ABSTRACTS

The experiment was carried out to investigate the properties of measurement of PVT.

Equipment used is Perfect Gas expansion. The experiment were conducted successfully. The

first experiment, it consist of two section but with three same conditions. The first section is

to prove Boyle’s law. All three condition gave a very good results with small difference, thus

verified Boyle’s law. The second section is for the determination of ratio of volume. The

results obtained is also very promising as the difference is very small for the ratio. The

second experiment was to determine gay-lussac law. It done for three times to get the average

value of Pressure and temperature. The average value was plotted and it does obey the law.

Next experiment was carried out to determine the specific heat capacity by using pressurized

and vacuum chamber. The results obtained had 16.07% deviation. For the determination of

isentrophic process, the results obtain yield small deviation and thus we can conclude that the

process is isentrophic.

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1. INTRODUCTION

Perfect gas also known as ideal gas. Equation of states is the simplest equation that can be

apply for substance in gas phase. This equation predicts the behavior of gas quite

accurately for its pressure, volume and temperature effects. It had been determined

experimentally that at low pressure, volume gas is proportional to its temperature. (Yunus

A. Cengel. , Michael A.Boles, 2013) That is:

Pv = RT

Where R is gas constant. The value of R is different for each gas and can be determined

by

R = Ru/M

Where R is universal gas constant and M stand for molar mass of the respective gas. Gas

that obey this law is called as an ideal gas. P is absolute temperature and T is the absolute

temperature while v is specific volume. The equation can also be written in other formed

as: (Yunus A. Cengel. , Michael A.Boles, 2013)

V=mv

That gives us :

PV= mRT

As for a fixed mass, the equation can be gain by relating two equation. The properties of

an ideal gas at two different states are related to each other by the equation of:

P1V1/T1 = P2V2/T2

2. OBJECTIVE

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2.1. Experiment 1 : Boyle’s law experiment & determination of ratio of volume

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

2.1.2. To compare the experimental results with theoretical values.

2.1.3. To determine the ratio of volume and compare it to the theoretical alues.

2.2. Gay-Lussac Law experiment.

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

2.3. Determination of ratio of heat capacity

To determine the ratio of heat capacity

2.4. Isentropic Expansion process

To demonstrate the isentropic expansion process.

3. THEORY

Boyle’s Law

Based on Boyle’s law, the pressure P and the volume V of gas held at constant

temperature will give product of pressure and volume to be nearly constant. Therefore,

the product of pressure and volume is exactly a constant for an ideal gas.

P x V = Constant

P: pressure of the system

V: Volume of the gas

C: Constant that represents constant value of pressure and volume

This law is used to predict the effect and the results that can be obtain of an ideal gas

introduced with change in volume and pressure only. The equation that can be used to

show the relationship between volume and pressure of fixed amount of gas before

expansion and after expansion process. The temperature is kept constant. (Benson, 2011)

P1V1 = P2V

Charle’s Law

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This law define that at constant pressure, volume of a given mass of an ideal gas will

increase or decrease with the temperature in Kelvin.

V/T = K

V : Volume

T : Temperature in kelvin

To ensure that K is remaining constant, the heating of gas in constant pressure volume

need to increase as temperature will increase. The exact value of K is crucial to ensure

that we can compare results obtain with the theoretical one. The relationship can be

obtain as below (Leon, 2001) :

V1/T1 = V2/T2

Gay-lussac law

This law states that at constant volume, pressure of a gas will be proportional to its

absolute temperature in kelvin. It can be express as :

P1/T1 =k

To show the relationship, the equation can be further express as:

P1/T1 = P2/T2

P1T2 = P2T1

Determination ratio of heat capacity theory

Specific heat can be defined as the energy needed to raise a temperature of a unit mass of

substances by one degree. The energy depends on how the process is carried out. There is

two kinds of specific heat that is interest which is specific heat at constant volume C v and

specific heat at constant pressure, Cp. Cv also can be defined as the energy needed to raise

the temperature of unit mass of substance by one degree as volume kept constant.

Meanwhile, Cp or specific heat at constant pressure is the energy needed to do the same as

pressure kept constant. The value of Cp is always larger than Cv due ti the fact that at

constant pressure the system is allowed to expand and the energy for this expansion work

must be supplied to the system. To define the Cv an Cp these equation is applicable:

(Yunus A. Cengel. , Michael A.Boles, 2013)

Cv = ( v

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Cp = ( p

The equation shows that for Cv it is calculated at different internal energy while Cp

calculated based on its enthalpy.

The heat capacity ration can be obtained by determination by these two steps:

1) Adiabatic reversible expansion for initial pressure, Pi to intermediate pressure

which is Pm.

2) A return of temperature to its original value to a constant volume at final pressure

Pf.

Cp/Cv = K

For ideal gas :

Cp = Cv + R

As for non ideal gas

dq= 0

First law of thermodynamics

dU = dq + dW

During the expansion process

dU = dW or dU = -PdV

while

dU = CvDt

This define that the heat capacity related the change in temperature to the change

in the internal energy as volume kept constant.

Substituting Cvdt to value of dU

CvdT = -PdV

Substitute into ideal gas law, and integrating the equation below is obtained

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Cv (in (Pm/pi) + ln (Vm/Vi) = -Rln(Vm/Vi)

Then we will obtained

In (Pm/Pi) =- (Cp/Cv)ln(Vm/Vi)

As temperature return to its initial value, these relationship obtained:

(Vm/Vi) = (Pi/Pf)

By substituting and rearranging we will get

Cp/Cv = (ln Pi – ln Pm)/(ln Pi – ln Pf)

Isentrophic expansion theory:

Isentrophic process defines as a process that take place with no change in

entrophy of the system throughout the process. This can be express as

S1 = S2

Or

If process is reversible and adiabatic, it is then an isnetrophic process, an

isentrophic process is an idealization of an actual process and serve as limiting for

the actual process. Adiabatic process involve no transfer of heat energy.

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4. APPARATUS AND MATERIALS

4.1. Perfect gas expansion apparatus.

5. PROCEDURE

5.1. General startup procedure

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

turned on.

5.1.2. All the valves was opened. The reading on the pressure panel was checked.

5.1.3. Close all valves.

5.1.4. The pipe from the compressive port was connected to pressurize chamber. The

pipe from vacuum pump connected to vacuum chamber.

5.1.5. Then, units were ready for use.

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Pressure relief valve

Pressure transmitter

Temperature sensor

Big glass

Electrode

Pressure transmitter

Big glass

Small glass

Vacuum pump

5.2. Experiment 1 : Boyle’s law experiment & Determination of ratio volume.

5.2.1. The general startup procedure was performed and all the valves were ensured

to be closed.

5.2.2. The compressive pump was switched on until the pressure inside the chamber

to increase up to 150 – 160 KPa. The pump was switched off and the hose were

removed from the respective chamber.

5.2.3. The pressure inside the chamber was monitored until it’s stabilized.

5.2.4. Reading of pressure for both chamber before expansion were recorded.

5.2.5. Valve 02 was fully opened to allow the pressurize air to flow to atmospheric

chamber.

5.2.6. The pressure for both chamber were recorded after expansion.

5.2.7. The experiment was repeated by using following conditions:

5.2.7.1. From atmospheric chamber to vacuum chamber.

5.2.7.2. From pressurized chamber to vacuum chamber.

5.2.7.2.1. For vacuum chamber procedure, the switched was turned on to

release the pressure to 50-60 KPa.

5.2.7.2.2. Valve 02 was fully open to allow the pressurize air to flow into

atmospheric chamber.

5.2.7.2.3. The reading after expansion for both chamber then recorded

5.2.8. PV values was calculated to prove Boyle’s law.

5.2.9. Ratio of volume was calculated and compared to theoretical values.

5.3. Experiment 2: Gay-Lussac law experiment

5.3.1. General start-up procedure was performed. All valves were fully closed.

5.3.2. The hose from the compressive pump was connected to pressurize chamber.

5.3.3. The compressive pump were turned on and the temperature was recorded for

every 10 KPa increment of pressure. The pump was stopped when pressure at

PT1 reached 160 KPa.

5.3.4. Valve 01 was then opened slightly to allow pressurize air to flow out. The

temperature was taken for every decrement of 10 KPa of pressure.

5.3.5. Experiment was stopped when pressure drop to atmospheric pressure.

5.3.6. Experiment was then repeated three times to get average values.

5.3.7. Graph of pressure vs temperature were plotted.

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5.4. Experiment 3 : Determination of heat capacity

5.4.1. General startup procedure was performed. All valves were ensured to be

closed.

5.4.2. The hose from compressive pump were connected to pressurized chamber.

5.4.3. The compressive pump was turned on and the pressure was allowed to

increase until about 160 KPa. The pump the switched off and the hose were

removed.

5.4.4. The pressure inside the chamber was monitored until it stabilized. Pressure at

PT1 and temperature at TT1 was recorded.

5.4.5. Valve 01 was fully opened for few moments before immediately closed again.

The pressure and temperature were then recorded as it stabilized.

5.4.6. The ratio of heat capacity with theoretical values were compared.

6. RESULTS

6.1. Experiment 1 : Boyle’s law experiment.(condition 1,2,3 respectively)

Before experiment After experimentPT1(Kpa

Abs) 152.6 135.8

PT2(Kpa Abs) 102.1 135.2

Before experiment After experimentPT1(Kpa

Abs) 102.3 89.6

PT2(Kpa Abs) 55.8 88.9

Before experiment After experimentPT1(Kpa

Abs) 155.5 123.6

PT2(Kpa Abs) 156.9 123.0

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Determination of ratio volume(Condition 1,2,3 respectively)

Before experiment After experiment

PT1(Kpa Abs) 153.1 136.6

PT2(Kpa Abs) 102.7 135.7

Before experiment After experiment

PT1(Kpa Abs) 103.5 88.6

PT2(Kpa Abs) 56.8 87.8

Before experiment After experiment

PT1(KPa Abs) 155.1 124.6

PT2(KPa Abs) 60.7 123.9

6.2. Experiment 2 : Gay Lussac law

Pressure(Kpa Abs)

Trial 1 Trial 2 Trial 3 Average

Temperature (OC) Temperature (OC) Temperature (OC) Temperature (OC)

Pressurize

vessel

Depressurize

vessel

Pressurize

vessel

Depressurize vessel

Pressurize

vessel

Depressurize

vessel

Pressurize

vessel

Depressurize vessel

110.0 27.8 27.2 26.5 27.1 26.5 27.5 26.9 27.3120.0 27.9 28.4 26.6 28.5 26.7 28.3 27.1 28.4130.0 28.3 29.5 27.4 29.5 27.4 29.2 27.7 29.4140.0 29.1 30.3 28.3 30.4 28.3 30.4 28.6 30.4150.0 29.7 31.0 29.3 31.2 29.2 30.9 29.4 31.0160.0 30.4 31.5 30.1 31.5 29.9 31.1 30.1 31.4

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6.3. Experiment 3 : Determination of heat capacity

Initial Intermediate FinalPT 1(Kpa

Abs) 160.3 103.3 110.3

TT 1(oC) 30.8 29.9 27.5Table 6.3 : The reading in determination of heat capacity.

6.4. Experiment 4 : Isentrophic expansion process

Before expansion After expansionPT 1(Kpa

Abs) 155.2 102.9

TT1(oC) 30.0 26.2

7. CALCULATIONS

7.1. Experiment 1 : Boyle’s law experiment.

7.1.1. Condition 1 : Pressurized vessel to atmospheric pressure (Fully open)

V1 : 0.025m3

V2 : 0.01237m3

By using Boyle’s law

P1V1 = P2V2

(152.6)(0.025) + (102.1)(0.01237) = (135.8)(0.025) + (135.2)(0.01237)

5.0780 = 5.0674

0.01 Difference, Boyle’s law verified.

7.1.2. From atmospheric chamber to vacuum chamber

P1V1 = P2V2

(102.3(0.025))+(55.8(0.01237)) = (89.6(0.025)) + (88.9(0.01237))

3.2477 = 3.3397

0.092 difference, Boyle’s law verified.

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7.1.3. From pressurized chamber to vacuum chamber.

(155.5(0.025)) + (56.9(0.01237)) = (123.6(0.025)) + (123(0.01237))

4.5913 = 4.61151

Difference 0.02, verified

Experiment 1 : Ratio Volume(open slightly)

7.1.4. Condition 1 : Pressurized vessel to atmospheric pressure

Volume 1/ Volume 2: (P2initial –P2final)/ (P1final – P1initial)

=

2.21 = 2 (Difference 0.021)

7.1.5. From atmospheric chamber to vacuum chamber

=

2.021 = 2.081 (Difference = 0.06)

7.1.6. From pressurized chamber to vacuum chamber.

=

2.021 = 2.072 (Difference 0.051)

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7.2. Experiment 2 : Gay lussac law

7.2.1. Pressurized graph (Trial 1)

7.2.2. Depressurize Graph (Trial 1)

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7.2.3. Graph of average of pressurized and depressurized

7.3. Experiment 3: determination of ratio of heat capacity

=

= 1.175

Ideal k, = 1.4

Deviation :

x 100 % = 16.07 %

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7.4. Experiment 4 : Isentrophic expansion process

0.8733 = 0.8891

Difference is 1.77% expansion is proven as isentrophic8. DISCUSSIO N

Based on the results obtained, for the first experiment the volume were kept constant. For

pressurize chamber, the volume is 0.025 m3 while for vacuum chamber the volume turn

out to be 0.01237 m3. The first experiment consist of two section, the first section is

where the valve is fully open and the second one is the valve is slightly open to get the

ratio volume. For both section, there were three test carried out for three different

condition which is pressurized vessel to atmospheric pressure, from atmospheric pressure

chamber to vacuum chamber and from pressurized chamber to vacuum chamber. For the

fully open, the first condition which is pressurized vessel to atmospheric pressure, the

calculated value using Boyle’s law is 5.0780 before expansion and 5.0674 after

expansion. There is 0.01 differences. Thus, boyles law is verified. For second condition,

which is from atmospheric chamber to vacuum chamber, before expansion the calculated

value of P x V is 3.2477 while after expansion is 3.3397. The calculated value shows

0.092 difference, thus boyle’s law verified. For the third condition of fully open valve,

initial calculation show 4.5913 while after expansion the calculation shows 4.6115. There

is 0.02 difference in reading, but it is relatively small and thus Boyle’s law is verified.

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For the determination of ratio volume, the valve were open slightlyt. By using the

same conditions, the first one ratio volume 1 over volume 2 is 2.21 while for pressure is

2. Difference 0.21. This is relatively small as compared to theoritical value. Second

condition gives 0.06 difference. And the third condition gives 0.051 difference which is

also relatively small.

As for gay-lussac experiment, graph of pressure vs temperature were plotted based on

the given results for pressurized and depressurized. The first trial of pressurized chamber

shows that, temperature is directly propotional to the pressure(7.2.1). This also valid for

graph of depressurized where there is a propotional relationship between temperature and

pressure.(7.2.2). As for the second and the third grapgh, it was plotted but put inside the

appendix. As for average, the graph also shows that temperature is directly propotional to

pressure.(7.2.3).

For determination of ratio of het capacity, the results shows that the calculated heat

capacity ratio is 1.175 with deviation of 16.07%. The intermediate pressure should be

lower than measured intermediate pressure theoretically. But, as there is loss in heat and

sensitivity of pressure sensor may cause the presence of such errors.

For isentrophic expansion process, the results turn out to be 0.8733 and 0.8891 as

calculated by using the given formula. There is a 1.77% difference which is relatively

small. Thus we can conclude that the process is isentrophic.

9. CONCLUSION

In conclusion, the results for first experiment valid that Boyles law does shows

P1VI=P2V2 relations. For gay lussac law, the results does prove that temperature it

directly propotional to pressure.While, heat capacity is near to the theoritical value which

is in range of 1.4-1.5. based on the test carried out, the process is isentrophic due to the

fact that value difference is so small between two calculated results.

10. RECOMMENDATIONS

To improve the results if experiment, the data should be taken accurately. This can be

carried out by really wait for the reading to be stabilize before taking reading as there

might be increase or decrease in reading after we had taken the results that results in

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deviation. Besides that, when taking out the hose form the respective chamber, it should

be done fast as it will affect the results and also our air inside the chamber. The pressure

inside were also ensure not to exceed 2 Btu as it may broke the chamber glass. The results

need to repeated three times to take the average value of the results thus it may help in

decreasing the deviation.

REFERENCES

Benson, T. (2011, march 07). Boyle's Law. Retrieved may 12, 2014, from NASA: http://www.grc.nasa.gov/WWW/k-12/airplane/boyle.html

Leon, P. N. (2001). Charles Law. Retrieved may 12, 2014, from Elementary Gas Laws:: http://www.iun.edu/~cpanhd/C101webnotes/index.html

Yunus A. Cengel. , Michael A.Boles. (2013). Thermodynamics : An engineering Approach. singapore: McGrawhill.

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APPEN DIX

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