IDEAL GAS LAB REPORT

1. 1
MECH252 THERMODYNAMICS EXPERIMENTAL RESULTS & REPORT
IDEAL GAS EXPANSION PROCESS

BEAUMONT PROUDFOOT 4610179
JASON FENG 4756897
ISAAC CHANAKIRA
NATHAN CURRY 4616540









Ideal Gas Expansion Process




Laboratory 6



May 4, 2015

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Table of Contents
Experiment A
Abstract.............................................................................................................3

Introduction...................................................................................................... 3

Method..............................................................................................................3

Procedure.........................................................................................................3

Results..............................................................................................................5

Discussion and conclusion…………………………………………………………6

Experiment B


Abstract.............................................................................................................9

Introduction.......................................................................................................9

Results............................................................................................................10

Discussion & Conclusion………………………………………………………….10

Calculations…………………………………………………………..…………….11

References…………………………………………………….……………………12















Abstract

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The aim of the experiment was to determine the adiabatic index of air at room
temperature by simulating an adiabatic expansion of air contained in a vessel.
Recording and using relevant pressure measurements could calculate values of the
adiabatic index.

Introduction
The experiment was conducted in order to determine the adiabatic index of air at
room temperature by allowing the air in a pressurized vessel to expand very briefly,
during a quick opening and closing action of a large valve - this ensured that the
expansion could be considered as adiabatic. Pressure readings were recorded before
and immediately after the expansion. The vessel contents were then allowed to come
back to room temperature and the final pressure was recorded. Pressure was the best
quantity to monitor, as compared to temperature or specific volume, and therefore, an
equation relating the adiabatic index to those three pressures had to be derived. The
derivation required the application of the First Law of Thermodynamics to the
adiabatic expansion process and the use of the Ideal Gas Law, assuming that air
behaves as an ideal gas. The relationship between the heat capacity at constant
volume and internal energy was also used in the derivation.

An average value for the adiabatic index was determined using the results from
several trials and the standard deviation was analyzed to verify the reliability of the
experiment.



Method
Apparatus
The apparatus consists of an airtight cylinder, which can be opened to the atmosphere
through ball valves at its top. It also has connections to an air pump, which allows
internal pressure to be increased, as well as to pressure and temperature sensors. The
latter are connected to a console comprising of a four-position switch. The switch
positions have been configured to monitor the gauge pressure and temperature of the
air in the cylinder.

Procedure

Before starting the experiment, the atmospheric pressure was measured using the
barometer - this was needed to determine the absolute pressures in the cylinder.
Valves ‘V1’ was closed and ‘V4’ opened and the air pump was then switched on.
‘V1’ controls opening of the vessel to the atmosphere while ‘V4’ controls the
connection to the air pump. When the gauge pressure indicated on the console
reached approximately 30kPa, the air pump was turned off and isolating valve ‘V4’
was closed. A slight fall in pressure was observed afterwards, accounted by the fact
that the vessel contents were cooling to room temperature. The pressure was therefore
allowed to stabilize and was recorded as the starting pressure, ps. Valve ‘V1’ was
then opened and closed very rapidly, with a snap action, to allow a small amount of
air to escape from the vessel, simulating a very quick adiabatic expansion. While the
opening-closing action was done, the minimum value of pressure indicated on the
console was recorded as pi. Again, the vessel contents were allowed to return to
ambient temperature so that the final pressure, pf, could be recorded.

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The absolute pressures p1, p2and p3 were then calculated by adding the value for
atmospheric pressure to ps, pi and pf respectively. The same procedure was then
repeated at different initial pressures in the vessel. The adiabatic index of air (at
prevailing ambient temperature),γ, was determined using p1, p2 and p3 from each
trial so that an average value could be calculated.





































RESULTS
-10.00
0.00
10.00
20.00
30.00
40.00
00:00 00:17 00:35 00:52 01:09 01:26 01:44 02:01 02:18 02:36 02:53
Pressure (kPa)
Time (s)
Pressure v time
P-T 1
P-T 2
P-T 3
P-T 4
P-T 5

5. 5

Pressure v time plot for each run.



The difference between temperature in the large vessel and ambient temperature for
run 5. Plotted with and exponential trendline.



Heat transfer rate for approximately a minute after time drop.

Calculation of specific heat ratio



The mean and standard deviation results were calculated using the average function
and the standard deviation function in Excel.







-0.00005
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
00:00 00:17 00:35 00:52 01:09 01:26
Heat transfer into cylinder
(W)
TIme(s)
Q as a function of time
Series1
Specific heat
ratio
Run 1 Run 2 Run 3 Run 4 Run 5
mean 1.72 1.43 2.43 1.44 1.6 2.07
standard
deviation
0.439758103

y = 11.234e
-8991x
0.00000000000000
2.00000000000000
4.00000000000000
6.00000000000000
8.00000000000000
10.00000000000000
00:00 00:09 00:17 00:26 00:35 00:43 00:52
Temp difference
Time(s)
Temp difference cylinder v ambient air
Series1
Expon. (Series1)

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Discussions and Conclusions
Reasons why the initial expansion process can be considered as adiabatic
For a process to be adiabatic, heat transfer should be minimised or eliminated, and the
experiment uses the fact that heat transfer is very slow to make the expansion as
adiabatic as possible. This is explained through the reasons below.
1.
A large bore valve was opened for a very short lapse of time (quick snap action). This
meant that a relatively large amount of air was allowed out in a very short time and
therefore, the rate of expansion was quite high. Hence, heat transfer would not have
had the time to occur during such an expansion.
2.
The reading of the pressure pi was taken immediately after the valve was closed and
the expansion had stopped by considering the minimum value to which the pressure
had dropped. This ensured that the value of pressure obtained was not affected by any
heat transfer and meant that the expansion could therefore be regarded as adiabatic.

Reliability of the experiment and the results
The expected adiabatic index of air at room temperature is around 1.4 and considering
the average value of 1.7 obtained from the experimental analysis, it can be said that
the results are relatively accurate. However, it should be underlined that only

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averaging leads to such accuracy while the individual trials did reveal some
variations. Although a standard deviation of only 0.44 implies that the results were
done to an average precision, there were many error sources in the experiment which
can account for the variations.



Differences in transient responses of the pressure and temperature sensors

When a considerable change in the property of a system occurs within a short time,
response time of sensors inevitably becomes an important factor in the accuracy of
measurements or readings for the said property. In the experiment, to monitor the
pressure, an electronic pressure sensor has been used while to monitor the
temperature, a platinum resistance thermometer has been used. The way in which the
two types of sensors detect the changes directly affects their respective transient
responses. The electronic pressure sensor, for instance, uses the movement of its
components brought about directly by a change in pressure to detect the latter. This
movement occurs instantaneously and can hence be readily interpreted as a new
pressure reading. However, in the case of the temperature sensor, the platinum
resistance should be in thermal equilibrium with the system for it to give the latter’s
actual temperature. Since thermal equilibrium requires heat transfer, a slow process,
transient responses of temperature sensors are not very accurate, unless the changes
are very small. Throughout the experiment, temperature had to remain almost
constant, implying very small changes, and therefore, accuracy of transient responses
of the temperature sensors was not an issue. On the other hand, pressure changes were
significant and occurred within a very short lapse of time. While the pressure sensors
can readily detect the changes, the speed at which the change is interpreted by the
circuits and displayed on the screen then becomes another factor affecting the overall
transient responses. Hence, in this experiment, the transient responses of temperature
sensors were more reliable than those of pressure sensors.

Overall conclusions and possible improvements

Considering the average value for the adiabatic index obtained from the experiment is
very close to the expected value and it can be concluded that the experiment is
reliable and so are the results. Yet, there were several sources of errors which could
have affected the accuracy of the results and they could have been revealed if more
trials had been done. Possible improvements could be the use of data logging which
would more effectively interpret the signals from the sensors and could be set to
record the relevant readings automatically. Besides, an electronically controlled valve
could be used for the expansion process, making the trials more consistent and the
results even more reliable.

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Experiment B:
Determination of Volumes Ratio Using an Isothermal Process




Abstract


The objective of this experiment is to determine the ratio of volumes for air in the two
vessels by using an isothermal expansion process. This demonstration gives
experience with properties of an ideal gas, adiabatic processes, and the first law of
thermodynamics. It also illustrates how P-V-T data can be used to measure other
thermodynamic properties.

Introduction

To determine the ratio of volumes using an isothermal process, one pressurized vessel
is permitted to leak slowly into another vessel of different size. At the end of the

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process, the two vessels are equilibrated and the final pressure is constant in both
vessels.





























Results



Experiment B
Run 1 Run 2







Excel functions were used to calculate the ratio of volumes.


Conclusion
Volume Ratio
V1/V2
2.448559671
Ratio of
volumes
V1/V2
Actual volume
ratio
2.4345898 2.467532468

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The volume ratios were very near the actual volume ratio, suggesting the results are
relatively accurate. The ratio of the volume of the gas indicates and expresses the
dynamics of compression and expansion of the gases. The substance onset pressure is
found to be affected by the way of system depressurization (frequency and time step
magnitude) since it has a direct bearing on the stabilization time. The difference
between the volume ratios and actual volume ratio were minimal, but still they were
different. This could’ve been due to environmental factors affecting the stability of
the pressure and temperature or random mistakes done during the experiment.

Discussion

As the pressures reach equilibrium, we seethe conservation of energy principle in
action. The pressure transfer goes from highest quantity to lowest quantity.
















Calculations

Derive ratio of volumes formula from first principals;
According to ideal gas equation of state. M1 for volume of first vessel m2 for volume
of second vessel. Substitute into equation. Cancel R and T and rearrange. Divide top
and bottom by Vol2 then rearrange for Vol1/Vol2.


(12)
(13)

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References

Carrington, G., "Basic Thermodynamics", Oxford University Press, (1994)

Atkins, P.W., "Physical Chemistry", Freeman (1998). Multi-media resource

Yusus A. Cengel, M. A. (2011). second low of thermodynamics. In Thermodynamics
an engineering approach (pp. 274-309). New York: Mc Graw Hill.

Reid, R., Prausnitz, J.M., and Sherwood, T.K. (1977)
The Properties of Gases and Liquids, 3
rd
Edition, McGraw-Hill.

F.W. Sears, G.L. Salinger , Thermodynamics, Kinetic Theory, and
Statistical Thermodynamics (Addison-Wesley, 3rd ed 1975)