Isentropic expansion

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Lab practical on Isentropic expansion

Transcript of 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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