ABSTRACTThis experiment involving a perfect gas or ideal gas has seven experiments. The equipment involved in this experiment is known as Perfect Gas Expansion and 7 experiments were conducted. The experiment is conducted to determine the relationship between ideal gas and various factors such as pressure, volume and temperature and the relation with first and second law of thermodynamics. The experiment is to determine the Boyles Law, Gay-Lussac Law, isentropic expansion process, ratio of heat volume also the heat capacity. The experiment is done to prove whether ideal gas obeys the Boyles Law also the Gay-Lussac Law and also to calculate the ratio of heat volume and heat capacity. Boyles Law and Gay-Lussac Law were proven in this experiment as the ideal gas obeys the law. The volume ratio of gas is varies for the different conditions. The value of volume ratio for condition 1, 2 and 3 are 1.890, 2.037 and 1.850 respectively. The heat capacity ratio is determined and the value 1.149 while the percentage error is 17.93%. The experiment was done and successfully conducted.

INTRODUCTIONThe Perfect Gas Expansion is related to First and Second Law of Thermodynamics and also the relationship with PVT. Expansion and compression of gas is essential in our daily life as well to the industry. This is because it is related to combustion, refrigerators, hot pumps and et cetera. This experiment of measurement properties is deals with ideal gas. This ideal gas obeys the equation of state of:

The equation of state relates the pressure, temperature and specific volume of physically homogenous element in thermodynamics equilibrium generally. In this definition, P and T represents the absolute temperature and absolute pressure respectively while R is gas constant and is the number of moles if the gas filling the container. The molecular weight of the gas will affect the gas constant.(Reid, Prausnitz & Sherwood, 1977) The equipment used is the perfect gas expansion apparatus. The equipment consists of 2 vessels which are pressure vessel and vacuum vessel. The vessels are made from glass and can withstand maximum pressure of apparatus can operate. During the supply of air into the vessel, gas particle in the vessel will collide more aggressive and more frequent with the wall and transfer the momentum when it is colliding. The gas pressure is equal to the momentum delivered to a unit area of a wall during a unit of time. Ideal gas does not collide with each other but only with the walls unlike the actual gas which collide with the wall and with each other. For ideal gas, the single particle moves arbitrarily along some directions until it strikes a wall. It then bounces back, changes direction and speed and moves towards another wall. The gas expansion equation is derived directly from the law of conservation of linear momentum and the law of conservation of energy. (Scars & Salinger. 1975)In this experiment, the several fundamentals thermodynamics process can be manipulated by monitored the digital indicator of control panel. The experiment should be conduct safely and all the precautions should be taken during the experiment. The most important thing is the valve should be open slowly when releasing the gas to the atmosphere due to high pressure inside the vessel.

AIMS Experiment 1 To determine the relationship between pressure and volume of an ideal gas and to compare the experimental results with theoretical results.

Experiment 2 To determine the relationship between pressure and the temperature of an ideal gas.

Experiment 3 To demonstrate the isentropic expansion process.

Experiment 4 To study the response of the pressurized vessel following stepwise depressurization.

Experiment 5 To study the response of the pressurized vessel following a brief depressurization.

Experiment 6 To determine the ratio of volume and compares it to the theoretical value.

Experiment 7 To determine the ratio heat capacity.

THEORY Perfect GasTheories of perfect gas can be divided into three which is Charless law, Boyles law and Gay-Lussacs 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 is 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:

The subscript R refers 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:

The properties of ideal gas at two different states are related to each other as long as they have one constant property throughout the experiment where:

Boyles LawThe behaviour of real gas using parameter of pressure, temperature and volume is considered at low density. Ideal gas also obeys the law of Boyles, Charless and Gay-Lussacs. Boyles law describe the relationship between the pressure and the volume of a gas. This law works when the pressure increases inversely with the volume of gas where the temperature held constant along the process. The gas inside a system is loosely packed and moves 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 Boyles Law

Charless LawSecond law is Charless 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 increases. Therefore the equation of Charless law simply shows 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 Charless law describe in a graph as follow:

Figure 2: Graph of Charless Law

Gay-Lussacs LawThe third law involving ideal gas is Gay-Lussacs law where the volume of the system becomes 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 constant volume.

Graph below show the relationship of temperature and pressure in the Gay-Lussacs law with constant volume. The conclusion is that the pressure directly proportional to the temperature.

Figure 3: Graph of Gay-Lussacs Law

First law of thermodynamics Based on first law of thermodynamics statement, energy can be neither created nor destroyed but it can only change in the form of energy. For example the change of energy of lamp, from electric energy converts to light and heat energy. Therefore, the conservation of energy principle introduced as the net change in the total energy of the system equivalent to the difference in the total energy enter the system and total energy leaving the system.

That equation also referred as energy balance equation that applicable to any kind system any kind of process. Since the energy has numerous form such as internal, kinetic, potential, electrical and magnetic and their sum constitutes the total energy of the system. Simple compressible system has the following equation which the change in the total energy of a system is the sum of the changes in its internal, kinetic, potential energy can be expressed as:

Where;Internal energy, Kinetic energy, Potential energy,

Energy can be transfer in or out of a system in three forms such as heat, work and mass flow. As there is one of any three form cross the boundary of an open system, it can be concluded as energy gained or lost during a process. In a closed system, there is only two form can pass through the boundary which can change the energy which are heat and work. Temperature difference in a system with its surrounding is not an energy interaction. Work interactions refer as rising piston and rotating shaft. Commonly sense when the work transfers into the system, the energy of the system increase and vice versa. As mass transfer in the system, energy also increases as the mass carries energy with it and vice versa. Equation below represents the concluded energy balance.

Amount of energy required to raise the temperature of a unit mass of a substance by one degree is a definition of specific heat. There are two specific heat uses widely which is specific heat at constant volume and specific heat at constant pressure. value larger than as at constant pressure system is allowed to expand and the energy must supplied to system. Specific heat capacity at constant pressure is the energy required to raise the temperature of the unit mass of a substance by one degree as the pressure remain constant. It can be concluded that is related to internal energy and involved enthalpy value

Internal energy is a function of temperature only. As the temperature high, then enthalpy value also big. Then the enthalpy value is representing the subscript h:

Where it can combine to become:

Since R is a constant the enthalpy of an ideal gas is also a function of temperature only, Therefore at a given temperature for an ideal gas, , , and will have fixed values regardless of the specific volume or pressure. Thus the differential changes in the internal energy and enthalpy of an ideal gas can expressed as:

and has special relationships for ideal gas by differentiating the to produce and by replacing by and by , the equation come out with:

Specific heat capacity also has the constant k by the relation of:

Ratio of volumes using isothermal process can be determined using isothermal process. One pressurized vessel is allowed to leak slowly into another vessel of different size. Finally, the pressure will be same for both vessels. Final pressure in vessel can be calculated by:

Both vessel was placed in room temperature before valve is opened lead the isothermal process and the initial temperature will be equal to the final temperature. Deriving:

Using these equation, substitute m1 and m2 into equation of and become:

Rearrange the equation and cancel the to give the ratio of the two volumes:

Stepwise DepressurizationStepwise 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 DepressurizationThis 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 observed which can be compared later. The graph should be higher gradient.

APPARATUS AND MATERIAL

Figure 1: Perfect Gas Expansion Apparatus

1. Pressure transmitter 2. Pressure relief valve3. Temperature sensor 4. Pressurized vessel5. Vacuum vessel6. Vacuum pump 7. Electrode

PROCEDUREA. General Start-up Procedures1. The equipment was connected to single phase power supply and then switched on the unit.2. All valves were fully opened and the pressure was checked at the panel.3. Then, all the valves were closed.4. The pipe from compressive port of the pump was connected to pressurized vessel or vacuum port of the pump to vacuum vessel.5. The unit is ready to use.

B. General Shut-down Procedures1. The pump was switched off and removed from both pipes of the vessels.2. The valves were fully open to release the air inside the vessel.3. The main switch and power supply is off.

Experiment 1: Boyles Law1. All the valves were fully closed.2. The compressive pump was switched on and the pressure inside the vessel increase to 150kPa. 3. The pump was switched off and the hose is removed from the vessel.4. The pressure reading inside the vessel was monitored until it stabilizes.5. The pressure reading for both vessels is recorded before expansion.6. The pressurized pump 2 was fully opened to allow air flow into the atmospheric vessel.7. The pressure reading for both vessels after expansion was recorded.8. The experiment is repeated under difference condition:a) From atmospheric vessel to vacuum vesselb) From pressurized vessel to vacuum vessel.9. The PV value was calculated then the Boyles Law was proven.Experiment 2: Gay-Lussac Law Experiment1. All valves were fully closed.2. The hose was connected from the compressive pump to pressurized vessel.3. The compressive pump was switched on and the temperature is recorded for every increment of 10kPa in the vessel. The pump is off when PT1 reached 160kPa.4. Then, the valve 01 was slightly opened and allowed the pressurized air to flow out. 5. The temperature was recorded for every decrement of 10kPa.6. The experiment is stopped when the pressure reaches atmospheric pressure.7. The experiment was repeated 3 times to get average value.8. The graph of pressure versus temperature was plotted.

Experiment 3: Isentropic Expansion Process1. All valves were full closed.2. The hose was connected from the compressive pump to pressurized vessel.3. The compressive pump was switched on and the pressure inside the vessel is increased until 160kPa.4. The pump was switched on the pump was remove from the vessel.5. The pressure reading inside the chamber is determined when it is stabilizes. 6. The pressure reading, PT1 and temperature, T1 were recorded.7. Then, the valve 01 is slightly opened to allow the air flow out slowly from the vessel until it reaches the atmospheric pressure.8. The pressure and temperature reading was recorded after the expansion process.9. The isentropic process was discussed.

Experiment 4: Stepwise Depressurization1. All valves were fully closed.2. The hose was connected from the compressive pump to pressurized vessel.3. The compressive pump was switched on and the pressure inside the vessel is allowed to increase to 160kPa. 4. Then, the pump is switched on and the hose was removed.5. The pressure reading inside the vessel is determined when it is stabilizes. The pressure reading, PT1 is recorded.6. The valve 01 was fully opened and closed instantly. The pressure reading PT1 is recorded until it becomes stable.7. The step 6 was repeated at least 3 times.8. The pressure reading graph is plotted and discussed.

Experiment 5: Brief Depressurization1. All valves were fully closed.2. The hose was connected from the compressive pump to pressurized vessel.3. The compressive pump was switched on and the pressure inside vessel is increase to 160kPa. 4. Then. The pump is switched off and the hose was removed.5. The pressure reading inside the vessel is determined until it stabilizes.6. The pressure reading, PT1 was recorded.7. The valve 01 was fully opened and closed after 3 seconds.8. The pressure reading, PT1 was recorded until it become stable.9. The pressure reading is displayed on the graph and being discussed.

Experiment 6: Determination of ratio of volume1. All valves were fully closed.2. The compressive pump is switched on and the pressure inside the vessel is increase to 150kPa.3. The pump was switched off and the hose was removed from the vessel.4. The pressure reading inside the vessel is monitored until it stabilizes.5. The pressure reading for both vessels before expansion was recorded.6. V 02 was opened and the pressurized air flow into the atmospheric vessel slowly.7. The pressure reading for both vessels after expansion was recorded.8. The experimental procedures repeated for the following conditions:a) From atmospheric vessel to vacuum vesselb) From pressurized vessel to vacuum vessel.9. The ratio of volume was calculated and compared with theoretical value.

Experiment 7: Determination of ratio of heat capacity1. All valves were fully closed.2. The hose from compressive pump was connected to the pressurized vessel.3. The compressive pump was switched on and the pressure inside the vessel is increase to 160kPa.4. The pump is switched on and the hose was removed from the vessel.5. The pressure reading inside the vessel is monitored until it stabilizes.6. The pressure, PT1 and temperature, T1 were recorded.7. The valve 01 was fully opened and closed it after a few seconds.8. The pressure and temperature reading was monitored and recorded until it stable.9. The ratio of heat capacity was determined and being compared with the theoretical value.

RESULTSExperiment 1: Boyles Law1. Condition 1Before expansionAfter expansion

PT 1 (kPa abs)148.8133.4

PT 2 (kPa abs)102.4132.6

2. Condition 2Before expansionAfter expansion

PT 1 (kPa abs)106.690.3

PT 2 (kPa abs)56.359.2

3. Condition 3Before expansionAfter expansion

PT 1 (kPa abs)150.8119.0

PT 2 (kPa abs)55.6118.3

37

Experiment 2: Gay-Lussac Law Experiment

Trial 1Trial 2Trial 3

Pressure (kPa abs)Temperature (oC)Temperature (oC)Temperature (oC)Average temperature (oC)

Pressurise vesselDepressurise vesselPressurise vesselDepressurise vesselPressurise vesselDepressurise vessel

11026.225.225.225.725.626.225.7

12026.525.425.626.225.827.226.1

13027.125.726.327.226.628.226.9

14028.126.127.228.627.629.227.8

15029.026.228.329.828.630.128.7

16029.927.729.130.329.831.029.6

Experiment 3: Isentropic Expansion ProcessBefore expansionAfter expansion

PT 1 (kPa abs)157.5103.1

TT 1 (oC)30.427.5

Experiment 4: Stepwise DepressurizationPressure (kPa abs)

InitialAfter first expansionAfter second expansionAfter third expansion

159.9135.4106.0102.1

135.5106.1102.2

135.6106.2102.3

135.7106.3102.4

135.8106.4102.5

135.9106.5102.6

136.0106.6102.7

136.1106.7102.8

136.2106.8102.9

136.3106.9103.0

136.4107.0103.1

136.5107.1103.2

136.6107.2103.3

136.7107.3103.4

136.8107.4103.4

136.9107.5

137.0107.6

137.1107.7

137.2107.8

137.3107.9

137.4108.0

137.5108.1

137.6108.2

137.6108.3

108.4

108.5

108.6

108.7

108.8

108.9

109.0

109.1

109.2

109.3

109.4

109.5

109.6

109.7

109.8

109.9

110.0

110.1

110.2

110.3

110.4

110.4

Experiment 5: Brief DepressurizationPT 1 (kPa abs)

InitialAfter brief expansion

162.5122.5

122.6

122.7

122.8

122.9

123.0

123.1

123.2

123.3

123.4

123.5

123.6

123.7

123.8

123.9

124.0

124.1

124.2

124.3

124.4

124.5

124.6

124.7

124.8

124.9

125.0

125.1

125.2

125.3

125.4

125.5

125.6

125.7

125.8

125.9

126.0

126.1

126.2

126.3

126.4

126.5

126.6

126.7

126.8

126.9

127.0

127.1

127.2

Experiment 6: Determination of Ratio Volume1. Condition 1PT 1 (kPa abs)PT 2 (kPa abs)

Before expansion145.4102.2

After expansion130.8129.8

2. Condition 2PT 1 (kPa abs)PT 2 (kPa abs)

Before expansion106.556.4

After expansion90.389.4

3. Condition 3PT 1 (kPa abs)PT 2 (kPa abs)

Before expansion150.556.6

After expansion117.9116.9

Experiment 7: Determination of Ration of Heat CapacityInitialIntermediateFinal

PT 1 (kPa abs)158.5103.2109.1

TT 1 (oC)30.829.727.7

CALCULATIONS Experiment 1: Boyles Law1. Condition 1: from pressurized vessel to atmospheric vessel

The difference is only 0.011426, therefore the Boyles Law is verified.

Experiment 2: Gay-Lussac Law

Pressure (kPa abs)Average Temperature (oC)

11025.7

12026.1

13026.9

14027.8

15028.7

16029.6

Graph 1: Graph of pressure versus temperature

Since the pressure is directly proportional to temperature in the figure above. Hence, the Gay-Lussacs Law is verified.

Experiment 3: Isentropic Expansion Process

For isentropic process,

The difference is 0.02%. The expansion process is proven as isentropic.

Experiment 4: Stepwise depressurization

Graph 2: Graph of response of pressurized vessel following the stepwise depressurization

Experiment 5: Brief depressurization

Graph 3: Graph of response of pressurized vessel following a brief depressurization

Experiment 6: Determination of Ratio Volume1. Condition 1

Difference = Percentage error =

Experiment 7: Determination of ratio of heat capacity

DISCUSSIONBoyles Law states that the pressure of gas is inversely proportional to the occupied volume. The difference value between before expansion and after expansion was calculated to prove the Boyles Law. The difference for condition 1, 2 and 3 are 0.011426, 0.371627 and 0.019401 respectively. These values are small and closed to the theoretical value, therefore the Boyles Law is proven. The difference is due to the error occurs during conducting the experiment. According to the data tabulated, the pressure and volume is inversely proportional to one another. As the pressure increases, the volume will start to decrease. This occurs due to the difference in volume of vessel with the equal amount of pressure being supplied in both vessels. The gas molecule in the small vessel will collide with wall and one another more frequent due to limited space rather than big vessel which have more space. The Gay-Lussac Law stated that the pressure is directly proportional to the temperature. According to the experiment, as the pressure in the vessel increase, the temperature inside the vessel will also increase. Thus, from the data tabulated, it can be said that the Gay-Lussac Law is verified. If the temperature of the gas in the vessel is increase, the heat energy of the system will transfer its energy to the gas molecules which help to increase the frequency of collision in the vessel. Hence, more pressure will be exerted. The isentropic expansion process happen when both systems in adiabatic and reversible condition so there will be no heat transferred within the system as well as no energy transformation occurs. The value of k is calculated in this experiment by using the pressure and temperature before and after expansion and it is constant. The value of k calculated is 1.309. It was obtained that both pressure and temperature of the gas before expansion is higher than after the expansion. The process said to be in isentropic process sic ether is no change of entropy throughout the system.The Stepwise depressurization shows the relationship between the pressure and temperature. From the graph obtained, it can be conclude that the pressure decrease accordingly with the temperature. Thus, the pressure is directly proportional to the temperature of the gas. The molecule in the vessel is affected when the amount of gas molecule is decreasing so, the gas will have more space in the vessel thus lowering the frequency of the collision. The Brief depressurization shows the same concept as the stepwise depressurization but the graph obtained from brief depressurization shows the gas decreasing more linear than in stepwise depressurization. The increasing of pressure in vessel will cause the expansion to occur in vessel. The expansion will decrease if the gas is allowed to flow out from the system. The ratio of volume can be determined by manipulating the Boyles Law equation. Boyles Law stated that , and after manipulating it to determine the volume ratio by . This experiment is conducted in 3 different conditions and the percentage error is calculated in the experiment. The theoretical value of the experiment is 2.021 and the percentage error for condition 1, 2 and 3 are 6.48%, 0.79% and 8.46% respectively. High value of percentage error obtained may due to the error occur during the experiment or the environmental factor. The experiment is considered successful because the percentage error obtained s less than 10%.The ratio of heat capacity is determined by using the expression of heat capacity ratio. The value of heat capacity ration is 1.149. The theoretical value of heat capacity ratio is 1.4. The percentage error calculated is 17.93%. Since the percentage error calculated is higher than 10%, so the experiment considered unsuccessful. The actual intermediate pressure supposed to be lowered than the value being measured. The intermediate pressure supposed to be the lowest pressure and being taken exactly at the moment when the valve was closed. Since the percentage error calculated is higher than 10%, so the experiment considered unsuccessful. There may be error occur during the experiment and also the environmental factor.

CONCLUSIONIn the conclusion, the experiment is to determine the properties of measurement or PVT according to the Boyles Law, Gay-Lussac Law, isentropic expansion, ratio of volume and the ratio of specific heat capacity. The Boyles Law and Gay-Lussac Law have a relationship with the pressure, temperature and volume and were verified as the gas obeys the law as well with the isentropic expansion process. The ratio of volume indicates the expansion and compression of gas while the heat capacity ratio expressed the amount of heat that could be taken up by gas during expansion process. The experiment is successfully done and the objective is achieved.

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 affect the results. The place where the experiment is conducted must be at stable and no vibration. 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.

REFERENCES1. Reid, R., Prausnitz, J.M., and Sherwood, T.K. (1977) The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill.1. F.W. Sears, G.L. Salinger, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (Addison-Wesley, 3rd ed 1975) 1. Reid, R. C, Prausnitz, J. M., and Sherwood, T. K. (1977)The Properties of Gases and Liquids, McGraw-Hill, New York.1. Irfan, M. H. (2013); Retrieved on November 2014 from The Perfect Gas Expansion Experiment (TH11) by Muhammad Haidharul Irfan . 1. Charles's Law; Retrieved on November 2014http://science.howstuffworks.com/dictionary/physics-terms/charles-law-info.html1. Boyles Law, retrieved on November 2014en.m.wikipedia.org/wiki/Boyle%27s_law

APPENDICESExperiment 1: Boyles Law1. Condition 2: from atmospheric vessel to vacuum vessel

The difference is only 0.371627, therefore the Boyles Law is verified.

2. Condition 3

The difference is only 0.019401, therefore the Boyles Law is verified.

Experiment 6: Determination of Ratio Volume1. Condition 2

Difference = Percentage error = 2. Condition 3

Difference = Percentage error =