# Isentropic expansion

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ABSTRACT

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

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

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

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

was used in this experiment. The objectives for each experiment were achieved. Boyles law

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

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

experiment was successful.

INTRODUCTION

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

unit designed to enable students to familiarize with some fundamental thermodynamic

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

conservation of energy (Sears & Salinger, 1975).

OBJECTIVES

Experiment 1: Boyles Law Experiment

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

To compare the experimental results with theoretical results.

Experiment 2: Gay-Lussac Law Experiment

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

Experiment 3: Isentropic Expansion process

2. To demonstrate the insentropic expansion process.

Experiment 4: Stepwise Depressurization

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

Experiment 5: Brief Depressurization

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

Experiment 6: Determination of ratio of volume

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

Experiment 7: Determination of ratio of heat capacity

6. To determine the ratio of heat capacity.

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THEORY

Boyles Law Experiment

The relationship between volume and pressure of a gas can be explained with Boyles

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

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

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

V

PV = constant or V =

According to the mathematical expressions derived from Boyles law above, provided

that T and n are fixed, pressure and volume are indirectly related to one another in a sense

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

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

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

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

hence the elevated pressure (Adamson, 1979).

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

pressure is hyperbolic (Boyles law). The gas temperature remains constant.

(Thomas, Stamatakis, 2009)

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Gay-Lussac Law Experiment

Ga-Lussac law is also commonly known as Charless law. The law explains about the

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

19th

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

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

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

However, in this lab practical, we are dealing with an alternative version of Charless

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

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

The expression is as shown:

p = constant x T (at constant volume)

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

temperature is reduced to zero (Atkins, 2002).

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

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

P T

P = constant T

P/T = constant

P1/T1 = P2/T2

P1T2 = P2T1

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

pressure and temperature of a gas.

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

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

Isentropic Expansion Process

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

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

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

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

of function:

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

Stot > 0

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

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

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

entropy (Atkins, 2002: 92).

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

the same from the initial to the state of completion.

S = 0

S1 = S2

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Stepwise Depressurization Experiment

The stepwise depressurization is conducted by depressurizing the pressurized

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

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

decreases with the expansion.

Brief Depressurization Experiment

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

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

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

Determination of Ratio of Volume Experiment

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

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

can be used to evaluate and calculate the values:

P1 V1 = P2 V2

V2/ V1 = P1/ P2

V2/ V1 = Ratio value

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

Determination of Ratio of Heat Capacity

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

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

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

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

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

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

Cp Cv = R

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