Embed Size (px)
Transcript of Isentropic expansion
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.
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
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).
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.
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:
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)
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
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 = 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.
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
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
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