Lab 5 Completed

1

ABSTRACT

There are seven objectives altogether for the analysis whereby the majority of the experiments

was conducted to study the relationship between pressure, temperature and volume of gas (P,

V and T). This experiment was conducted by using Perfect Gas Expansion Apparatus to

understand the First Law of Thermodynamics, Second Law of Thermodynamics which

consists of Boyles Law, Gay-Lussac Law, Isentropic Expansion Process, Brief

Depressurization and Determination of Ratio of Heat Capacity. Almost the same procedure

used for each experiment. Gay-Lussacs law was proven in experiment 2 and results obtained

in experiment 1 shown that the relationship between pressure, volume and temperature are

parallel to the Boyles law. According to the result, as the pressure increases in the chambers,

the temperature also increases. This confirmed that the experiment is successful because of

following the Gay-Lussac law. Pressure and temperature relationship was observed in

experiment 3. Graph obtained from experiment 5 shows that pressure and temperature

increase proportionally and in experiment 6 and 7, it manages to prove the difference between

theoretical and actual values of gas ratio which has a percentage difference of 2.583% where

it is acceptable.

2

INTRODUCTION

Gases, unlike solids and liquids have indefinite shape and indefinite volume. As a result, they

are subject to pressure changes, volume changes and temperature changes. Volume and

temperature are familiar concepts. Pressure is defined as a force per area. When gas molecules

collide with the sides of a container, they are exerting a force over that area of the container.

This gives rise to the pressure inside the container.

The Perfect Gas Law Apparatus is customarily designed and developed to provide a

comprehensive understanding of First Law of Thermodynamics, Second Law of

Thermodynamics and relationship between P, V and T. The Perfect Gas Expansion Apparatus

helps to make a good understanding in energy conservation law and the direction in which the

processes proceed.

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

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.

3

OBJECTIVE

For this particular experiment, 7 experiment was conducted and the objectives are as follows;

Boyles Law Experiment To determine the relationship between pressure and volume of an ideal gas

To compare the experimental results with theoretical results

Gay-Lussac Law Experiment

To determine the relationship between pressure and temperature of an ideal gas Isentropic Expansion Process

To demonstrate the isentropic expansion process Stepwise Depressurization

To study the response of the pressurized vessel following stepwise depressurization

Brief Depressurization

To study the response of the pressurized vessel following a brief depressurization

Determination of ratio of volume

To determine the ratio of volume and compares it to the theoretical value

Determination of ratio of heat capacity

To determine the ratio of heat capacity

4

THEORY

This part will discuss about some of the basic definition on the theorem applied for this

experiments. It will cover two theorem, which is Boyles Law and Gay-Lussac Law.

Boyles Law, according to the (Whitman, 2005), it was developed by an Ireland citizens,

Robert Boyle, in early 1600s. The law stated that the volume of the gas varies inversely with

the absolute pressure, provided the temperature reamins constant. The formula of the Boyles

Law is as folows;

P1V1= P2V2

Where; P1 = Original absolute pressure

P2 = New pressure

V1 = Original volume

V2 = New volume

Figure 1

Figure 1 shows that absolute pressure in a cylinder doubles when the volume is reduced by

half.

Next is the Gay-Lussac Law. This law stated that the relationship between pressure and

temperature, which is pressure is directly proportional with temperature (Myers, 2006). One

of the significance of the law that it provide a method in order to determine the value of

absolute zero. This law is presented by this equation;

1

1=

2

2

Where; P1= original pressure

T1= original temperature

5

P2= new pressure

T2= new temperature

Figure 2 Volume VS Temperature

Figure 2 demonstrate by using the Gay-Lussac Law, to determine the absolute zero.

6

APPARATUS

1) Pressure Transmitter

2) Pressure Relief Valve

3) Temperature Sensor

4) Big Glass

5) Small Glass

6) Vacuum Pump

7) Electrode

7

PROCEDURES

1.1 General Operating Procedures

1.1.1 General Start-up Procedures

1. The equipment was connected to single phase power supply and the unit was

switched on.

2. All valves were fully opened and the pressure reading was checked on the

panel. This is to make sure that the chambers are under atmospheric pressure.

3. Then, all the valves were closed.

4. The pipe was connected from compressive port of the pump to pressurized

chamber or the pipe was connected from vacuum port of the pump to vacuum

chamber.

5. The unit was ready to be used.

1.1.2 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.

Experiment 1: Boyles Law Experiment

1) The general start up procedures was performed in section 1.1.1 and all valves are fully

closed.

2) The compressive pump was switched on allowing the pressure inside chamber to increase

up to about 150kPa. Then, the pump was switched off and removed the hose from the

chamber.

3) The pressure reading inside the chamber are monitored until it stabilizes.

4) The pressure reading for both chambers before expansion are recorded.

5) V 02 was fully opened allowing the pressurized air flows into the atmospheric chamber.

6) The pressure reading for both chambers after expansion was then recorded.

7) The experimental procedures was then repeated for the following conditions: from

pressurized chamber to vacuum chamber

8) The PV value was calculated and the Boyles Law is proven.

8

Experiment 2: Gay-Lussac Law Experiment

1) The general start up procedures is performed. Make sure all valves are fully closed.

2) The hose is connected from compressive pump to pressurized chamber.

3) The compressive pump is switched on and the temperature is recorded for every

increment of 10kPa in the chamber. The pump is stopped when the pressure PT 1 reaches

about 160kPa.

4) Then, valve V 01 is slightly opened and the pressurized air is allowed to flow out. The

temperature reading is recorded for every decrement of 10kPa.

5) The experiment is stopped when the pressure reaches atmospheric pressure.

6) The experiment is repeated for three times to get the average value.

7) The graph of pressure versus temperature is plotted.

Experiment 3: Isentropic Expansion Process



3) The compressive pump is switched on and the pressure inside chamber is allowed to

increase until about 160kPa. Then, switch off the pump switched off and the hose is

removed from the chamber.

4) The pressure reading inside the chamber is monitored until it is stabilized. The pressure

reading PT 1 and temperature TT 1 is recorded.

5) Then, valve V 01 is opened slightly and the air is allowed to flow out slowly until it

reaches atmospheric pressure.

6) The pressure reading and temperature reading after the expansion process is recorded.

9

Experiment 4: Stepwise Depressurization

Experimental procedures:

1) The general start up procedures was performed in section 1.1.1. Ensure that all valves

were fully closed.

2) The hose was connected from compressive pump to pressurized chamber.

3) The compressive pump was connected and the pressure inside 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 stabilizes. The pressure

reading PT 1 was recorded.

5) Valve V 01 was fully opened and was bring it back to the closed position instantly. The

pressure reading PT 1 was monitored and recorded until it becomes stable.

6) Step 5 was repeated for at least four times.

7) The pressure reading on a graph is displayed and discussed.

Experiment 5: Brief Depressurization



3) The compressive pump is switched on and the pressure inside chamber is allowed to

increase until about 160kPa. Then, switch off the pump switched off and the hose is


4) The pressure reading inside the chamber is monitored until it is stabilized. The pressure

reading PT 1 is recorded.

5) Then, valve V 01 is opened fully and is turned back to close position after few seconds.

The pressure reading PT 1 is monitored and recorded until it becomes stable.

6) The pressure reading on a graph is displayed and discussed.

10

Experiment 6: Determination of ratio of volume

1) Perform the general start up procedures in section 5.1. Make sure all valves are fully

closed.

2) 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.

3) Monitor the pressure reading inside the chamber until it stabilizes.

4) Record the pressure reading for both chambers before expansion.

5) Open V 02 and allow the pressurized air flows into the atmospheric chamber slowly.

6) Record the pressure reading for both chambers after expansion.

7) The experimental procedures can be repeated for the following conditions: from

pressurized chamber to vacuum chamber

8) Calculate the ratio of volume and compares it with the theoretical value.

Experiment 7: Determination of ratio of heat capacity

1) The general start up procedures was performed in section 1.1.1. All valves were fully

closed.

2) The hose was connected from compressive pump to pressurized chamber.

3) The compressive pump was switched on and the pressure inside chamber was allowed to

increase until about 160kPa. Then, the pump was switched off and the hose wwas


4) The pressure reading inside the chamber have been monitored until it stabilizes. The

pressure reading PT 1 and temperature TT 1 was recorded.

5) Valve V 01 was fully opened and bring it back to the closed position after few seconds.

The pressure reading PT 1 and TT1 was recorded and monitored until it becomes stable.

6) The ratio of heat capacity have been determined and compared with the theoretical value.

11

RESULT AND CALCULATION

Experiment 1: Boyles Law Experiment

Condition 1: From pressurised vessel to atmosphere vessel

Before expansion After expansion

PT 1 (kPa abs) 153.6 136.3

PT 2 (kPa abs) 102.4 135.7

Condition 2: From pressurised vessel to vacuum vessel


PT 1 (kPa abs) 103.8 87.5

PT 2 (kPa abs) 53.3 87.0

Condition 3: From atmospheric vessel to vacuum vessel


PT 1 (kPa abs) 152.1 120.5

PT 2 (kPa abs) 54.6 119.7

Ideal gas equation, PV=RT. For Boyles law, temperature is constant at room temperature

Hence, R= 8.314 L kPa K-1mol-1, T= 298 @ 25C

i) From pressurized vessel to atmospheric vessel

P1= 153.6Pa, P2= 136.3kPa. Then V1and V2 is calculated

V1= RT/P1

= (8.314 L kPa K-1mol-1) (298.15 K) / (153.6kPa)

=16.14L

12

V2 = (8.314 L kPa K-1mol-1) (298.15 K) / (136.3kPa)

=18.19L

According to Boyles law: P1V1=P2V2

P1V1= (153.6kPa) (16.14L) = 2479.10L kPa

P2V2= (136.3kPa) (18.19L) = 2479.30L kPa

ii) From pressurized vessel to vacuum vessel

P1= 103.8kPa, P2= 87.5kPa. Then V1and V2 is calculated

V1= RT/P1

= (8.314 L kPa K-1mol-1) (298.15 K) / (103.8kPa)

=23.88L

V2 = (8.314 L kPa K-1mol-1) (298.15 K) / (87.5kPa)

=28.33L


P1V1= (103.8kPa) (23.88L) = 2478.74L kPa

P2V2= (87.5kPa) (28.33L) = 2478.88 L kPa

iii) From atmospheric vessel to vacuum vessel

P1= 152.1kPa, P2= 120.5kPa. Then V1and V2 is calculated

V1= RT/P1

= (8.314 L kPa K-1mol-1) (298.15 K) / (152.1kPa)

13

=16.30L

V2 = (8.314 L kPa K-1mol-1) (298.15 K) / (120.5kPa)

=20.57L


P1V1= (152.1kPa) (16.30L) = 2479.23L kPa

P2V2= (120.5kPa) (20.57L) = 2478.69 L kPa

Experiment 2: Gay-Lussac Law Experiment

Trial 1 Trial 2 Trial 3

Pressure

(kPa abs)

Temperature (oC)

Pressurise

vessel

Depressurise

vessel

Pressurise

vessel

Depressurise

vessel

Pressurise

vessel

Depressurise

vessel

110 27.3 26.9 26.8 26.9 26.8 27.5

120 27.7 27.2 27.0 27.0 27.0 28.4

130 28.6 27.9 27.7 27.5 27.8 29.5

140 29.5 29.2 28.7 28.5 28.8 30.7

150 30.4 31.0 29.7 29.5 29.8 31.7

160 31.3 31.8 30.7 30.6 30.8 32.2

14

Trial 1

increase

decrease

0

20

40

60

80

100

120

140

160

180

27 28 29 30 31 32

Pre

ssu

re

Temperature

Gas expansion

0

20

40

60

80

100

120

140

160

180

26 27 28 29 30 31 32 33

Pre

ssu

re

Temperature

Gas expansion

15

Trial 2

Increase

Decrease

0

20

40

60

80

100

120

140

160

180

26 27 28 29 30 31

Pre

ssu

re

Temperature

Gas expansion

0

20

40

60

80

100

120

140

160

180

26 27 28 29 30 31

Pre

ssu

re

Temperature

Gas expansion

16

Trial 3

Increase

Decrease

0

20

40

60

80

100

120

140

160

180

26 27 28 29 30 31

Pre

ssu

re

Temperature

Gas expansion

0

20

40

60

80

100

120

140

160

180

27 28 29 30 31 32 33

Pre

ssu

re

Temperature

Gas expansion

17

Experiment 3: Isentropic Expansion Process


PT 1 (kPa abs) 156.0 103.5

PT 2 (kPa abs) 30.1 27.5

Experiment 4: Stepwise Depressurization

Initial PT 1 (kPa abs)

After 1st expansion After 2nd expansion After 3rd expansion After 4th expansion

160 144.7 125.0 116.9 110

144.8 125.1 117.0 110.1

144.9 125.2 117.1 110.2

145.0 125.3 117.2 110.3

145.1 125.4 117.3 110.4

145.2 125.5 117.4 110.5

145.3 125.6 117.5 110.6

145.4 125.6 117.6 110.7

145.5 125.7 117.7 110.8

145.6 125.8 117.8 110.9

145.7 125.9 117.9 111.0

145.8 126.0 118.0 111.1

145.9 126.1 118.1

146.0 126.2 118.2

146.1 126.3 118.3

146.2 126.4

146.3 126.5

146.4

146.5

146.6

146.7

18

146.8

146.9

100

110

120

130

140

150

160

RESPONSE OF PRESSURISED VESSEL FOLLOWING STEPWISE DEPRESSURISATION

19

Experiment 5: Brief Depressurization

PT 1 (kPa abs)

Initial After brief

expansion

160.3 103.2

103.4

103.5

103.6

103.7

103.8

103.9

104.0

110.4

20

Experiment 6: Determination Of Ratio Volume

Condition 1 : From pressurised vessel to atmosphere vessel

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

Before expansion 149.5 102.7

After expansion 134.1 133.2

Condition 2 : From pressurised vacuum to vacuum vessel


Before expansion 106.3 55.2


Condition 3 : From atmospheric vessel to vacuum vessel


Before expansion 158.2 53


0

50

100

150

200

0 2 4 6 8 10

Pre

ssu

re

Expansion

RESPONSE OF PRESSURISED VESSEL FOLLOWING STEPWISE

DEPRESSURISATION

Series1

21

i) From pressurized vessel to atmospheric vessel

P1V1 = P2V2

V2

V1 =

P1P2

V2

V1 = 149.5/102.7 = 1.456

ii) From pressurized vessel to vacuum vessel

P1V1 = P2V2

V2

V1 =

P1P2

V2

V1 = 106.3/55.2 = 1.926

iii) From atmospheric vessel to vacuum vessel

P1V1 = P2V2

V2

V1 =

P1P2

V2

V1 = 158.2/53 = 2.985

Theoretical value: V2

V1 = 12.37/ 25.00L = 0.4948

PT1 to PT2 : P1/P2 = 134.1/149.5 = 0.8969

22

Experiment 7: Determination Of Heat Capacity

Initial Intermediate Final

PT 1 (kPa abs) 156.7 109.9 111.6

TT 1 (oC) 29.6 28.6 27.7

The expression of heat capacity ratio is

Cv

Rln

T2T1

= 21

2

1=

11

22

8.314 11ln (

300.85

302.75) = ln (

156.7(302.75)

111.6(300.85))

Cv = 456.54 11

Cp = Cv + R

456.54 + 8.314 = 464.854 kPa K1mol1

Ratio:

=

464.854

456.54= 1.0182

Theoretical value of

is

=

ln 156.7ln 109.9

156.7ln 111.6= 1.0452

23

DISCUSSION

Regarding to Boyle Rule, the pressure of the gas is inversely proportional to the volume it

occupies and can be calculated by using the ideal gas formula PV = RT. After that by using this

formula, P1V1=P2V2, we can prove Boyles law. From the calculation, we can see that the P1V1 is

nearly equal to the value of P2V2. It means there are same error happened during the experiment.

Hence, we can say that the experiment to prove Boyles law is successful.

In the next experiment, the relationship between pressure and temperature was studied. The

graph shows how the pressure and temperature vary according to Gay-Lussac Law. Based on

Gay-Lussac it stated that the pressure exerted on a containers sides by an ideal is proportional to

the absolute temperature of the gas. According to our result, as the pressure increases in the

chambers, the temperature also increases. This confirmed that our experiment is successful

because of following the Gay- Lussac law (Charles law).

Another two experiments, the volume ratio and the heat capacity ratio were determined. The

percentage in difference of the volume theoretical value with the result acquired is small or

almost zero. For the heat capacity, the difference between the resulted value of heat capacity

ratio and the theoretical value is about 2.583 percent.

CONCLUSION

From the experiment, we can concluded that the experiment was succeed after considering all the

objectives were achieved although deviation between the theoretical values and obtained values.

The result shown over our expectation because we manage to get what we want such as in

experiment one which me manage to prove the Boyles law that is when pressure decrease the

volume will increase and vice versa. We also manage to prove the Gay-Lussac law that is

pressure is proportional to temperature. In conclusion, this experiment is successfully done and

the objective of the experiment is achieved.

24

RECOMMENDATION

1) Make sure to be fully equipped with personal protective equipment so that any injuries

can be avoided during the conduction of the experiment.

2) It is best to wait around 3 to 5 minutes for the pressure inside each vessel to be stabilized

before recording the obtained results.

3) The general start up and shut down procedure should be read thoroughly and carefully in

the lab manual before conducting any of the experiments.

REFERENCES

1) Thermo fluid laboratory lab manual

2) Ideal Gas Law. Retrieved May 22, 2014, from

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

3) Boyles Law. Retrieved May 22, 2014, from

https://www.boundless.com/chemistry/gases/gas-laws/boyle-s-law-volume-and-pressure/

4) PVT Laboratory Measurements. Retrieved May 22, 2014, from

http://my.safaribooksonline.com/book/petroleum-engineering/9780132485210/reservoir-

fluid-sampling-and-pvt-laboratory-measurements/ch05lev1sec6

5) Cengel, Y.A & Boles, M.A. (2011). Thermodynamics an Engineering Approach

Singapore: McGrawHill.

25

APPENDICES

Lab 5 Completed

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