1

ABSTRACT

The lab practical is divided into seven different experiments, each with objectives to

study the relationship between ideal gas and various other factors to deliver better

understanding of the First Law of Thermodynamics, Second Law of Thermodynamics and

relationship between P-V-T to the students. Perfect Gas Expansion Apparatus (Model TH11)

was used in this experiment. The objectives for each experiment were achieved. Boyle’s law

and Gay-Lussac law were proven in this experiment when the ideal gas behaved accordingly.

The volume ratio and heat capacity were also determined and they are 6.42 and 1.054. The

experiment was successful.

INTRODUCTION

The Perfect Gas Expansion Apparatus (Model: TH 11) is a self-sufficient bench top

unit designed to enable students to familiarize with some fundamental thermodynamic

processes. Comprehensive understanding of First Law of Thermodynamics, Second Law of

Thermodynamics and the P-V-T relationship is fundamentally important in the applications

of thermodynamics in the industry. The apparatus comes with one pressure vessel and one

vacuum vessel and both are made of glass tubes. The vessels are linked to one another with a

set of piping and valves. A large diameter pipe provides gradual or instant change.

Air pump is included to enable us to pressurize or evacuate air inside the large vessels

provided the valves configures appropriately during the experiment. The pressure and

temperature sensors are used to monitor and manipulate the pressure and temperature inside

the vessels and the digital indicator will display the pressure and temperature on the control

panel. This experiment dealt a lot with the properties of an ideal gas and its relationship with

the various environmental factors. An ideal gas is said to be a gas which obeys the P-V-T

relationship. A PVT relationship is one of the forms of the equations of state, which relates

the pressure, molar volume V and the temperature T of physically homogeneous media in

thermodynamic equilibrium (Reid, Prausnitz & Sherwood, 1977).

Other than that, ideal gas is also a gas that exhibits simple linear relationships among

volume, pressure, temperature and amount (Silberberg, 2007: 143). Gas particles in a box

collide with its walls and transfer momentum to them during each collision. The gas pressure

is equal to the momentum delivered to a unit area of a wall, during a unit time. However,

ideal gas particles do not collide with each other but only with the walls. A single particle

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moves arbitrarily along some direction until it strikes a wall. It then bounces back, changes

direction and speed and moves towards another wall. The gas expansion equations are

derived directly from the law of conservation of linear momentum and the law of

conservation of energy (Sears & Salinger, 1975).

OBJECTIVES

Experiment 1: Boyle’s Law Experiment

To determine the relationship between pressure and volume of an ideal gas.

To compare the experimental results with theoretical results.

Experiment 2: Gay-Lussac Law Experiment

1. To determine the relationship between pressure and temperature of an ideal gas.

Experiment 3: Isentropic Expansion process

2. To demonstrate the insentropic expansion process.

Experiment 4: Stepwise Depressurization

3. To study the response of the pressurized vessel following stepwise depressurization.

Experiment 5: Brief Depressurization

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

Experiment 6: Determination of ratio of volume

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

Experiment 7: Determination of ratio of heat capacity

6. To determine the ratio of heat capacity.

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THEORY

Boyle’s Law Experiment

The relationship between volume and pressure of a gas can be explained with Boyle’s

law: at constant temperature, the volume occupied by a fixed amount of gas is inversely

proportional to the applied (external) pressure (Silberberg, 2007: 144).

Or it can also be expressed in terms of equation as below:

V ∝

PV = constant or V =

According to the mathematical expressions derived from Boyle’s law above, provided

that ‘T’ and ‘n’ are fixed, pressure and volume are indirectly related to one another in a sense

that if the volume increases, then the pressure shall decrease, and vice versa. This can also be

explained through gas particles collisions theory (kinetic molecular theory) in which when

the volume of a chamber containing a gas is reduced, the probability of gas particles to come

in contact with one another during collision and with the walls of the container will increase,

hence the elevated pressure (Adamson, 1979).

Figure 1: Mathematical/Graphical relationship between the volume of a fixed mass of gas and

pressure is hyperbolic (Boyle’s law). The gas temperature remains constant.

(Thomas, Stamatakis, 2009)

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Gay-Lussac Law Experiment

Ga-Lussac law is also commonly known as Charles’s law. The law explains about the

relationship between pressure and temperature of gases. The law was established in the early

19th

century by Jacques Charles and Joseph Louis Gay-Lussac who did a study on the effect

of temperature on the volume of a sample of gas subjected to constant pressure (Atkins,

2002). Charles did the original work, which was then verified by Gay-Lussac (grc.nasa.gov).

However, in this lab practical, we are dealing with an alternative version of Charles’s

law instead. The volume is kept constant in change for pressure instead as the objective of the

experiment is to determine the relationship between pressure and temperature of ideal gas.

The expression is as shown:

p = constant x T (at constant volume)

*This version of law also indicates that the pressure of gas falls to zero as the

temperature is reduced to zero (Atkins, 2002).

Thus it can be seen that gas pressure and the temperature are directly proportional to

one another. When the pressure increases, the temperature also increases, and vice versa.

P ∝ T

P = constant T

P/T = constant

P1/T1 = P2/T2

P1T2 = P2T1

The equations above apply in the gas of dealing with the relationship between

pressure and temperature of a gas.

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Figure 2: Mathematical/Graphical relationship between pressure of a fixed mass of

gas with temperature at a constant volume is linear. The volume is constant.

Isentropic Expansion Process

Isentropic basically means no change in entropy. According to grc.nasa.gov, entropy

has a variety of physical interpretations, including the statistical disorder of the system, but

often perceived to be just another property of the system, like enthalpy or temperature. The

Second Law of thermodynamics can be expressed in terms of the entropy, S, as another state

of function:

The entropy of an isolated system increases in the course of a spontaneous change:

ΔStot > 0

Where Stot is the total energy of the system and its surroundings. Thermodynamically

irreversible processes (like cooling to the temperature of surroundings and the free expansion

of gases) are spontaneous processes, and hence must be accompanied by an increase in total

entropy (Atkins, 2002: 92).

However, for a reversible and an adiabatic process, the value of entropy, S, remains

the same from the initial to the state of completion.

S = 0

S1 = S2

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Stepwise Depressurization Experiment

The stepwise depressurization is conducted by depressurizing the pressurized

chamber or tank gradually by releasing the gas expansion at every instance the valves are

opened and closed to see the gradual changes in pressure within the container. Pressure

decreases with the expansion.

Brief Depressurization Experiment

Similar procedures as previous lab practical, but the time interval of valves opening

increased to a few seconds. This is so that the effects or response of brief depressurization of

the gas could be observed. With the increased time interval, the gas should expand faster.

Determination of Ratio of Volume Experiment

The ratio of volume of gas expansion between the chambers and the atmosphere

should be the same (or at least almost) with the theoretical value. The following equations

can be used to evaluate and calculate the values:

P1 V1 = P2 V2

V2/ V1 = P1/ P2

V2/ V1 = Ratio value

*And then the value is compared to the theoretical value of the volume ratio which is:

Determination of Ratio of Heat Capacity

The heat capacity is a constant that tells how much heat is added per unit temperature

rise (ngr.nasa.gov). The heat capacity can be represented as Cp, which indicates the heat

capacity of a gas in a system with constant pressure. Also, the heat capacity can be

represented as Cv, for heat capacity of a gas in a system with constant volume (Materials and

Enegery Balance). These are derived for an equation of relating to the isobaric and isochoric

processes, which finally led to a simple equation for the heat capacity of ideal gas:

Cp – Cv = R

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For the ideal gas state, the heat capacity may be expressed through statistical

mechanics in terms of the contributions to the translational and internal energies of the

molecules (Rushbrooke, 1949). In turn, some of the internal contribution arising from

rotational, vibrational and electronic modes of motion can often then be determined from

spectroscopic measurement of the frequencies of the normal mode of motion of the molecule.

For many molecules, this process provides a more accurate means of determining the ideal-

gas heat capacity of the material than direct measurement (de Reuck & Craven, 1993).

As the density is increased from the ideal gas state, the energy of the ensemble of

molecules acquires a component arising from the interactions between molecules (the

configurational part) and this cannot be evaluated theoretically for any but the simplest

molecules so that the only source of information on the heat capacity is then from direct or

indirect measurement. When there are no measurements available it is necessary to have

recourse to estimation methods (Reid, Prausnitz & Sherwood, 1975).

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APPARATUS

There was only one equipment used for this lab practical (10) for all the experiments, and that

is the Solteq® Perfect Gas Expansion Apparatus (Model: TH11).

Figure 3: Solteq® Perfect Gas Expansion Apparatus (Model: TH11).

Including:

- Pressure Transmitter (1), Pressure Relief Valve (2), Temperature Sensor (3), Big

Glass (4), Small Glass (5), Vacuum Pump (6) and Electrode (7).

METHOD

General Operation:

Start-up:

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

turned on.

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

This is to make sure that the chambers were all under atmospheric pressure.

3. The valves were all closed again afterwards.

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

5. The unit was ready for use.

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Experiment 1:

1. The general start up method as previously mentioned was performed and the

valves were once again made sure to be fully closed.

2. The compressive pump was switched on and the pressure inside the chamber

was allowed to increase up to about 150kPa. Then, the pump was switched off

and the hose was removed from the chamber.

3. The pressure reading inside the chamber was monitored until it stabilized.

4. The pressure reading for both chambers before expansion was recorded.

5. The V 02 was fully opened and the pressurized air flows were allowed into the

atmospheric chamber.

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

7. The experimental methodology was repeated for the following conditions:

From atmospheric chamber to vacuum chamber;

From pressurized chamber to vacuum chamber.

8. The PV value was calculated and Boyle’s Law was proven in further sections.

Experiment 2:

1. The general start up method was performed again.

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

3. The compressive pump was switched on and the temperature for every

increment of 10kPa in the chamber was recorded. The pump was stopped

when the pressure PT 1 reaches about 160kPa.

4. Then, the valve V 01 was slightly opened and the pressurized air was allowed

to flow out. The temperature reading for every decrement of 10kPa was

recorded.

5. The experiment was stopped when the pressure reached atmospheric pressure.

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

7. A graph was plotted to represent the pressure versus temperature.

Experiment 3:

1. The general start up procedures was performed.

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

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3. The compressive pump was switched on and the pressure inside the chamber

was allowed to increase until about 160kPa. Then, the pump was switched off

and the hose was removed from the chamber.

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

pressure reading PT 1 and temperature TT 1 were recorded.

5. Valve V 01 was slightly opened and air was allowed to flow out slowly until it

reached atmospheric pressure.

6. The pressure reading and the temperature reading after the expansion process

were recorded.

7. The isentropic expansion process was discussed in further section.

Experiment 4:

1. The general start up procedure was performed.

2. The hose from the compressive pump was connected to the pressurized

chamber.

3. The compressive pump was switched on and the pressure inside the chamber

was allowed to increase until about 160kPa. The pump was then switched off

and the hose was removed from its chamber.

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

pressure reading PT 1 was recorded.

5. The valve V 01 was fully opened and brought back to closed position

instantly. The pressure reading PT 1 was monitored and recorded until it

became stable.

6. Step 5 was repeated at least four times.

Experiment 5:

1. General start up procedure was performed.

2. The hose was connected from the compressive pump to the pressurized

chamber.

3. The compressive pump was switched on and allowed to increase the pressure

inside the chamber until about 160kPa. Then it was switched off and the hose

was removed.

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

pressure reading was recorded as PT 1.

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5. The valve V 01 was fully opened and brought back to closed position after a

few seconds. The pressure reading after expansion was monitored and

recorded as PT 1 until it became stable.

6. The result was displayed on graph and further discussed.

Experiment 6:

1. General start up procedure was performed and valves were made sure to be

closed.

2. Compressive pump was switched on and the pressure inside the chamber was

allowed to increase up to about 150kPa. Then, the pump was switched off and

the hose was removed from the chamber.

3. The pressure reading inside the chamber was monitored until it stabilized.

4. The pressure reading for both chambers was recorded before expansion.

5. Valve V 02 was opened and the pressurized air was allowed to flow into the

atmospheric chamber slowly.

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

7. The experimental procedures were repeated for the following conditions:

From atmospheric chamber to vacuum chamber.

From pressurized chamber to vacuum chamber.

8. The ratio of volume was calculated and compared with the theoretical value.

Experiment 7:

1. The general start up method was performed.

2. The compressive pump was connected to pressurized chamber.

3. The compressive pump was switched on and the pressure inside the chamber

was allowed to increase until about 160kPa. Then, the pump was switched off

and the hose was removed from the chamber.

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

pressure reading PT1 and temperature TT1were recorded.

5. The valve V 01 was fully opened and brought back to closed until after a few

seconds. The reading PT1 and temperature TT1 were monitored and recorded

until they became stable.

6. The ratio of the heat capacity was determined and then compared with the

theoretical value.

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RESULTS

A. Experiment 1

Pressure (kPa)

Part PT 1 PT 2

Before expansion After expansion Before expansion After expansion

PT 1 to PT 2 159.1 102.0 140.2 140.1

PT 2 to PT 1 102.4 165.4 122.4 122.2

Both PT 1 and PT 2 158.6 161.8 159.5 159.3

B. Experiment 2

Pressure

(kPa)

Temperature oC

Trial 1 Trial 2 Trial 3

Pressurized Depressurized Pressurized Depresurized Pressurized Depresurrized

112 28.4 27.5 27.4 28.2 27.6 28.7

122 29.0 27.7 27.9 28.6 28.0 29.8

132 29.7 28.3 28.9 29.4 28.9 30.7

142 30.5 29.1 29.9 30.4 30.0 31.9

152 31.5 30.8 30.9 32.0 30.9 32.5

162 32.1 32.1 31.8 32.1 31.9 32.7

C. Experiment 3

Before expansion After expansion

Pressure (kPa) 163.4 102.1

Temperature (oC) 30.8 27.3

D. Experiment 4

Pressure (kPa)

Before expansion After expansion

1st 2nd 3rd 4th

162.3 144.3 133.8 120.1 101.2

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E. Experiment 5

Pressure (kPa)

Before expansion After expansion

162.2 123.4

F. Experiment 6

Pressure (kPa)

Part PT 1 PT 2

Before expansion After expansion Before expansion After expansion

PT 1 to PT 2 159.0 102.0 140.0 139.9

PT 2 to PT 1 102.2 160.8 121.5 121.4

Both PT 1 and PT 2 159.5 160.3 159.6 159.5

G. Experiment 7

Before expansion After expansion

Pressure (kPa) 159.7 139.2

Temperature (oC) 32.4 30

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SAMPLE CALCULATIONS

A. Experiment 1

PT1 to PT2:

P1 = 159.1 – 102.0 P1VI = 57.1 x 25

= 57.1kPa = 1427.5kPa.L

P2 = 140.2 – 140.1 P2V2 = 0.1 x 12.3

= 0.1kPa = 1.23kPa.L

B. Experiment 2

Pressure (kPa)

Average

Teamperature (oC)

Pressurized Depressurized

112.00 27.80 28.13

122.00 28.30 28.70

132.00 29.17 29.47

142.00 30.13 30.47

152.00 31.10 31.77

162.00 31.93 32.30

Pressurization Process

27.50

28.00

28.50

29.00

29.50

30.00

30.50

31.00

31.50

32.00

32.50

0.00 50.00 100.00 150.00 200.00

Pre

ssu

re (

kPa)

Temperature (oC)

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Depressurization Process

C. Experiment 3

K = 0.4818

D. Experiment 4

27.50

28.00

28.50

29.00

29.50

30.00

30.50

31.00

31.50

32.00

32.50

33.00

0.00 50.00 100.00 150.00 200.00

Pre

ssu

re (

kPa)

Temperature (oC)

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6

Pre

ssu

re (

kPa)

Expansion

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E. Experiment 5

F. Experiment 6

P1V1 = P2V2

P1/P2 = V2/V1

Theoretical value: V2/V1 = 12.37L/25.00L

= 0.49

PT 1 to PT 2 : P1/P2 = 102.0kPa/159.0kPa

= 0.642

G. Experiment 7

[

] [

]

0

20

40

60

80

100

120

140

160

180

0 0.5 1 1.5 2 2.5

Pre

ssu

re (

kPa)

Expansion

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Ratio:

Theoretical value of

is 1.4

DISCUSSION

From what Boyle’s law states about the relationship between the pressure and of a gas

and its volume, which is that they are inversely proportional to one another; this can be seen

and proven with the result obtained for this experiment. According to the tabulated data of

our result and calculations, they confirm our theory earlier and the pressure and volume of the

gas are indirectly proportional to one another. As the pressure increases, the volume starts to

decrease, and vice versa.

Take one big container and a smaller one. The bigger container will have lower gas

pressure of a fixed mass compared to the smaller one provided that the temperature for both

containers is constant. This is because the gas particles in the bigger container have a more

spacious room to avoid collisions with one another and against the walls of the container

which could exert pressure. Whilst in the smaller container, the gas particles have limited

space and thus random collisions with one another and against the walls occur frequently

exerting force (momentum) and causing the intense pressure. This collision theory can help to

explain the theory and result (Silberberg, 2007).

The volume(s) of the gas can be calculated using the ideal gas formula PV = RT and

after they are obtained, it can be used in the P1V1 = P2V2 to prove Boyle’s law. In the next

experiment, the Gay-Lussac law (Charles law) was studied in determining the relationship

between pressure and temperature. According to our result, as the pressure increases in the

chamber(s) when the compressive pump pressurized them, the temperature increases. This

confirmed Charles and Gay-Lussac’s work and theory as well as the law. When volume is

held at a constant level, the temperature of a fixed mass of gas is directly proportional to its

absolute pressure: P/T = k. Gases expand when heated – that is, density decreases – and thus

warm air rises (Turner & Cooper, 2012).

The Second Law of Thermodynamics is also the basis of the thermodynamic (Kelvin)

temperature scale and defines entropy, a new state function. Calculations of the entropy

changes for isothermal, isobaric, isochoric processes and for phase transitions and can be

described (Fegley, 2013). In this experiment, the isentropic behaviour of the process was

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studied. With the result gained, it seems that both the temperature and pressure of the gas

before expansion were higher compared to after expansion. However, to be discussed is

really the mechanism behind the process. The process is claimed to be isentropic, which

means there was no change in entropy throughout out the process. This is only valid for

spontaneous process and irreversible ones according to a book of fundamental

thermodynamics study by Peter Atkins written in 2002. At the same time, on the other hand

the process conducted with the apparatus was claimed to be adiabatic and reversible.

In the stepwise and brief depressurization experiments, the strategy to adopt an equal-

time-stepwise depressurization approach in this study yielded a more reliable result for

example in the production sector in industries. The substance onset pressure is found to be

affected by the way of system depressurization (frequency and time step magnitude) since it

has a direct bearing on the stabilization time (Petrowiki.org). With the last 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 about 31 percent which is pretty large.

This could’ve been due to environmental factors affecting the stability of the pressure and

temperature or random mistakes done during the experiment. For the heat capacity, the

difference between the resulted value of heat capacity ratio and the theoretical value is about

24.71 percent. This also deviated really much from the theoretical value and can be explained

by the accidental mistakes done.

CONCLUSIONS

Basically the experiment was a success considering all the objectives were achieved

despite the large deviation of figures between the theoretical ratio values and the obtained

figures. Throughout the studies, it is found that some of the gas laws for the perfect or ideal

gas are just limiting laws because gas don’t actually behave perfectly in the real world.

Nevertheless, in this experiment, the gas seemed to have obeyed Boyle’s law and Gay-Lussac

law in the relationship between pressure, volume and temperature. The ratio of the volume of

the gas indicates and expresses the dynamics of compression and expansion of the gases. The

ratio of heat capacity gives the capacity or amount of heat that could be taken up by the gas in

expansion process.

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RECOMMENDATIONS

The experiments must be done under the ideal gas properties measurement and

obeying the P-V-T relationship. Before the experiment begun, the general start up method

had to be performed repeatedly in order to minimize side effects which could in turn also

jeopardize the results. The apparatus must be handled carefully to avoid any accidents in the

lab such as explosion due to excessive pressure within the chambers. They must all be

adjusted and connected to the right ports. The valves had to be watched and opened carefully

in accordance to the procedures or manuals given to avoid any mistakes. Lastly always keep

eyes on the sensor while monitoring the board because the temperature or pressure could

increase or decrease really fast.

REFERENCES

1. Reid, R., Prausnitz, J.M., and Sherwood, T.K. (1977) The Properties of Gases and

Liquids, 3rd

Edition, McGraw-Hill.

2. F.W. Sears, G.L. Salinger, Thermodynamics, Kinetic Theory, and Statistical

Thermodynamics (Addison-Wesley, 3rd ed 1975) pp 254-266, 354-360.

3. Gary Thomas, Stephen Stamakis, (2009) Anaesthesia & Intensive Care Medicine:

Physics of Gases, Elsevier.

4. Reid, R. C, Prausnitz, J. M., and Sherwood, T. K. (1977) The Properties of Gases and

Liquids, McGraw-Hill, New York.

5. Rushbrooke, G. S. (1949) Introduction to Statistical Mechanics, Clarendon, Oxford.

6. de Reuck, K. M. and Craven, R. J. B. (1993) International Thermodynamic Tables of

the Fluid State—12: Methanol, Blackwell Scientific, Oxford.

7. http://www.grc.nasa.gov/WWW/k-12/airplane/aglussac.html

8. http://www.grc.nasa.gov/WWW/K-12/airplane/thermo2.html

9. http://www.grc.nasa.gov/WWW/k-12/airplane/specheat.html

10. www.petrowiki.org

11. Arthur W. Adamson, (1979), A Textbook of Physical Chemistry: Chapter Six: The

Second and Third Laws of Thermodynamics & Chapter 14, 2nd

Edition, University of

Southern California, Page 173-225, 543-601.

12. Martin Silberberg, 2007, Principles of General Chemistry, 1st Edition, McGraw-Hill.

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13. Peter Atkins & Julio de Paula, 2002, Physical Chemistry, 7th

Edition, Oxford, Page 8-

10, 92 & 103.

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APPENDICES

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