Lab 6(Final)

Abstract/Summary

This experiment is conducted at UiTM Pilot Plant. The aim of this experiment is to

determine the properties of measurement. During this experiment been conducted, 5 were

successfully conducted and the equipment that had been used were ‘Perfect Gas’. The first

experiment were conducted to show the Boyle’s Law and to determine the relationship

between pressure and the volume of an ideal gas. This experiment were run/done for three

times from the pressurized chamber to the vacuum chamber, from the atmospheric chamber

to pressurized chamber and increase the gas of both chamber. The next experiment were

conducted to determine the Gay-Lussac Law and were done three times to get the average

value of the temperature at pressurized and depressurize vessels. The graph of pressure versus

temperature is plotted after getting the total average value. To determine the isentropic

expansion gases, the third experiment were conducted where pressure and temperature of

pressurized chamber is taken before and after expansion. After that, for the fourth experiment

done is to determine the ratio of heat volume by getting the before and after temperature and

pressure expansion. Only pressurised chamber and compressive pump were used during this

experiment. The last experiment is to determine the ratio of heat capacity. The pressurised

chamber is the only one that used and by taken the value of pressure and temperature before,

intermediate and final. This experiment have been successfully done and all the data is

recorded.

Introduction

The perfect Gas Expansion is related to First Law of Thermodynamics, Second Law

of Thermodynamics and relationship between P-V-T. Due to expansion and compression of

gasses is one of the most important and very useful in our daily day. This is because due to

related to combustion of engines, refrigerators, heat pumps , hot air balloons , gas storage ,f

fire extinguisher and a host of other practical applications .Besides that, it is also problems

that related to the macroscopic reasoning of thermodynamics to microscopic picture of the

kinetic molecular theory. In this experiment of measurement properties or PVT deals with

ideal gas. An ideal gas is a gas that obeys the relationship PV=nRT. In this definition P and T

are the absolute pressure and absolute temperature respectively and R is the particular gas

constant which is R= 8.3145 J/mol.K and n is the number of moles of the gas filling the

container. The molecular weight of the gas influences the particular gas constant. In this

experiment, where students will able to familiarize with several fundamental thermodynamics

processes can be manipulate by monitored the digital indicator on the control panel.

Therefore, this apparatus should not harm students. However, students should take care about

their safety during the experiment. The most important thing that during students opens the

valve should be slowly when releasing the gas inside the vessel to atmosphere because due to

high pressure gas inside the vessel that being released by the valve that can be harm to

students. The equipment that used is perfect gas expansion apparatus, TH11 as such like

below:

Figure 2.1 Perfect Gas Expansion TH11

From the figure 2.1, there are 2 boxes of cylinders which are pressure chamber and vacuum

chamber. During supply the air into the pressure chamber, gas particles in a box will collide

more aggressive and frequently 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. But, for the ideal gas particles do not collide with each other but only with the

walls. There are different between the ideal gas and actual gas. During a single particle

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.

3.0 Aims:

For each experiment, it comes with a different type of aims and objective which listed as

below;

Experiment 1: Boyle’s Law Experiment

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

-To compare the experiment result with then theoretical result

Experiment 2: Gay-Lussac Law Experiment

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

Experiment 3: Isentropic Expansion Experiment

-To demonstrate the isentropic expansion process

Experiment 4: Stepwise Depressurization

-To study the respond of the pressurize vessel following stepwise depressurization.

Experiment 5: Brief Depressurization

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

Experiment 6: Determination of ratio volume

-To determine the ratio and compares it to the theoretical value.

Experiment 7: Determine of Ration of Heat Capacity

-To determine the ratio of heat capacity.

4.0 Theory

4.1 PERFECT GAS

First, the theory will start with ideal gas or known as perfect gas. An ideal gas is

defined as one in which all collisions between atoms or molecules are perfectly elastic and

there is no intermolecular force. One can visualize it as a collection of perfectly hard spheres

which collide but which otherwise do not interact with each other. In such a gas, all the

internal energy is in the form of kinetic energy and any change in internal energy is

accompanied by a change in temperature. An ideal gas is an imaginary substance that obeys

the ideal gas equation of state. J. Charles and J. Gay-Lussac find out that at low pressure, the

volume of gas is proportional to its temperature. Where the constant of proportionality R is

called the gas constant and is different for each gas which known as ideal gas equation of

state.

In this equation, any gas that obeys this equation’s law called as ideal gas. P is refer to

absolute pressure, T is absolute temperature and υ is specific volume. The ideal gas equation

also can be written as

V = mv

Thus,

PV = mRT

We can relate the both equation for a fixed mass. The properties of ideal gas at two different

state can be relate as

The ideal gas relation experimentally observed are approximately the P-v-T behaviour of real

gases at low density. When low pressure, high temperature, density of gas will decrease and

the gas will behave as ideal gas. The ideal gas also obey the following law which is Boyle’s

Law, Charles’ Law and Gay-Lussac’s Law

4.2 BOYLE’S LAW

First of all, we start with Boyle’s law. Boyle’s law is inversely proportional

relationship between the absolute pressure and volume of gas in closed system with constant

temperature. The equation of Boyle’s law is

PV = k

Where:

P = pressure of the system

V = volume of the gas

k = constant value representative of the pressure and volume of the system

At same amount of energy and at constant temperature, the value of k will constant

theoretically. However, with volume increase, the pressure must decrease proportionally. In

short, the volume decreasing with pressure increasing. The Boyle’s law equation is to relate

the volume and pressure at fixed amount of gas before and after expansion process with

constant temperature.

P1V1=P2V2

4.3 CHARLES’ LAW

Next is Charles’ law. Charles’ law has stated that at constant pressure, the volume of

given mass of ideal gas increases as the absolute temperature increases.

Where:

V = volume of the gas

T = temperature of the gas (measured in Kelvin)

k = constant

The constant k must be maintain during the heating of gas at fixed pressure with volume

increasing. In contrast, the volume of gas will decrease in cooling process. The volume

increases as the temperature increase.

4.4 GAY-LUSSAC’S LAW

The pressure of a fixed quantity of gas at constant volume, is directly proportional to

its temperature in Kelvin. The equation of Gay-Lussac’s law is

Where:

P = pressure of the gas

T = temperature of the gas (measured in Kelvin)

k = constant

4.5 FIRST LAW OF THERMODYNAMICS

First law of thermodynamics state that the energy can be neither created nor

destroyed. But it can change form. This law also known as the conservation of energy

principle. It can be expressed as the net change of total energy in the system is equal to

difference between total energy entering and leaving the system during the process. The

equation for energy balance as below:

Ein – Eout = Esystem

The energy change of a system during process involves the energy change of the

system at beginning and the end of the process which is:

Energy change = energy at final state – energy at initial state.

Energy is exist as internal, potential, electrical, magnetic kinetic and many more. However, in

simple compressible system, the change in total energy of system is the sum of change of

energy in form if internal, kinetic and potential energy.

Where:

∆u= m (u2 – u1)

∆KE=1/2 m(v2−v2)

∆PE= mg (z2-z1)

Therefore energy can be in form of heat, work and mass flow. The boundary system

in energy interaction indicate of energy is gained or lost during the process. The energy only

involved heat and work in closed system. For the open system, the energy involved all form

of energy which is work, heat and mass flow. The internal energy of system increase as the

heat transfer increases when the heat into the system meanwhile the energy transfer of system

decreases when energy is out as heat from the system. For the work, the energy is that

involves rising the piston or rotating shaft. Work transfer into the system increase the energy

while work out from system will decrease the energy of system. For the mass flow, the

energy increases when mass entering the system and decreases when mass out from system.

Ein-Eout = (Qin-Qout) - (Win-Wout) – (Emass,in-Emass,out) = ∆ESystem

4.6 SPECIFIC HEATS

Definition of specific heat is the energy required to raise the temperature of unit mass

of a substance by one degree. In general, the energy depends on how process executed. There

are two kinds of specific heat that we are interested in thermodynamics which is specific heat

at constant volume Cv and specific heat at constant pressure cp. The specific heat at constant

volume can be define as energy required to raise temperature of unit mass of substance by

one degree at maintain pressure meanwhile specific heat at constant volume can be view as

the energy required to raise the temperature of the unit mass of a substance by one degree as

the volume is maintained constant. Then, the Cp is always larger that Cv because at constant

pressure the system allowed to expand and the energy for expansion must supply to system.

From the equation, it shows that the Cv is a measure of the variation of internal

energy of a substance with temperature, and Cp is a measure of the variation of enthalpy of a

substance with temperature.

From the equation, it shows that the Cv is a measure of the variation of internal

energy of a substance with temperature and Cp is a measure of the variation of enthalpy of a

substance with temperature.

4.7 INTERNAL ENERGY, ENTHALPY AND SPECIFIC HEATS OF IDEAL GASES

We define an ideal gas as a gas which temperature, pressure and specific volume

related by

Pv=RT

It has been demonstrated mathematically and experimentally by Joule for and ideal

gas the internal energy is function of temperature only.

u=u(T)

In experiment, Joule has submerged two tanks connected with pipe and a valve I

water bath. One tank contain air at high pressure and other is evacuated. Then he opened the

valve when thermal equilibrium was attained. This is to let air pass from one tank to another

tank until the pressure is same. Joule observed that no change in temperature of water bath.

He assumed that no heat transfer during the process. And also no work done by or on the

system. Because of that, he make a conclusion that internal energy did not change even the

pressure and volume has changed. Then he make another conclusion state that internal energy

is function of temperature and not function of pressure and specific volume. Using the

definition of enthalpy and equation state of ideal gas,

h = u + Pv and Pv = RT

then the equation will become h = u + RT

since R is a constant and u= u(T), the enthalpy of an ideal gas is also a function of

temperature only :

h = h (T)

Therefore, at a given temperature for an ideal gas, u, h, Cv and Cp 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 be expressed as:

du = Cv(T)dT

dh = Cp(T)dT

4.8 DETERMINATION OF THE HEAT CAPACITY RATIO

The heat capacity ratio, k is to determine for air near standard pressure and

temperature by two steps process. First, an adiabatic reversible expansion from initial

pressure, Pi to an intermediate pressure Pm. Second is a return of temperature to original

value, T0 at constant volume with final pressure Pf

For an ideal gas,

Cp = Cv + R

For a non-ideal gas, a reversible adiabatic expansion dq = 0. According to the first law

of thermodynamics,

dU = dq + dW

During the expansion process:

dU = dW

dU = -PdV (24)

The heat capacity related the change in temperature to the change in internal energy

when the volume is held constant.

dU = CvdT

substituting CvdT into equation dU = -PdV. Then ,

CvdT = -PdV

By substitute the equation into the ideal gas law,

Rearrange and substitute the equation,

During the return of the temperature to its initial value, the following relationship is known

Rearranging it to obtain a heat capacity ratio and compare the theoretical value with the

experimental heat capacity ratios. Thus;

4.9 DETERMINATION OF RATIO OF VOLUMES USING AN ISOTHERMAL

PROCESS

The ratio of volume using an isothermal process can be determined when one

pressurized vessel allowed to leak slowly to another vessel of different size. At the end of the

process, two vessels are equilibrate and final pressure become constant. The final equilibrium

absolute pressure, Pabs, be determined by ideal gas equation.

The process is under isothermal process therefore the initial and final temperature are same.

By taking the ideal gas equation;

The process is under isothermal process therefore the initial and final temperature are same.

By taking the ideal gas equation;

By combines the equation;

4.10 STEPWISE DEPRESSURIZATION

Stepwise depressurization can be explained by depressurizing the chamber or tank

step by step slowly by release the gas. The gas will expand at every instant opened and closed

to identify gradual change in pressure and temperature with the contrary decreases with

expansion.

4.11 BRIEF DEPRESSURIZATION

Brief depressurization is reduced in terms of time. The time interval increased to a

few seconds. Therefore, the effect on the pressure and temperature can be observes which can

be compared later. Thus, the graph should be higher in gradient.

5.0 Apparatus

-Pressure transmitter

-Pressure relief valve

-Temperature sensor

-Vacuum chamber

-Pressure chamber

-Vacuum pump

-Electrode

6.0 Procedures:

6.1 GENERAL START-UP

1. The equipment is connected to a single phase power supply and the unit is switched on.

2. Next, all valves and the pressure reading panel is opened. After that, all the valves is

closed.

3. Next, the pipe from compressive port of the pump to pressure chamber is connected or the

pipe from vacuum port of the pump to vacuum chamber is connected. Now, the unit is ready

to use.

6.2 EXPERIMENT 1

1. The general start up procedure is performed. All valve is being make sure that is fully

closed.

2. Compressive pump is switched on and the pressure inside the chamber is allowed to

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

the chamber.

3. The pressure reading inside the chamber is being monitored until the reading stabilizes.

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

5. V02 is fully opened and the pressurized air is allowed to flow into the atmospheric

chamber.

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

7. The experiment is repeated under difference condition:

a) From atmospheric chamber to vacuum chamber.

b) From pressurized chamber to vacuum chamber.

8. Then, the PV value is calculated and the Boyles’ Law is being proven.

6.3 EXPERIMENT 2

1. The general start up is being performed. All valves is being make-sure to fully close.

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

3. The compressive pump is switched on and the temperature for every increment of 10kPa I

the chamber is recorded. The pump stop went the pressure PT1 reaches about 160kPa.

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

reading for every decrement of 10kPa is being recorded.

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

6. The experiment is repeated for 3 times to get the average value.

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

6.4 EXPERIMENT 3

1. The general start up is performed and all valve is being make sure to fully close.

2. The hose form compressive pump is connected to pressurized chamber.

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

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

chamber.

4. The pressure reading inside is monitored until it is stabilizes. The pressure reading PT1 and

temperature reading TT1 are recorded.

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

atmospheric pressure.

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

recorded.

7. The isentropic expansion process is discussed.

6.5 EXPERIMENT 4

1. The general start up procedures is performed. All valve are make sure to fully close.

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

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

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

chamber.

4. The pressure reading is monitored until it is stabilizes. Recorded the pressure reading PT1.

5. The valves V 01 is fully opened and bring it back to the closed position instantly. The

pressure reading PT1 is monitored and recorded until it became stable.

6. Step5 is repeated for at least 4 times.

7. The pressure is plotted on the graph and being discussed.

6.6 EXPERIMENT 5

1. The general start up procedure is performed. Make sure all valve is closed.

2. The compressive pump is connected to the pressurized chamber.

3. The compressive pump is switch on and allows the pressure inside the chamber to increase

until 160kPa. Then, the pump is switched off and the hose is removed from the chamber.

4. The reading inside the chamber is monitored until it is stabilizes. The pressure reading PT1

is recorded.

5. Valve V 01 is fully opened and bring it back to the closed position after few second. The

pressure reading PT1 is recorded and monitored until it becomes stable.

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

6.7 EXPERIMENT 6

1. The general start up procedure is performed. Make sure all valve is close

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

increase up to 150kPa. Then, switched off the pump and the hose is removed from the

chamber.

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

4. The pressure reading for both chambers before the expansion is recorded.

5. The V 02 is opened and the pressure air is allowed flow into the atmospheric chamber

slowly.

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

7. The experiment procedure is repeated for difference condition

a) From atmospheric chamber to vacuum chamber.

b) From pressurized chamber to vacuum chamber.

8. Then, the ratio of the volume is calculated and compare with the theoretical value.

6.8 EXPERIMENT 7

1. The general start up is performed. Make sure all valve is fully close.

2. The compressive pump is connected to pressurized chamber.

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

increase until about 160kPa. Then, switch off the pump and remove the hose from the

chamber.

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

reading PT1 and temperature TT1 is recorded.

5. The valve V 01 is fully opened and bring it to close until after a few seconds. The reading

PT1 and temperature TT1 is monitored and recorded until it become stable.

6. The ratio of the heat capacity is determined and then it being compared with the theoretical

value.

7.0 Results

7.1 Experiment 1: Boyle’s Law Experiment

Before expansion After expansion

PT 1(kPa abs) Pressure(kPa) Temperature

(°C)

Pressure(kPa) Temperature

(°C)

152 27.4 135.2 25.9

PT 2(kPa abs) 102.5 26.9 134.6 26.4

7.2 Experiment 2: Gay-Lussac Law Experiment

Trial 1 Trial 2 Trial 3

Pressure(kPa

abs)

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

Pressurise

Vessel

Depressurise

Vessel

Pressurise

Vessel

Depressurise

Vessel

Pressurise

Vessel

Depressurise

Vessel

110 25.8 25.7 25.2 28.0 26.1 29.3

120 26.4 26.0 25.4 28.6 26.4 30.1

130 27.5 26.9 25.8 29.2 26.9 30.5

140 28.3 28.0 26.7 29.7 27.7 30.7

150 29.0 29.2 27.9 30.4 28.9 30.9

160 29.9 30.1 28.9 30.7 29.8 30.8

7.3 Experiment 3: Isentropic Expansion Process Experiment

Before expansion After expansion

PT 1 (kPa aba) 158.6 109.6

TT 1 (°C) 31.2 26.4

7.4 Experiment 4: Stepwise Depressurization Experiment

PT 1(kPa abs)

Initial After expansion After expansion After third

expansion

After fourth

expansion

159.1 122.9 115.6 108.1 103.5

123.7 115.7 108.2 103.6

124.8 115.8 108.3 103.7

125.0 115.9 108.4 103.8

125.2 116.0 108.5 103.9

125.3 116.1 108.6 104.0

125.5 116.2 108.7 104.1

125.6 116.3 108.8 104.2

125.7 116.4 108.9 104.3

125.8 116.5 109.0 104.4

125.9 116.6 109.1 104.5

126.0 116.7 109.2 104.6

126.5 116.8 109.3 104.7

126.6 116.9 109.4 104.8

126.7 117.0 109.5 104.9

126.8 117.1 109.6 105.0

126.9 117.2 105.1

7.5 Experiment 5: Brief Depressurization

PT 1 (kPa abs)Initial After brief expansion155.3 105.3

106.5107.1107.9108.4108.7109.0109.3109.5109.6109.7109.8109.9110.0110.1110.2110.3

7.6 Experiment 6: Determination of Ratio of Volume

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

Before expansion 149.0 57.3

After expansion 133.3 88.1

7.7 Experiment 7: Determination of Ratio of Heat Capacity

Initial Intermediate Final

PT 1(kPa abs) 155.2 132.1 109.0

TT 1 (°C) 29.8 27.9 26.0

8.0 Calculation:

8.1 Experiment 1

Ideal gas equation, PV=RT. For Boyle’s law, temperature is constant at room temperature

Hence, R= 8.314 L kPa K-1mol-1, T= 298.15 @ 25°C

i) From pressurized chamber to atmospheric chamber

a) For PT 1

P1=152 kPa, P2=135.2 kPa. Then V1 and V2 is calculated

V1=RT/P1

= (8.314 L kPa K−1 mol−1)(298.15K)/(152 kPa)

V1=16.3L

V2=(8.314 L kPa K−1 mol−1)(298.15K)/(135.2 kPa)

V2=18.33L

According to Boyle’s law: P1V1=P2V2

P1V1= (152 kPa) (16.3 L) = 2478.0 kPa.L

P2V2= (135.2 kPa) (18.33 L) = 2478.2 kPa.L

P1V1≈P2V2 (proved)

b) For PT 2

P1=102.5 kPa, P2=134.6 kPa. Then V1 and V2 is calculated

V1=RT/P1

= (8.314 L kPa K−1 mol−1)(298.15K)/(102.5 kPa)

V1=24.18L

V2=(8.314 L kPa K−1 mol−1)(298.15K)/(134.6 kPa)

V2=18.42L


P1V1= (102.5 kPa) (24.18 L) = 2479.0 kPa.L

P2V2= (134.6 kPa) (18.42 L) = 2479.3 kPa.L


ii) From the atmospheric chamber to vacuum chamber

a) For PT 1

P1= 102.9 kPa, P2= 87.5 kPa. Then V1 and V2 is calculated

V1= RT/P1

= (8.314 L kPa K−1 mol−1)(298.15 K) / (102.9 kPa)

V1 =24.09L

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

V2 =28.33L


P1V1= (102.9 kPa) (24.09 L) = 2478.9 kPa.L

P2V2= (87.5 kPa) (28.33 L) = 2478.9 kPa.L


b) For PT 2


V1=RT/P1

= (8.314 L kPa K−1 mol−1)(298.15K)/(55 kPa)

V1=45.07L

V2=(8.314 L kPa K−1 mol−1)(298.15K)/(86.9 kPa)

V2=28.52L


P1V1= (55 kPa) (45.07L) = 2478.85 kPa.L

P2V2= (86.9 kPa) (28.52L) = 2478.38 kPa.L


iii) From the pressure chamber to vacuum chamber

a) For PT 1

P1= 155.1 kPa, P2= 121 kPa. Then V1 and V2 is calculated

V1= RT/P1

= (8.314 L kPa K−1 mol−1)(298.15 K) / (155.1 kPa)

V1 =15.98L

V2 = (8.314 L kPa K−1 mol−1)(298.15 K) / (121 kPa)

V2 =20.49L


P1V1= (155.1 kPa) (15.98L) = 2478.5 kPa.L

P2V2= (121 kPa) (20.49L) = 2479.3 kPa.L


b) For PT 2


V1=RT/P1

= (8.314 L kPa K−1 mol−1)(298.15K)/(52 kPa)

V1=47.67L

V2=(8.314 L kPa K−1 mol−1)(298.15K)/(120.7 kPa)

V2=20.53L


P1V1= (52 kPa) (47.67L) = 2478.84 kPa.L

P2V2= (120.7 kPa) (20.53L) = 2479.0 kPa.L


8.2 Experiment 2

111.6

111.8

112

112.2

112.4

112.6

112.8

113

113.2

113.4

113.6

Pressurise Vessel

Pressure (kPa)

Tem

pera

ture

(°C)

113.5 113.6 113.7 113.8 114.3 114.5110

115

120

125

130

135

140

145

150

Deressurise Vpessel

Pressure (kPa)

Tem

pera

ture

(°C)

8.3 Experiment 3

T2/T1 = (P2 / P1)(k-1 / k)

(26.4) / (31.2) = [(109.2) / (158.6](k-1 / k)

0.8462 = (0.6885) (k-1 / k)

ln 0.8462 = [ (k-1)/ k] ln 0.6885

k = 0.6901

8.4 Experiment 4

8.5 Experiment 5

8.6 Experiment 6

Theoretical value of ratio of volume,

V2/V1 = 12.37/25

= 0.495

Percentage error = [(Theoretical value - Actual value) / Actual value] × 100

a) PT 1

P1V1 = P2V2

V2/V1 = P1/P2

V2/V1 = 149.0/57.3

V2/V1 = 2.600

Percentage error = [(0.495-2.600)/2.600] × 100

= -80.97% = 80.97%

b) PT 2

P1V1 = P2V2

V2/V1 = P1/P2

V2/V1 = 133.3/88.1

V2/V1 = 1.513

Percentage error = (0.495-1.513)/1.513

= -67.29% = 67.29%

8.7 Experiment 7

Calculate the value of heat capacity ratio, by the given formula of Cv,

The expression of heat capacity ratio is:

Cpcv

= lnPi−lnPmlnPi−lnPf

¿ ln 155.2−ln132.1ln 155.2−ln109.0

=0.4561

Theoretical value CpCv

of is 1.4

The percentage error = [(Theoretical value – Actual value) / Actual value] × 100

= [(1.4 – 0.4561) / 0.4561] × 100

= 206.97 %

9.0 DISCUSSION

This experiment involved First Law of Thermodynamics, Second Law of

Thermodynamics and relationship between P-v-T. The experiment also involve several law

such Boyle’s law, Gay-Lussac’s law and Charles’ law.

For the experiment 1, Boyle’s Law experiment. Boyle’s law state that absolute pressure and

volume of given mass are inversely proportional with constant temperature. The relationship

of Boyle’s law can be expressed as P1V1=P2V2. For from pressurized chamber to

atmospheric chamber, the initial pressure is 13.8kPa and after expansion 152kPa for PT 1 and

for PT 2 is 102.5kPa for initial and 134.6kPa for after expansion. The volume is calculated by

using equation PV=RT. Volume for V1 is 16.3 L, V2 is 18.33 L and V1 is 24.18L, V2 is

18.42L for PT 1 and PT 2 respectively. From atmospheric chamber to vacuum chamber, the

initial pressure is 102.9kPa and after expansion is 87.5kPa for PT 1 and for PT 2 is 55kPa for

initial and 86.9kPa for after expansion. The V1 is 24.09 L, V2 is 28.33L and V1 is 45.07L,

V2 is 28.52L for PT 1 and PT 2 respectively. And lastly for from pressure chamber to

vacuum chamber, the pressure before expansion for PT 1 is 155.1kPa and 121 kPa after

expansion for PT 1 and for PT 2 is 52kPa for initial and 120.7kPa for after expansion. V1 is

15.98 L, V2 is 20.49 L and V1 is 47.67L, V2 is 20.53L for PT 1 and PT 2 respectively. The

Boyle’s law was proven with equation of P1V1=P2V2. The value obtain from both side is

approximately equal. Gay-Lussac’s Law stated that the pressure is directly proportional to the

temperature which is means if the pressure increase the temperature also increase with

constant volume. Depressurize means reduction of air pressure in vessel or procedure that

allow air to flow out. The experiment was repeated thrice so that we can get the average

reading of pressure. From the data recorded and graph plotted, it can be said that the Gay-

Lussac’s Law is verified.

Experiment 3 is about Isentropic Expansion Process. This experiment determine the

ratio of heat capacity which is k. If compression or expansion of gas take place with no flow

of heat energy either into or out, the process called as isentropic or adiabatic process. The k is

the ratio of both type specific heat capacity which is cp/cv. The equation of isentropic also as

pvk=constant. No heat is added to the flow and no energy form due to friction or dissipative

effects. From the result, the pressure decrease proportionally to the temperature. This is due

to air flow out from the chamber. The value for k in this experiment is 1.5207 calculating by

using T2/T1 = (P2 / P1)(k-1 / k) equation. Which is P is absolute pressure and T is absolute

temperature.

Stepwise depressurization is a strategy to adopt an equal time-stepwise depressurization

approach. In this study yield more reliable result for an example in the production sector in

industries. The molecule in the chamber affected when the number of the decreasing slowly

as they do not have to collide between them more often. The depressurization shown that

pressure decrease with time and also affecting the temperature.

For experiment 5, brief depressurization shown in graph plotted in result which is decrease

linearly compared to stepwise. The expansion occur when the pressure of gas increase.

Expansion of gas decrease as the gas is free to flow out time by time.

Next is experiment 6 which is determination the ratio of volume. By using Boyle’s law

equation, P1V1=P2V2the ratio of volume is solved. After arranging the equation, the ratio of

volume is V2/V1=P1/P2. This experiment carried out in three condition which is from

pressurized chamber to atmospheric chamber, from vacuum chamber to atmospheric chamber

and lastly from pressurized chamber to vacuum chamber. The theoretically value ratio of

volume also can be determine which is 0.495. For first condition (pressurize to atmosphere),

the ratio of volume is 2.600 and the percentage error is 80.97% for PT 1, while for PT 2 the

ratio of volume is 1.513 and percentage error is 67.29%. The percentage error is high due to

some error during conducting the experiment. Some of air probably left from chamber due to

not properly close the valve or before the experiment, the gas did not left out completely from

the chamber.

From the result the determination of ratio of heat capacity is 0.4561. The theoretical

value is 1.4. The deviation is 206.97%. The deviation is due to the measurement error. The

actual intermediate pressure supposed to be lowered and from the data obtained the

intermediate pressure is lowered that the initial and final reading. Since the percentage

difference is more than 10% the experiment can be declare as failed.

10.0 CONCLUSION

In the conclusion, the experiment was to determine the properties of measurement

/PVT according to the Boyle’s law, Gay-Lussac’s Law, isentropic expansion, and heat

capacity equation. We have proven the Boyle’s law and Gay-Lussac’s law based on their law.

Although there is fail experiment but we have the reason behind the failure. For experiment

7, the failure is due to the intermediate pressure not be taken after the valve is closed. Finally,

the experiment is successfully done and the objective of the experiment is achieved.

11.0 RECOMMENDATIONS

There are several recommendation has to be taken during conduct this experiment.

First during experiment, we must always concentrate observed pressure reading whether the

pressure is exceed 200 kPa and the change of pressure and temperature. If the pressure is too

high inside the chamber, the glass probably will break even though there are pressure relief

valve. Pressure relief valve function as release pressure when the pressure inside the chamber

very high.

Next is the procedure of general start-up and shut-down must properly followed so that no

gas is left inside the chamber. For experiment 2, the average value must be taken by repeating

the experiment three times. So that the result become more accurate. Lastly, for safety student

has to wear google because of possibility for glass vessel to break.

12 .0 REFERENCE

1. Coulson & Richardson’s Chemical Engineering, Volume 1, Sixth Edition, J.M.

Coulson, J.F. Richardson, J.R. Backhurst, J.H Harker, Elsevier Butterworth-

Heinemann (1954)

2. “Gas Law” from http://en.wikipedia.org/wiki/gaslaw.

3. Gas Law 7th Edition, Robert L. Street, Gary Z. Watters, John K. Vennard, John Wiley

& Sons Inc.

13.0 Appendices

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

Documents

Lab 6(Final)