D
DR
RA
AFFT
T
Thermodynamics
Pressure-Volume Work Determination
On a P-V diagram, the net work done is equal to the area inside of a closed loop. In this
lab you will find that work value and relate it to actual work done.
Purpose:
To find the work done by a gas while lifting a weight.
Equipment:
Pasco Heat Engine
Vernier Gas Pressure Sensor
Vernier LabPro Interface
Pasco Rotary Motion Sensor
Ring Stand
String with attached Mass Hanger
Slotted masses
i-Book computer
Ruler
Aluminum Air Chamber
Cautions:
This equipment is delicate. Everything should go together with the lightest of touches.
Do not force anything!
You may find that some of the setup procedure has already been done for you. Check
each step to make sure that it is done properly. The success of your work depends upon
correct setup!
Procedure to set up the heat engine
1. Prepare two containers of water,
one at room temperature and one
with ice.
2. Place the heat engine on the ring
stand base.
3. Attach the rotary motion sensor to
the ring stand at the top of the rod,
extending over the heat engine.
4. Loosen the thumbscrew holding the
heat engine piston, lift the piston to
a point midway in its travel, and
retighten the thumbscrew. Tighten
this screw lightly, just enough to
hold the piston in position.
5. Wrap the string clockwise around
the middle pulley of the rotary
motion sensor, then bring the hook
down and hook it under the tray of
the heat engine. There is a small
Rotary
Motion
Sensor
Hanging
Mass
(35g)
Mass
Platform
Heat
Engin
e
Pressure
Sensor
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Hook
Aluminum Air
Chamber
Ring
Stand
Page 1
D
DR
RA
AFFT
T
hole in this tray to accept the end of the wire hook. Allow the mass holder to hang
freely.
6. Wind the string around the middle pulley until the mass holder is approximately
15cm below the pulley. You may lower the position of the rotary motion sensor on
the ring stand a little to get close to the 15cm dimension.
7. Adjust the heat engine so that the string from it to the pulley is vertical.
8. Connect the tube from the aluminum air chamber to one port of the heat engine. Push
and twist slightly to lock the tube in place.
9. Connect the tube from the pressure sensor to the other port of the heat engine. Push
and twist slightly to lock the tube in place.
10. Connect the gas pressure sensor to the “CH 1” port of the LabPro interface.
11. Connect the rotary motion sensor to the “DIG/SONIC “1 port of the LabPro interface.
12. Connect the LabPro interface to the iBook computer with the USB cable.
13. Plug the LabPro sensor into a power outlet. After a short pause, it will beep merrily.
14. Plug the i-Book computer in with its power adapter.
15. Turn on the i-Book and wait for it to boot up.
16. Log on to the computer with the username “student” and password “student”.
17. Launch the “Heat Engine” Activity by double-clicking it.
18. A Sensor confirmation window will appear. Make sure that both the sensors are
checked and click on OK to confirm.
Data Collection:
1. Loosen the thumbscrew on the Heat engine, allowing the piston to move freely. It
should stay pretty much in place as it is counterbalanced by the hanging weight.
2. Immerse the aluminum air chamber in the ice water bath. The piston should move
down a bit as the water cools the aluminum air chamber.
3. Wait one minute for the aluminum air chamber to cool down properly.
4. Click on the zero button.
5. Make sure the rotary motion sensor is selected and the gas pressure sensor is not.
6. Click on OK to zero the rotary motion sensor.
The next few steps must be done with minimum delay for best data.
7. Start the data collection process by clicking on the Collect button.
8. Once data begins to show on the computer screen in the data table, gently place the
100g mass on the platform of the heat engine and immediately move the aluminum
air chamber from the ice water bath to the room temperature water bath.
9. Watch the “Change in Volume value at the bottom left of the screen. It will increase
as the air in the aluminum air chamber is warmed.
10. When the “Change in Volume” value stays steady for more than one second, remove
the mass from the platform of the heat engine and immediately move the aluminum
air chamber from the room temperature bath to the ice water bath.
11. Watch the “Change in Volume” value at the bottom of the screen. It will decrease as
the air in the aluminum air chamber is cooled.
12. When the “Change in Volume” value reaches zero, click on the Stop button to end
data collection. Do not allow this value to go negative as this will cause errors in
your data analysis.
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 2
D
DR
RA
AFFT
T
Recording your data
1. Click on the Integrate button (just to the right of the STAT button). The area inside
the loop will fill and the area data will be displayed (it is labeled as “integral” in the
integration box.
2. Record the integral value in the data table.
3. Click once in the graph window to select it.
4. To determine the maximum height of the piston (Hmax), click and drag across the
lower right corner of the graph. The corresponding data points will be highlighted in
the data table. You may have to scroll within the data table to find the highlighted
points. Find the maximum piston height in the distance column and record that value
in the data table.
Data Table:
Mass (kg)
Area inside closed loop
(kPa* m3)
Hmax (m)
0.05
0.10
0.20
Analyzing your data
1. The area of the loop is given in kPa*m3, but we need it in Pa*m3 (which is the same
as Joules). To do this, multiply the work value from above by 1000 Pa/kPa and record
the Warea of loop in the calculation table below.
2. Determine the work done in lifting the mass using the following formula:
W = m g Hmax
(m in kg, H in m)
3. Record the work Wlifting mass in the calculation table below.
4. Calculate the percent difference between the two work values below using the
following formula:
| (Workarea of loop - Worklifting mass) / Workarea of loop | * 100
5. Repeat the data collection and data analysis for masses of 50g and 200g. Complete
the data table.
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 3
D
DR
RA
AFFT
T
Calculation Table:
Mass (kg)
Workarea of loop
(J)
Worklifting mass
(J)
% Difference
0.05
0.10
0.20
Questions:
1. Draw the typical P-V diagram in this space. You do not have to label values; just
draw the shape of the diagram you see on the display.
P
V
2. Compare the two work values for each mass in your calculation table. Were they the
same? If not, how close were they? Should they have been the same? Why or why
not?
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 4
D
DR
RA
AFFT
T
3. Did the values for the area inside the loop and the value for work go up together as
the weight was increased?
4. Name at least two sources of error that were present in the lab and describe how each
would have affected the results of the lab? (no human error)
Extension question:
1. Describe what would happen to the graph if the room temperature water were replaced
with water at 90C.
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 5
D
DR
RA
AFFT
T
Teacher Reference Pages
Introduction:
On a P-V diagram, the area inside of a closed loop describes the net work done by a
system. In this experiment, a heat engine will be used to lift masses while recording data
for pressure and piston position. The piston position data is used to determine the change
in volume within the cylinder as well as the distance that the mass was lifted. Students
will determine the area inside the P-V loop as well as the work done on the mass and then
compare the two values. If the experiment is done properly the two values should be
within 5 percent of each other.
Experimental goals:
After completing this experiment, students will be able to describe the relationship
between the area within a loop of a P-V diagram and the work done by the system. They
will be able to compute the work done on a mass being lifted. They will be able to
evaluate the accuracy of their measurements and cite possible sources of errors in the
experiment.
California Science Standards addressed in this laboratory activity:
2(b) Students know how to calculate changes in gravitational potential energy
near Earth by using the formula (change in potential energy) =mgh (h is the
change in the elevation).
3(a) Students know heat flow and work are two forms of energy transfer between
systems.
3(b) Students know that the work done by a heat engine that is working in a cycle
is the difference between the heat flow into the engine at high temperature and the
heat flow out at a lower temperature (first law of thermodynamics) and that this is
an example of the law of conservation of energy..
3(g) Students know how to solve problems involving heat flow, work, and
efficiency in a heat engine and know that all real engines lose some heat to their
surroundings.
Investigation & Experimentation:
1(a) Select and use appropriate tools and technology (such as computer-linked
probes, spreadsheets, and graphing calculators) to perform tests, collect data,
analyze relationships, and display data.
1(b) Identify and communicate sources of unavoidable experimental error.
1(c) Identify possible reasons for inconsistent results, such as sources of error or
uncontrolled conditions.
1(d) Formulate explanations by using logic and evidence.
1(l)Analyze situations and solve problems that require combining and applying
concepts from more than one area of science.
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 6
D
DR
RA
AFFT
T
Equipment:
Pasco Heat Engine
Vernier Gas Pressure Sensor
Vernier LabPro Interface
Pasco Rotary Motion Sensor
Ring Stand
String with attached Mass Hanger
Slotted masses
i-Book computer
Ruler
Key words: work, pressure, volume, gravitational potential energy
Procedure notes:
Each lab group needs a minimum of 2 students
Students must complete the experiment in a timely fashion. Waiting too long for any part
of the experiment will result in degraded results.
Answers to questions:
1. The drawing should look like this:
P
V
2. The values should be within 5% if the experiment was done carefully. It is nearly
impossible to get identical values, but they SHOULD have been the same because we
were measuring the same thing two ways.
3. Area should increase when mass increases and decrease when mass decreases.
4. Sources of error may include leaking by the piston, errors in the sensors, friction in
the piston, mistakes made in the performance of the experiment, etc.
Extension Question
1. Using hotter water will extend right side of the P-V diagram.
References
Pasco equipment guide
Vernier equipment guide
California Science Standards
TOPS Thermo_P-V_Work_07_08.doc (Lyle, Adler) - DRAFT
Page 7