PASCO TD-8565 User Manual
IDEAL GAS LAWS
Experiments for Physics, Chemistry and Engineering Science
Using the Adiabatic Gas Law Apparatus
© 2009 Physics Enterprises
By Mickey Kutzner
and Peter Wong
Copyright © 2009 Physics Enterprises, Andrews University. All rights reserved.
This publication is designed for teaching purposes only. Not for resale.
Thank you for your cooperation on this project:
Dr. Mickey Kutzner—Professor of Physics, Andrews University
Dr. Peter Wong—Professor of Chemistry, Andrews University
Sarah Lee—Ambient Light, Photography
Lubica Mueller—Graphic Design
IMC — Editing
For more information, visit us at www.physicsenterprises.com
Ron Johnson, Director
Lubica Mueller, Business Developer
Physics Enterprises
Andrews University
Berrien Springs MI 49104-0384
Ph: 269-471-3503
Fax: 269-471-3509
E-mail: aupe@andrews.edu
or contact us:
2
Table of Contents
Experiment 1: Ideal Gas Law 4
Experiment 2: Isothermal Processes 7
Experiment 2A: Boyle’s Law
Experiment 2B: Work Done by an Isothermal Process
Experiment 3: Adiabatic Processes 11
Experiment 3A: Adiabatic Gas Law
Experiment 3B: Work Done by an Adiabatic Process
Experiment 4: Complete Cycle 16
Experiment 5: Heat Capacity of Gas from PVT Data 20
Appendix A: Calibration of V 22
Appendix B: Additional Analysis to Improve Adiabatic Gas Law Results 23
References 24
© 2009 Physics Enterprises 3
T
M
ρ
Experiment 1: Ideal Gas Law
Target Students
High school and introductory college physics and chemistry.
Objectives
To show that PV/T = nR for an ideal gas and determine the value of R.
Physical Principles
The well-known relationship between absolute pressure (P), volume (V), and absolute
temperature (T), of an ideal gas is:
nRTPV =
where n is the number of mol in the sample and R is the ideal gas constant. For a closed
system with n fixed, placing all variables on the left-hand side of the equation yields the
constant value,
PV
=
The number of mol, n, is related to the density of the gas (ρ), the molecular mass of the gas
molecules (M), and the volume (V), via the relation,
(1.1)
nR
(1.2)
V
=
n
(1.3)
Procedure
A. Connections
Power the Adiabatic Gas Law unit via the AC adapter. Insert the Pressure, Volume and
Temperature din connectors into channels A, B and C of the Science Workshop interface,
respectively. Open Data Studio and indicate that a voltage sensor is connected to each
channel. Adjust the Sample Rate to 1,000 Hz.
© 2009 Physics Enterprises 4
Experiment 1: Ideal Gas Law
B. Graphical Display
Drag-and-drop the Graph icon from the Displays menu onto Voltage, Ch A(V) in the Data
menu. Drag-and-drop the Graph1 icon onto Voltage, Ch B(V) and then Voltage, Ch C(V). In
this way, graphs of Pressure, Volume and Temperature will all be displayed with a
common time axis.
C. Collecting the Data
With a stopcock valve open, set the piston to the approximate middle of its range at the
10 cm mark and close both stopcocks.
Record the height of the piston at atmospheric pressure:
h
= __________ cm
0
Raise the piston to its highest position, click on Start and, over a span of approximately
five seconds, slowly and steadily move the piston to its lowest position, then click Stop.
Notice that the plots of voltages show the Pressure increasing as the Volume decreases.
Analysis
A. Conversions from voltages to P, V and T
Open the Calculate tool in Data Studio menu and change the Definition to
P = 100000∙x (Pa)
as noted on the calibration label on the back of the Adiabatic Gas Law Apparatus and
define variable “x” to be Data Measurement with Voltage, ChA(V). Then Accept this
calculation.
In the Calculate tool, click New and define V as the volume according to the linear
calibration expression on the label. This time the variable “x” is defined as Voltage, ChB(V).
Then Accept this calculation. (If you have an older unit or wish to perform the volume
calibration by hand, please refer to Appendix A.
In the Calculate tool, click New and Calculate the Temperature using the linear expression
on the label and defining x as the measurement from ChC.
© 2009 Physics Enterprises 5
Experiment 1: Ideal Gas Law
ρ
Use the calculator to define nR = P∙V/T and choose Properties to ensure that the Numeric
display shows at least three significant figures. Plot a graph of nR by selecting the
appropriate title on the vertical axis.
Use the Σ icon on the Graph menu to display the mean value of nR as well as the
standard deviation.
nR
= ______________ J/K Std. Dev. = _____________ J/K
mean
What percentage of the mean is the standard deviation?
%random error = 100%∙Std. Dev./mean = _________ %
This is an estimate of the random errors associated with the experiment.
B. Number of mol, n
Calculate the volume of air (in cm3) at the initial 10 cm height when the stopcock was
open to the atmosphere using
V0 = π r2 ho = _________ (cm3)
where r is half the diameter displayed on the label of the Adiabatic Gas Law Apparatus.
Calculate the number of mol of gas from Eq. (1.3), with the density of air at STP of ρ =
0.00129 g/cm3, the volume V0, and the molecular weight of air M
= (0.8*28+0.2*32) g/
air
mol (assuming 80% nitrogen and 20% oxygen).
V
air
M
0
= __________ mol
air
n
=
Compute your measured value of R.
R
mean
= (nR
)/n = ___________ J/mol·K
mean
Compare your measurement with the generally accepted value of R = 8.314 J/mol∙K.
R
−
%
Err
mean
= %100
314.8
314.8
=×
____________%
Is this percentage greater or less than the standard deviation percentage?
Should the errors in this experiment be considered primarily random or systematic?
© 2009 Physics Enterprises 6
Experiment 2: Isothermal Processes
Experiment 2A: Boyle’s Law
Target Students
High school and introductory college physics and chemistry.
Objectives
To observe that PV = const for constant temperature.
Physical Principles
When a process occurs with the system in contact with a heat reservoir to keep the
temperature fixed the process is considered “isothermal.” For such a process, the pressure is
inversely related to the volume, i.e.,
constPV =
(2.1a)
Since Eq. (2.1a), Boyle’s Law, can be rewritten as
() () ( )
constVP lnlnln +−=
(2.2a)
one sees that a plot of ln(P) vs. ln(V) should be a straight line with a slope of –1.
Procedure
Convert voltages to Pressure and Volume as in Experiment I using the Calculator in Data
Studio. Set up a graph of P vs. V.
Follow the procedure for the ideal gas law measurements (Experiment I) but slow the
Sample rate to one second and perform the compression slowly and steadily (quasi-
statically) over the course of a minute-or-so. This allows the temperature of the gas to always
remain at room temperature (isothermal). McNairy [1] recommends suspending a bucket
from the end of the handle and easing weights into the bucket. As you collect data, you can
watch the Pressure adjust to the slow change in Volume.
© 2009 Physics Enterprises 7
Experiment 2A: Boyle’s Law
ρ
Analysis
A. Use the Calculator to compute the ln(P) and ln(V) and make a graph of ln(P) on the y-axis
vs. ln(V) on the x-axis. Perform a linear fit and record the slope:
Slope = __________
Compare this with -1.0 as expected for an inverse proportion.
B. Since P = nRT/V, use the Calculator to obtain 1/V and plot P vs. 1/V. Perform a linear fit and
record the slope:
nRT = Slope = _____________
Calculate the volume of air (in cm3) at the initial 10 cm height when the stopcock was
open to the atmosphere using
V0 = π r2 h = _________ (cm3)
where r is half the diameter displayed on the label of the Adiabatic Gas Law Apparatus.
Calculate the number of mol of gas from Eq. (1.3), with the density of air at STP of ρ =
0.00129 g/cm3, the volume V0, and the molecular weight of air M
mol (assuming 80% nitrogen and 20% oxygen).
V
air
M
0
= __________ mol
air
n
=
= (0.8*28+0.2*32) g/
air
From a plot of T vs. time, use the Σ statistics tool to find the mean (room temperature),
T = __________ K
Now calculate R, R = (nRT)/n·T = (slope)/n·T = __________
Compare your measurement with the generally accepted value of R = 8.314 J/mol∙K.
−
%
R
mean
= %100
Err
314.8
314.8
© 2009 Physics Enterprises 8
=×
____________%
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