Fatin 2019.docx

GAS EXPANSION LAB EXPERIMENT 2 EH243 3C GROUP 3 MOHD AMIR HILMI BIN IBRAHIM MADIHI BIN NORHADI NURFATINI AMAL BINTI CHE AB AZHAR

2018441438 2018441524 2018657618

ABSTRACT This experiment involving a perfect gas or ideal gas has four 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 last experiment, we are investigating about isentropic expansion process, by releasing the gas inside chamber bit by bit. 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.

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.

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: 𝑇

𝑃 = 𝑅(𝑉) 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 GayLussac’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 constantvolume.

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

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.

Material and Apparatus 1) Gas 2) Gas Pump 3) Pressure Chamber 4) Vacuum Chamber

Gas Expansion Apparatus

Valve 1

Valve 2

Monitor Pressure and Temperature

Valve 3

Methodology General Start-up 1. The equipment are connected to single phase power supply and the unit is switch on. 2. Then, open all valves and the pressure reading panel. This is to make sure that thechambers are under atmospheric pressure. 3. After that, close all the valves. 4. Next, connect the pipe from compressive port of the pump to pressure chamber orc onnect the pipe from vacuum port of the pump to vacuum chamber. The connect mustnot does at the same time. 5. Now, the unit is ready to use.

Experiment 1: Boyle’s Law 1. The general start up procedure is performed. Make sure all valve are fully closed. 2. Compressive pump is switch on and allowed the pressure inside the chamber to increaseup to about 150kPa. Then, switch off the pump and remove the hose from the chamber. 3. The pressure reading inside the chamber is monitor until the reading stabilizes. 4. The pressure reading for both chambers is recorded before expansion.

5. Open V02 fully and allowed the pressurized air flow into the atmospheric chamber. 6. The pressure reading for both chambers after expansion is recorded. 7. The experiment is repeated under difference condition: a)From atmospheric chamber to vacuum chamber. b)From pressurized chamber to vacuum chamber.

8.Then, calculated the PV value and prove the Boyles’ Law.

Experiment 2: Gay-Lusac Law 1. Perform the general start up. Make sure all e valves are fully closed. 2. The hose from the compressive pump is connected to pressurized chamber. 3. The compressive pump is switch on and the temperature for every increment of 10kPa in the chamber is recorded. The pump stop went the pressure PT1 reaches about 160kPa. 4. Then, open valve V 01 and allowed the pressurized air to flow out. Recorded the temperature reading for every decrement of 10kPa. 5. Stop the experiment when the pressure reaches atmospheric pressure. 6. The experiment is repeated for 3 times to get the average value.

7. The graph of the pressure versus temperature Plot. Experiment 3: Isentropic Expansion Process 1. The general start up is perform make sure all valve are fully closed. 2. The hose from compressive pump is connected to pressurized chamber. 3. The compressive pump is switch on and allowed the pressure inside the chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber. 4. The pressure reading inside is monitor until it is stabilizes. The pressure reading PT1 and temperature reading TT1 are recorded. 5. Then, open the valve V 01 slightly and allow the air flow out slowly until it reach atmospheric pressure. 6. The pressure of the reading and the temperature reading after the expansion process are recorded. 7. The isentropic expansion process is discussed. Experiment 4: Stepwise Depressurization. 1. The general start up is perform make sure all valve are fully closed 2. The hose from compressive pump is connected to pressurized chamber. 3. The compressive pump is switch on and allowed the pressure inside the chamber to increase until about 160kPa. Then, switch off the pump and remove the hose from the chamber 4. The pressure reading inside is monitor until it is stabilizes. The pressure reading at PT1 are recorded. 5. Valve V 01 will be opened fully and instantly closed. Pressure reading at PT 1 are monitored until it becomes stable and recorded. 6. Step 5 must be repeated for at least four times. 7. Pressure reading are displayed using graph and discussed. DATA AND RESULTS

Experiment I :

Conditions Pressure To Atmosphere (at Pressure Chamber)

Before

After

Atmospheric To Vaccum (at Vacuum Chamber)

Before

After

Before

Pressurized mixed Vacuum (at both of Vaccum and Pressure Chamber)

After

Pressure, kPa

Temperature, oc

PT1 - 150.2

TT1 – 31.5

PT2 - 102.8

TT2 – 31.0

PT1 - 134.1

TT1 – 30.9

PT2 – 132.7

TT2 - 32.2

PT1 – 105.0

TT1 – 31.2

PT2 – 58.1

TT2 – 30.8

PT1 – 91.2

TT1- 31.0

PT2 – 89.7

TT2 – 32.0

PT1 – 154.1

TT1 – 32.8

PT2 – 55.2

TT2 – 30.5

PT1 – 121.6

TT1- 31.2

PT2 - 120.3

TT2- 33.1

Experiment II :

Pressure (kPa abs)

Trial 1

Trial 2

Trial 3

Temperature oc

Temperature oc

Temperature oc

Pressurise vessel

Depressuri se vessel

Pressurise vessel

Depressur Pressurise Depressur ise vessel vessel ise vessel

100

31.0

30.7

30.6

30.6

30.6

31.4

110

31.2

30.8

31.0

30.8

30.6

31.7

120

31.5

31.5

31.8

31.5

31.0

32.6

130

32.1

32.2

32.7

32.2

31.6

33.6

140

33.1

33.3

33.7

33.2

32.6

34.6

150

34.0

34.7

34.5

33.6

33.5

35.7

160

34.8

35.9

34.9

34.8

34.4

35.5

Average Trial

Pressure (kPa abs)

Temperature oc Pressurise vessel

Depressurise vessel

100

30.73

30.90

110

30.93

31.10

120

31.43

31.87

130

32.13

32.67

140

33.13

33.70

150

34.00

34.67

160

34.70

35.40

PT1 (kPa abs)

TT1 (Oc)

Before Expansion

153.6

32.2

After Expansion

104.3

30.1

Experiment III :

Experiment IV :

Initial Pressure (kPa abs)

153.6

First (open- Second (openclosed valve) closed valve)

133.9

123.5

Fourth

Third (openclosed valve)

(open-closed valve)

156.5

110.6

RESULT AND CALCULATION

Experiment I:

Conditions Pressure To Atmosphere (at Pressure Chamber)

Before After

Atmospheric To Vaccum (at Vacuum Chamber)

Before After

Pressurized mixed Vacuum (at both of Vaccum and Pressure Chamber)

Before After

Pressure, kPa PT1 - 150.2 PT2 - 102.8 PT1 - 134.1 PT2 – 132.7 PT1 – 105.0 PT2 – 58.1 PT1 – 91.2 PT2 – 89.7 PT1 – 154.1 PT2 – 55.2 PT1 – 121.6 PT2- 120.3

Temperature, oc TT1 – 31.5 TT2 – 31.0 TT1 – 30.9 TT2 -32.2 TT1 – 31.2 TT2 – 30.8 TT1- 31.0 TT2 – 32.0 TT1 – 32.8 TT2 – 30.5 TT1- 31.2 TT2- 33.1

Ideal gas equation, PV=RT. For Boyle’s law, temperature is constant at room temperature Hence, R= 8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 , T= 298 @ 25°C

i)From atmospheric chamber to pressurized chamber P1 = 150.2 kPa, P2 = 134.1 kPa. Then 𝑉1 and 𝑉2 is calculated 𝑉1= RT/𝑃1 = (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ,) (298.15 K) / (150.2 kPa) = 16.50L 𝑉2= (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ) (298.15 K) / (134.1 kPa)

= 18.48L According to Boyle’s law: 𝑃1 𝑉1=𝑃2 𝑉2 𝑃1 𝑉1= (150.2kPa) (16.50L) = 2478.3 L.kPa 𝑃2 𝑉2 = (134.1kPa) (18.48L) = 2478.17 L.kPa i) From the atmospheric chamber to vacuum chamber P 𝑃1 = 105.0 kPa, 𝑃2 = 91.2 kPa. Then 𝑉1 and 𝑉2 is calculated 𝑉1 = RT/𝑃1 = (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ,) (298.15 K) / (105.0 kPa) = 23.61L 𝑉2 = (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ) (298.15 K) / (91.2 kPa) = 27.18L According to Boyle’s law: 𝑃1 𝑉1=𝑃2 𝑉2 𝑃1 𝑉1 = (105.0 kPa) (23.61L) = 2479.05 L.kPa 𝑃2 𝑉2 = (91.2 kPa) (27.18L) = 2478.82 L.kPa

ii) From pressure chamber to vacuum chamber 𝑃1 = 154.1 kPa, 𝑃2 = 121.6 kPa. Then 𝑉1 and 𝑉2 is calculated 𝑉1 = RT/𝑃1 = (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ,) (298.15 K) / (154.1 kPa) =16.09 L 𝑉2= (8.314 L kPa 𝐾 −1 𝑚𝑜𝑙 −1 ) (298.15 K) / (121.6 kPa) =20.36 L

According to Boyle’s law: 𝑃1 𝑉1=𝑃2 𝑉2 𝑃1 𝑉1= (154.1kPa) (16.09L) = 2479.47 L.kPa 𝑃2 𝑉2 = (121.6kPa) (20.36L) = 2475.78 L.kPa

Experiment II:

Pressure (kPa abs) 100 110 120 130 140 150 160

Trial 1 Temperature oC Pressurize Depressuriz vessel e vessel 31 30.7 31.2 30.8 31.5 31.5 32.1 32.2 33.1 33.3 34 34.7 34.8 35.9 Pressure (kPa abs) 100 110 120 130 140 150 160

30.7 30.9 31.4 32.1 33.1 34.0 34.7

Trial 2 Temperature oC Pressurize Depressuri vessel ze vessel 30.6 30.6 31 30.8 31.8 31.5 32.7 32.2 33.7 33.2 34.5 33.6 34.9 34.8

Trial 3 Temperature oC Pressurize Depressuri vessel ze vessel 30.6 31.4 30.6 31.7 31 32.6 31.6 33.6 32.6 34.6 33.5 35.7 34.4 35.5

Average Trial Temperature oC Pressurize vessel Depressurize vessel 30.9 31.1 31.9 32.7 33.7 34.7 35.4

Graph of Pressure vs Temperature Temperature

36 34 32 30 28 100

110

120

130

140

150

160

Pressure Pressurise temperature

Depressurise temperature

Experiment III:

Before Expansion After Expansion

T 2  P2    T 1  P1 

k 1 k

k 1

30.0 104.3  101k.31  k 30.1 T 2 = P 2  k   .8  33.9 153.6 32.2  154 T 1  P1  𝐾−1k 1 0.935 𝐾  kk1 0.654 0.885=0.679 30.0  101.3  k    k 1  330.9.885  154 ln  .8   ln 0.654  k k 1 0.885  0k.654  1  k  1.22     0.425 kk 1   ln 0.885    ln 0.654

PT1 (kPa abs) 153.6 104.3

TT1 (Oc) 32.2 30.1

𝑙𝑛0.935 = [ −0.067 = [ 0.173 = [

𝑘−1 ] 𝑙𝑛0.679 𝑘

𝑘−1 ] (−0.387) 𝑘

𝑘−1 ] 𝑘

0.173𝑘 = 𝑘 − 1

𝑘 = 1.23

Experiment IV:

Initial Pressure (kPa abs)

First (openclosed valve)

156.5

156.5 152.4 148.2 144.7 139.8

Second (openclosed valve) 139.8 136.5 133.4 130.2 128.3

Third (openclosed valve) 128.3 125.3 122.8 120.4 118.3

Fourth (openclosed valve) 118.3 115.2 113.7 111.3 108.3

1st Expansion 160 155 150 145 140

156.5 152.4 148.2 144.7 139.8

135 130

1st Reading 2nd Reading 3rd Reading 4th Reading 5th Reading Graph of response of pressurized vessel following stepwise depressurization

2nd Expansion 142 140 138 136 134 132 130 128 126 124 122

139.8 136.5 133.4 130.2 128.3

1st Reading 2nd Reading 3rd Reading 4th Reading 5th Reading Graph of response of pressurized vessel following stepwise depressurization

3rd Expansion 130

128.3 125.3

125

122.8 120.4

120

118.3

115 110 1st Reading 2nd Reading 3rd Reading 4th Reading

5th Reading

Graph of response of pressurized vessel following stepwise depressurization

4th Expansion 120 118 116 114 112 110 108 106 104 102

118.3 115.2

113.7

111.3 108.3

1st Reading

2nd Reading 3rd Reading

4th Reading

5th Reading

Graph of response of pressurized vessel following stepwise depressurization

DISCUSSION The first experiment was Boyle’s Law which is according to the law, P1V1=P2V2. By calculating using the data acquired during the experiment, it shown that P1V1 value is close to the value P2V2, Thus, this shows that there is error while conducting the experiment. This error maybe happened because of human error which is some of our member are not aware with the pressure drop. Another reason why we got the error reading was we do not wait until the pressure truly stabilized. Hence, we can say that the experiment to prove Boyle’s law is successful.

From the ideal gas equation, PV=RT the volume is calculated for each of the pressure of the experiment 1. In first condition, the pressurized to the atmospheric the value of volume are V1=15.5L then expend V2 =18.48L. In the second condition, atmospheric to vacuum the volume are V1 =23.61L then expend to V2 =27.18L. For the last condition pressurized to vacuum, the reading is taken separately for pressure chamber and vacuum chamber. In pressure chamber, V1= 16.09L before expansion while V2= 20.36L after expansion.

In the experiment 2, according to Gay-Lussac law where the pressure is proportional to temperature. From the plotted graph, the pressure is proportional to temperature where it follows the Gay-Lussac Law. As the pressure is increased the temperature also increases in a constant volume. In the graph, the depressurized is line has a higher temperature as the pressure increase than pressurize line in the graph that show in the result.

For the third experiment that is isentropic experiment where the isentropic expansion process happen went both reversible and adiabatic, there will be no heat transferred within the system, and no energy transformation occurs. Given that, pVk= constant Where, k is constant. Given the value of temperature and pressure before and after expansion, we can find the value of k Thus, the calculated value of k in this experiment is 1.23.In this experiment the pressure is drop from 153.6kPa to 104.3kPa and the temperature also decrease from 32.2 °C to 30.1°C.This is because due to the volume is kept constant thus the temperature and pressure is increase. In fact, during contact this experiment no heat flow occurs in the system and no energy transformation change .Therefore, the change of the gas in entropy also is zero. In conclude that, when isentropic expansion processes the work done by the gas is equal the decrease in the internal energy of gas.

Lastly, for the experiment 4 which is stepwise depressurization. In this experiment, we can conclude that every time we open the valve instantly whether in short period, it will effect most of the gas molecule. If the pressure is higher, there are more gas molecule will effect even the valve is open instantly. This is because gas molecule are moving freely and light and even smaller.

CONCLUSION In conclusion , the experiment is conducted to determining the PVT measurement properties based on Boyle’s Law, Gay-Lussac Law, Isentropic expansion process and Stepwise depressurization. All of the experiment can determine the properties of gases under few condition for each of the experiment. During conducting the experiment we make some parallax error and error in measuring time. However, we still can manage to get the result to prove the hypothesis that when pressure decrease the volume will increase and vice versa for Boyle’s Law experiment. In fact,the result shown that the Gay-Lusac law is where pressure is proportional to temperature. For Isentropic expansion process, the experiment was completed with no error and problem. In a nutshell, this experiment is successfully done and the objective of the experiment is achieved.