston and rotating shaft. Commonly sense when the work transfer into the system, the energy of the system increase and vice versa. As mass transfer in the system, energy also increase as the mass carries energy with it and vice versa. Equation below represent the concluded energy balance.

Amount of energy required to raise the temperature of a unit mass of a substance by one degree is a definition of specific heat. There are two specific heat use widely which

is specific heat at constant volume and specific heat at constant pressure. Cp value larger than Cv as at constant pressure system is allowed to expand and the energy must supplied to system. Specific heat capacity at constant pressure is the energy required to raisethe temperature of the unit mass of a substance by one degree as the pressure remain constant. It can be concluded that Cv is related to internal energy and Cp involved enthalpy value.

Internal energy is a function of temperature only. As the temperature high, then enthalpy value also big. Then the enthalpy value is represent with subscript h:

Where it can combine to become:

Cp and Cv has special relationships for ideal gas by differentiating the h = u + RT to produce dh = du + RT and by replacing dh by CpdT and du by CvdT, the equation come out with:

Specific heat capacity also has the constant k by the relation of:

Ratio of volumes using isothermal process can be determine using isothermal process. One pressurized vessel is allowed to leak slowly into another vessel of different size.

Finally, the pressure will be same for both vessel. Final pressure in vessel can be calculated by:

Both vessel was placed in room temperature before valve is opened lead the isothermal process and the initial temperature will be equal to the final temperature. Deriving :

Using these equation, substitute m1 and m2 into equation of Pabsf and become:

Rearrange the equation and cancel the RT to give the ratio of the two volume:

Stepwise Depressurization

Stepwise depressurization is conducted by depressurizing the chamber or tank step by step slowly or gradually by flowing out the gas which they would expand at every instant opened and closed in order to identify gradual changes in pressure and temperature within the contrary decreases with the expansion.

Brief Depressurization

This is similar to stepwise depressurization but reduced in terms of time. The time interval increased to a few seconds. This is to make sure that, the effect on the pressure and temperature can be observe which can be compared later. The graph should be more higher gradient.

PROCEDURES

GENERAL OPERATING PROCEDURES

A. GENERAL START-UP PROCEDURES1. Equipment was connected to single phase power supply and the unit was switched on.2. All valve was fully opened and the pressure reading on the panel was checked just to

make sure the pressure was at atmospheric pressure.3. All valve was closed.4. Pipe from compressive pump connected to pressurized chamber or the pipe from

vacuum pump connected to vacuum chamber.5. The unit was ready to use.

B. GENERAL SHUT-DOWN PROCEDURES1. Pump was switched and the pump was removed from the chamber.2. The valve was fully open in order to release out the air inside the chamber.3. The switch and power supply was switched off.

EXPERIMENT 1 : Boyle’s law

A. EXPERIMENT 1.1 : condition 11. All valve was fully closed.2. Compressive pump, Tank 1 was filled with air until 150kPa.3. The gas was transferred from tank 1 to tank 2 by opening the valve between tanks.4. The temperature and pressure was recorded.

B. EXPERIMENY 1.2 : condition 21. All valve was fully closed.2. Tank 2 was filled with air until 50kPa.3. The gas was then transferred from tank 2 to tank 1 by opening the valve between tanks.4. The temperature and pressure was recorded.

C. EXPERIMENT 1.3 : condition 31. All valve was fully closed.2. Both tank 1 and tank 2 filled with air until 150kPa and 50kPa.3. The valve between tanks was opened.4. The pressure and temperature was recorded.

EXPERIMENT 2 : Gay-Lussac Law Experiment

1. All valve was fully closed.

2. The hose from compressive pump was connected to pressurize chamber. 3. Compressive pump was turned on and the temperature was recorded for every

increment of 10kPa in the chamber and the pump stopped when the pressure in tank 1 has achieved 160kPa.

4. The valve was slightly opened and the pressurized air are allowed to flow out. The temperature was recorded for every decrement in 10kPa.

5. The experiment stopped when the pressure in tank 1 has reached atmospheric pressure that is 101.3kPa.

6. The experiment repeated for three times in order to get the average value. 7. A graph of pressure versus temperature was plotted.

EXPERIMENT 3 : Isentropic Expansion Process

1. All valve was fully closed.2. Hose was connected from compressive pump to pressurized chamber.3. Compressive pump was switched on and the chamber was pressurized until 160kP.

Pump was switched off and the hose was removed from the chamber.4. The pressure was monitored until the reading was stabilized. The pressure and

temperature was recorded.5. The valve was slightly opened and the air was flow out slowly until reached the

atmospheric pressure. 6. The pressure and temperature reading was recorded after the expansion process.7. The isentropic process was discussed.

EXPERIMENT 4 : Stepwise depressurization

1. All valve was fully closed.2. Tank 1 was filled with air until 160kPa and record the data.3. The valve 1 was opened and closed quickly for 5 times.4. The data was recorded.

EXPERIMENT 5 : Brief depressurization

1. All valve was fully closed.

2. Tank 1 was filled with air until 150kPa and the data was recorded.3. Valve 1 was open for 3 seconds.4. The data was recorded.

EXPERIMENT 6 : Determination of ratio volume

1. All valve was fully closed.2. Tank 1 or pressurized tank was filled with air at about 150kPa.3. The data was recorded.4. Valve 2 was slightly opened and the data was recorded.5. The experiment was repeated by passing air from tank 2 to tank 1 and tank 1 to tank 2

by using the pressure of 150kPa for tank 1 and 50kPa for tank2.

EXPERIMENT 7 : Determination of Ration of Heat Capacity

1. General start up was done and the valve was fully closed.2. The hose from the compressive pump was connected to the pressurized chamber.3. Compressive pump was switched on and the chamber was pressurized until 160kPa.

Then, the pump was switched off and the hose was removed from the chamber.4. C. The pressure and temperature was recorded.8. The valve one was fully open and closed after few seconds. The pressure and

temperature was monitored and recorded right after the reading was stabilized. 5. The ratio of heat capacity and the theoretical value was compared.

APPARATUS

1) Pressure transmitter2) Pressure relief valve3) Temperature sensor4) Big glass5) Small glass6) Vacuum pump7) Electrode

RESULTS

EXPERIMENT 1

A. EXPERIMENT 1.1

Before expansion After expansion

PT 1 (kPa abs) 153.4 135.8

PT 2 (kPa abs) 103.2 135.2

B. EXPERIMENT 1.2


PT 1 (kPa abs) 105.0 88.8

PT 2 (kPa abs) 57.9 88.7

C. EXPERIMENT 1.3


PT 1 (kPa abs) 150.8 119.4

PT 2 (kPa abs) 59.1 118.9

EXPERIMENT 2

TRIAL 1 TRIAL 2 TRIAL 3

PRESSURE (kPa abs)

TEMPERATURE ( ͦC) TEMPERATURE ( ͦC) TEMPERATURE ( ͦC)

PRESSURIZED

VESSEL

DEPRESSURIZED VESSEL

PRESSURIZED

VESSEL


PRESSURIZED

VESSEL


103.3 26.3 25.0 25.0 25.4 25.3 25.6

110 264 25.6 25.1 26.6 25.3 27.4

120 26.7 26.6 25.5 27.7 25.7 28.4

130 27.4 27.7 26.2 28.7 26.3 29.0

140 28.1 28.7 27.2 29.2 27.2 29.4

150 28.9 29.2 28.0 29.7 28.1 29.8

160 29.7 29.3 29.0 29.8 28.8 29.7

EXPERIMENT 3

BEFORE EXPANSION AFTER EXPANSION

PT 1 (kPa abs) 160.6 103.5

TT 1 ( ͦC) 27.3 25.0

EXPERIMENT 4

PT 1 (kPa abs)

INITIAL AFTER FIRST EXPANSION AFTER SECOND EXPANSION

160.0 104.5 104.3

EXPERIMENT 5

PT 1 (kPa abs)

INITIAL AFTER BRIED EXPANSION

150.0 121.3

EXPERIMENT 6

A. PRESSURIZED AIR FLOW FROM TANK 1 TO TANK 2

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

BEFORE EXPANSION 149.3 103.3

AFTER EXPANSION 132.4 131.6

B. PRESSURIZED AIR FLOW FROM TANK 2 TO TANK 1




C. BOTH TANK 1 AND 2 WAS PRESSURIZED




EXPERIEMENT 7

INITIAL INTERMEDIATE FINAL

PT 1 (kPa abs) 160.5 141.0 121.5

TT 1 ( ͦC) 27.4 27.3 27.2

RECOMMENDATION

Before starts the experiment, each of the experiment must do the start-up and shut-down

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. The pump

pressure must not be above 2bar as excessive pressure may results in glass breaking. The

valves must be opened slowly and not abruptly opened or else may results in explosion.

Before experiment is proceed, the initial reading must at atmospheric pressure for both

chamber. Tighten the hose before pumping.

REFERENCES

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.rhtml

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.

5. (n.d.). PERFECT GAS EXPANSION APPARATUS. PUNCHONG, SELANGOR, MALAYSIA: SOLUTION ENGINEERING SDN. BHD.

APPENDIX

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 if the pressure increase, the temperature also increase with constant volume. Experiment two has been conducted in order to know the relationship between pressure and temperature. Therefore, 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.

Isentropic expansion process occur when the system are reversible and adiabatic where no heat will be transferred in or out and no energy transformation occurs. From the data recorded, a constant k are now known which is equal to 1.814. 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.

ΔS=0 or S1=S2 (KJol/kg.K)

An isentropic process is an idealization of an actual process, and serves as a limiting case for an actual process.

The relations of entropy change for ideal gases are:

(1) and

(2)

An Isentropic Process of Ideal Gases on a T-s Diagram.

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 by V2/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 than 10%, 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

fine 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. The boyle’s law cannot be proven. The relationship of pressure is

linearly proportional to temperature. The heat capacity ratio experimental is k=1.400 where

as the theoretical value is 1.3996. The isentropic process is shown.

Pvt Lab Report

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