PVT expe

ABSTRACT

The name of this experiment is the Properties Measurement or PVT. This

experiment demonstrates the fundamental thermodynamics processes that deal with

an ideal gas. There were five separate experiments conducted with this unit which

consisted of Boyle’s Law Experiment, Gay-Lussac’s Law, the isentropic expansion,

determination of ratio volume and heat capacity. This experiment mainly focuses on

the relationship of between the pressure, volume and temperature of an ideal gas. As

an example of the connection between the variables; when the temperature of a gas

increases, so does its pressure but when the volume increases, the pressure decreases.

With the results obtained, each theory of the experiments were proven through the

graph and calculations made.

INTRODUCTION

The Properties Measurement Apparatus is an apparatus used to study the

fundamental processes of thermodynamics. It deals with ideal gas and can be used to

understand the Law of Conservation of Energy or First Law of Thermodynamics,

Second Law of Thermodynamics and the relationship between the pressure,

temperature and volume of a gas.

An ideal gas is a hypothetical gas which obeys the formula PV=nRT where P

and T are the absolute pressure and absolute temperature respectively and R is the

constant of the particular gas. Under a set of conditions, a real gas can also behave as

an ideal gas. Apart from this equation, an ideal gas also obeys other laws such as

Boyle’s Law and Gay-Lussac’s law.

Without us knowing, the applications of these laws are used a lot more

frequently in our daily lives. As an example; when inhaling, the diaphragm expands

which causes the pressure within the thoracic cavity to decrease and allow air to enter

as proposed through Boyle’s Law. Meanwhile when exhaling, the opposite occurs as

the pressure within our thoracic cavity increases, allowing air to be removed from our

body. Apart from that, we see that a hot air balloon is able to float above the clouds

Properties Measurement/PVT 1

despite being attached to a heavy basket with loads. This was made possible by the

understanding of Charles’ Law. The heating of air inside the balloon increases its

pressure, making it greater than the surrounding atmospheric pressure which allows it

to soar across the sky.

The knowledge of thermodynamics and relationship of ideal gas has generated

many inventions and possibilities in our world today. Therefore, it is crucial that this

field of knowledge not to be studied just as a form of numbers and fact, but with our

hope and enthusiasm of engineering a better tomorrow.

AIMS

Boyle’s Law Experiment

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

To determine 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.

Determination of ratio volume

To determine the ratio of volume and compare it with the theoretical value

Determination of ratio of heat capacity


To determine the ratio of heat capacity.

THEORY

An ideal gas, or also called as perfect gas is a hypothetical gas whose

pressure, volume, and temperature corresponds with the ideal gas law that is:

PV = nRT

Although an ideal gas is imaginary, at low pressure and high temperature, the

density of a real gas decreases making it able to behave like an ideal gas. This gas

abides not only the ideal gas equation of state but also Boyle’s Law and Gay-Lussac’s

Law.

Boyle's Law states that the product of the pressure and volume of gas is a

constant at a constant temperature. This law can be used to predict the change in

pressure of the same gaseous substance after an expansion or compression in the

volume.

PV = k

P1V1 = P2V2

Graph of Boyle’s Law

From the graph, it shows that the pressure is inversely proportional to volume

at a constant temperature. This is because under compression, the molecules within

the confined space experiences a higher frequency of effective collision with each


other as well as with the walls of the container. Vice versa, under expansion, the

situation proceeds in the opposite direction.

Gay-Lussac Law or also known as Charles’ Law states that the pressure of a

gas of fixed mass and volume is directly proportional its absolute temperature.

Therefore, when comparing a same substance under two different sets of conditions, it

can be written as:

P1T2 = P2T1

4, 2012

The graph shows the proportionality between the pressure and temperature of

a gas This follows the kinetic theory which states that by increasing the temperature,

the molecules gain speed which increases the frequency of effective collision

An isentropic process is a process takes place from initiation to completion

without an increase or decrease in the entropy of the system.

ΔS = 0

Or S1 = S2

Also, when a gas is in an this process, the ratio of temperature after the expansion and

before can be calculated

If a process is both reversible and adiabatic (insulated), then it is an isentropic

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


limiting case for an actual process. The equation of a gas in an isentropic process is:

T2

T1=

P2

k−1k

P1

where k =1.4

When determining the ratio of volume, the ratio of volume after the

exapansion and before should be equal to the ratio of pressure after the expansion and

before. This can be described as:

V 1

V 2=

( P2 ,initial−P2, final)( P1 ,final−P1 ,initial )

For an ideal gas, the heat capacity can be determined by the formula:

Cp = Cv + R

Where Cp = molar heat capacity at constant pressure and

Cv = molar heat capacity at constant volume

After a series of differentiation and processes, the ratio of heat capacity can be

expressed as:

Cp

C v=ln Pi−ln

P∫¿

ln Pi−ln Pf¿

where Pi , Pint, and Pf are the initial, intermediate and final pressures respectively and

the theoretical value of Cp

C v is 1.4

APPARATUS

Perfect Gas Expansion Apparatus (Model : TH 11)

PROCEDURE


General start-up

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

switch on.

2. All valves, V1, V2 and V3 were opened. This was to make sure that the

chambers were under atmospheric pressure.

3. The valves were then closed.

4. A hose from the pump was connected to the pressurized chamber or to the

vacuumed chamber. (The tubes had not been connected at the same time)

5. The unit was ready application.

General Shut-down Procedure

1. The pump was switched off and both hoses were removed from the chambers.

2. All valves, V1, V2 and V3 were opened to release the air from inside the

chambers.

3. Power supply and main switched was turned off.

Experiment 1: Boyle’s Law Experiment

1. The general start up procedure was performed and all valve were fully closed.

2. Compressive pump was switch on and allowed the pressure inside the

pressurized chamber to increase up to about 150kPa. Then, the pump was

turned off and removed from the hose ofthe chamber.

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

stabilized.

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

expansion.

5. Valve 2 was fully opened and allowed the pressurized air to flow into the

atmospheric chamber.

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

7. The experiment is repeated with 2 other different conditions:

a) From atmospheric chamber to vacuum chamber.

b) From pressurized chamber to vacuum chamber.


8. The PV value was then calculated.

Experiment 2: Gay-Lussac Law Experiment

1. The general start up procedure was performed. All valves were fully closed.

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

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

of 10kPa in the chamber was recorded. The pump was turned off when the

pressure PT1 reached about 160kPa.

4. Then, V1 was opened and allowed the pressurized air to flow out.

Temperature reading for every decrement of 10kPa was recorded.

5. The experiment was halted when the pressure reached an atmospheric

pressure.

6. The experiment was repeated twice to get the average value.

7. The graph of the pressure versus temperature was plotted.

Experiment 3: Determination of ratio of heat capacity

1. The general start up was performed and all valve were fully closed.

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

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

chamber to increase until 160 kPa. Then, the pump was switch off as well as

the hose removed from the chamber.

4. The pressure reading inside was monitored until it is stabilized. The pressure

reading PT1 and temperature reading TT1 were recorded.

5. Then, V1 was slightly opened to allow the air to flow out slowly until it

reached theatmospheric pressure.

6. The pressure and temperature reading after the expansionprocess were

recorded.

7. The isentropic expansion process was discussed.


Experiment 4: Isentropic Expansion Process

1. The general start up procedure was performed and all valve were fully closed.

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

chamber.

3. The compressive pump was switch on and allowed the pressure inside the

chamber to increase until 160 kPa. Then, the pump was switched off while the

hose was remove from the chamber.

4. The pressure reading was monitored until it is stabilized. Pressure reading of

PT1 was recorded.

5. The valve V1 was opened briefly for 30 seconds and was later closed. The

pressure reading of PT1 was recorded until it became stable.

6. The pressure is display on the graph and discuss.

RESULTS

Experiment 1: Boyle’s Law

1st trial:

Before expansion After expansion

PT 1 (kPa abs) 151.1 135.6

PT 2 (kPa abs) 104.1 135.2

2nd trial:


PT 1 (kPa abs) 103.5 89.2

PT 2 (kPa abs) 59.1 88.7

3rd trial:


PT 1 (kPa abs) 126.4 103.7

PT 2 (kPa abs) 57.0 103.3


Experiment 2: Gay-Lussac Law

Trial 1 Trial 2 Trial 3

Pressu

re

Temperature (°C) Temperature (°C) Temperature (°C)

(kPa

abs)

Pressuriz

ed vessel

Depresurriz

ed vessel

Pressuriz

ed vessel

Depresurriz

ed vessel

Pressuriz

ed vessel

Depresurriz

ed vessel

110 28.9 28.0 27.6 28.3 27.4 29.5

120 29.0 28.9 27.9 28.9 27.8 30.2

130 29.9 30.2 28.5 29.9 28.5 31.2

140 30.4 31.3 29.5 31.0 29.4 31.9

150 31.5 32.5 30.4 31.7 30.2 32.3

160 32.4 32.4 31.4 32.4 31.3 32.4

Pressure (kPa abs) Average temperature (°C)

110 28.3

120 28.8

130 29.7

140 30.6

150 31.5

160 32.08


28 28.5 29 29.5 30 30.5 31 31.5 32 32.50

20406080

100120140160180

Graph of Pressure agaisnt Temper-ature

Temperature (°C)

Pre

ssu

re (

kP

a)

Graph of Gay-Lussac’s Law



PT 1 (kPa abs) 156.2 102.8

T1 1 (°C) 29.1 27.3

Experiment 4: Determination of Ratio Volume

Condition 1: From pressurized vessel to atmospheric vessel

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

Before expansion 148.0 102.3

After expansion 133.2 132.8

Condition 2: From pressurized vessel to vacuumed vessel





Condition 3: From atmospheric vessel to vacuumed vessel




Experiment 5: Determination of Heat Capacity

Initial Intermediate Final

PT 1 (kPa abs) 156.1 108.3 120.0

T1 1 (°C) 30.2 27.3 28.0

SAMPLE CALCULATION

Experiment 1: Boyle’s Law

(For condition 1: from pressurized chamber to atmospheric chamber)

P1,initial = 151 kPa P2,initial = 104.1 kPa

P1,final = 135.6 kPa P2,final = 135.2 kPa

V1 = 0.025 m3

V2 = 0.01237 m3

From Boyle’s law,

P1V1 = P2V2

P1,initialV1 + P2,initialV2 = P1, finalV1 + P2,finalV2

(151 x 0.025)+ (104.1 x 0.01237) = (135.6 x 0.025) +(135.2 x .01237)

3.775 + 1.2877 = 3.39 + 1.6724

5.0627 = 5.0624

The difference by 0.0003. Therefore, result is true for Boyle’s Law.


Experiment 2: Guy-Lussac’s Law

P1 = 110 kPa T1 = 28.3 + 273 = 301.3 K

P2 = 120 kPa T2 = 28.8 + 273 = 301.8 K

P1T1 = P2T2

(110 kPa)( 301.3 K) = (120 kPa)( 301.8 K)

33143 = 36216

Percentage difference = | 33143−36216(33143+36216)/2|x100 %=8.86 %

Since the percentage difference is only 8.86%, the result is valid.


T2 = 27.3 °C P2 = 102.8 kPa

T1 = 29.1 °C P1 = 156.2 kPa

T2

T1=

P2

k−1k

P1

where k = 1.4

27.329.1

=( 102.8156.2 )(

1.4−11.4 )

0.938=0.8873

Percentage difference | 0.938−0.8873(0.938+0.8873)/2|x 100 %=5.55 %

The difference is 5.55% therefore the result is proven isentropic.


Experiment 4: Determination of Ratio Volume.

(Condition 1: from pressurized chamber to atmospheric chamber)

P1,initial = 148.0 kPa P2,initial = 102.3 kPa

P1,final = 133.2 kPa P2,final = 132.8 kPa

V1 = 0.025 m3

V2 = 0.01237 m3

V 1

V 2=

( P2 ,initial−P2, final)( P1 ,final−P1 ,initial )

0.0250.01237

= (102.3−132.8 )(133.2−148.0 )

2.02=2.06

Difference is 0.04 therefore result is valid.

Experiment 5: Determination of heat capacity

Pi = 156.1 kPa Pint = 108.3 Pf = 120.0

Cp

C v=ln Pi−ln

P∫¿

ln Pi−ln Pf¿

Cp

C v= ln 156.1−ln108.3

ln 156.1−ln120.0

Cp

C v=1.40


Since value obtained is equal to the theoretical ratio, the result is valid.

DISCUSSION

As quoted from Boyle’s Law, the pressure of a gas is inversely proportional to

the volume that it occupies. In this context, when the volume of a container holding a

gas increases, the pressure within it decreases meanwhile when the volume decreases,

the pressure increases. This can be explained through the kinetic theory of molecules.

As the volume decreases, the area of collision between the gaseous particles becomes

smaller. This leads to a more frequent collision between the molecules as well as with

the wall of the container. Eventually, the collision causes the pressure to increase.

Apart from that, Boyle’s equation is more often than not used to determine the

pressure or volume of a same gaseous substance once it undergoes a set of change in

either one of the variables. This is can be calculated through the formula of P1V1 =

P2V2. As carried out in the calculation section, it has been proven that even though the

gas went through expansion, the product between the two variables from before and

after the process are still the same, or if not with a slight/minor difference.

Moving onto Gay-Lussac’s Law or Charles’ Law, it states that the pressure of

a gas is directly proportional to its temperature. Opposing to Boyle’s Law, when the

temperature increases, so will the pressure. Again as mentioned again through the

kinetic theory of molecules, when heat is applied to a gaseous particle in a confined

space, they gain kinetic energy which prompts them to a higher frequency of

collision. This then leads to a higher pressure inside the space.

From the graph of Pressure (kPa) against Temperature (°C) plotted above, it

clearly shows the proportionality between the two. Because of this, when a gas

undergoes a series of change in either one of the two variables, the initial or final

unknown can be calculated by the formula proposed as P1T2 = P2T1.

Isentropic is a state of a process where there is no change in the entropy of a

system. Entropy is defined as a measure of the disorder or randomness. However, for

an isentropic expansion process, it is where there is no heat transfer occurring within

the system. This is also known as an adiabatic process. Thus, in this situation, the


formula T2

T1=

P2

k−1k

P1

was applied and was proven that the experiment was in isentropic

state.

In the determination of heat capacity ratio, there was a step in the procedure

which required V1 to be fully opened briefly before closing it back. This was to

record the intermediate pressure. The intermediate pressure is mentioned where the

pressure in the chamber was at its lowest. This short step is defined as a non-quasi

static equilibrium. When the valve was opened, the gas from inside immediately

escaped, causing a sudden decrease in pressure. As it was closed back, the gaseous

molecules then had to collect themselves to achieved equilibrium. Although before

that happened, the molecules in the chamber were fully spread out - giving it the

lowest pressure. This was then taken as the pressure at the intermediate.

CONCLUSION

As a conclusion, this experiment proved the theories and laws of

thermodynamics that involved an ideal gas. This is shown from the calculation where

the results were in accordance to their theoretical values. Despite having a small

difference that was due to some experimental errors, it still managed to show the

relation of Boyle’s Law, Gay-Lussac’s Law, the isentropic expansion process and the

determination of ratio volume and heat capacity. As for Boyle’s Law, the pressure of

gas was proven to be inversely proportional to its volume whereas for Gay-Lussac’s,

the temperature was directly proportional to the volume. All in all, the experiment

was conducted successfully.

RECOMMENDATIONS

1. Before the start of each experiment, the general start up procedure should

always be conducted first so that the chambers are in atmospheric pressure.

2. When switching on the pump, make sure that the pressure within the chambers

would be set with the range as mentioned in the procedures as this greatly

affects the results of the experiments.


3. Make sure that the hose is removed from the chamber and the pump switch is

turned off once the desired pressure has been achieved so that this will not

alter the values.

4. A proper reading should be taken with the increment intervals of pressure and

temperature.

5. Repeat the experiments at least 3 times to get the average reading as this yields

a more accurate data.

REFERENCES

1. Mathsisfun.com,. (2014). Percentage Difference. Retrieved 11 May 2014,

from http://www.mathsisfun.com/percentage-difference.html

2. Wikipedia,. (2014). Isentropic process. Retrieved 11 May 2014, from

http://en.wikipedia.org/wiki/Isentropic_process

3. Anne Marie Helmenstine, P. (2014). Gay-Lussac's Law Definition - Definition

of Gay-Lussac's Law. About.com Chemistry. Retrieved 11 May 2014, from

http://chemistry.about.com/od/chemistryglossary/g/Gay-Lussacs-Law-

Definition.htm

4. Wikipedia,. (2014). Ideal gas law. Retrieved 11 May 2014, from

http://en.wikipedia.org/wiki/Ideal_gas_law

5. Wikipedia,. (2014). Boyle's law. Retrieved 11 May 2014, from

http://en.wikipedia.org/wiki/Boyle's_law


http://en.wikipedia.org/wiki/Ideal_gas_law

http://chemistry.about.com/od/chemistryglossary/g/Gay-Lussacs-Law-Definition.htm

http://chemistry.about.com/od/chemistryglossary/g/Gay-Lussacs-Law-Definition.htm

http://en.wikipedia.org/wiki/Isentropic_process

http://www.mathsisfun.com/percentage-difference.html

APPENDIX

PVT Unit


Documents

PVT expe