PHYSICS EXPERIMENTS — 132
10-1
Experiment 10
Adiabatic Compression
In this experiment you investigate a
thermodynamic cycle by systematically
squeezing and releasing air in a sealed container.
It is not a particularly useful cycle, however, as it
takes work to run it! This process, like any real
process, is complicated and difficult to
understand in great detail. It can be simplified
with a model that utilizes a series of simple ideal
gas processes. You apply the model to your
measurements to determine the ratio of specific
heats of air.
Preliminaries.
The equipment consists of a 2-liter plastic
bottle, hand air pump, pressure gauge connected
to computer, a wood block to protect knuckles,
and a wood rod to squeeze the bottle. When set
up, the equipment is arranged as shown in Figure
1. Note that part of the tubing is shown hanging
over the edge of the table. The figure is drawn in
this manner for clarity; normally the pressure
gauge and squeeze bulb also rest on the table.
wood bar
2-liter plastic bottle
wood
block
eye bolt
pump
interface
table clamp
pressure
computer gauge
The thermodynamic cycle consists of the
following steps:
Starting with an inflated (pressurized) bottle of
air,
(1) squeeze rapidly
(2) hold (until back to equilibrium at room
temperature).
(3) release rapidly
(4) hold (until back to equilibrium at room
temperature).
Steps 1 and 3 are modeled as adiabatic
processes as they take place rapidly with no time
for heat exchange with the environment.
Steps 2 and 4 are modeled as isometric (or
isochoric) processes.
The model for the cycle on a PV diagram is
shown in Figure 2 where, as usual, the gas
pressure P is plotted on the vertical and the gas
volume V is plotted on the horizontal.
tubing
clamp
Figure 1. Schematic of experiment
The gas pressure gauge allows you to measure
and record pressure as a function of time
throughout the experiment. The pressure gauge
should be connected to the interface and then to
the computer.
Figure 2. PV diagram for the cycle
The curved segments in Figure 2 are
adiabats, corresponding to steps 1 and 3. These
curves are described by the equations


p V  = p V  
1 1
2 2
p3V3 = p4V4
(eqs.1)
where the exponent  is a property of the gas in
the process (in this case, air). is called the ratio
of specific heats and is defined as
= Cp/CV
where Cp (CV) is the specific heat of the gas at
constant pressure (volume).
PHYSICS EXPERIMENTS — 132
can be determined from the pressure values
in the cycle for each adiabat, using equations 1
and the ideal gas law as:
æpö
æp ö
logç 1 ÷
logç 3 ÷
è p2 ø
è p4 ø
(eq. 2)
g=
g=
æ p1 ö
æ p3 ö
logç ÷
logç ÷
è p3 ø
è p1 ø
where the first equation arises from
consideration of the adiabatic compression
(Step 1) and the second equation arises from
the adiabatic expansion (Step 3).
Procedure
• Double-click on the icon labeled pressure
on the computer desktop. This will load the
experiment file. If asked about loading a
calibration click Yes. You should now see a
graph of pressure vs. time displayed on the
computer screen. The pressure scale should be 02 atm and the time should be 0-30 s. If not,
adjust it. (To change the axes scale click on the
minimum or maximum value shown. It will turn
into a little text entry box, you can enter a new
number.) The current pressure is indicated on the
left in the lower portion of the graph window.
• Check the plumbing to make sure valves are
closed to airflow from the room. Pump up the
bottle until the air pressure is about 1.5 atm. The
pump has a clamp between it and the rest of the
tubing since it seems to be the worst source of air
leaks. Clamp the tube tightly after initially
pressurizing the plastic bottle.
• As the air in the bottle readjusts back to room
temperature, the pressure drops until reaching a
constant value. (If the pressure reading does not
eventually stay constant, then the system has a
leak!) This is p1 on Figure 2 at room temperature
T1.
• Click the "Start" button to begin taking data.
A horizontal line at p1 starts to appear.
• Quickly crush the bottle so the wood rod rests
on the wood block: this is the adiabatic
10-2
compression process.
Hold the rod steady
against the block; this may take some effort. The
pressure is a maximum p2.
• Still holding the wood rod against the block,
watch as the pressure gauge slowly drops: this is
a constant volume cooling process. The pressure
drops until the temperature in the bottle T3 is
again at room temperature T1. Wait until the
pressure has leveled out at the new pressure P3.
• Quickly release the wood rod: this is an
adiabatic expansion. The pressure drops to a
minimum pressure p4.
• Wait as the air heats at constant volume,
returning to room temperature and the cycle is
completed. If everything works perfectly then the
pressure should return to p1. This will not
always happen due to leaks in the system and
deformations in the plastic materials.
• Once you have a good data set you can save it
using File/Save As… or print out your graph
using the File/Print Graph menu choice.
Select Examine from the Analyze menu.
Move the cursor to each of the points on the
graph and record accurate values for the
pressures p1 through p4.
• Use each of equations 2 to calculate the ratio
of specific heats for air. Take the average of the
two calculations as your best value.
Questions (Answer clearly and completely).
1. What value do you determine experimentally
for the ratio of specific heats? What is the
percent error of this value from the theoretical
value of 1.4 for air (consisting of diatomic
molecules)?
2. Use the ideal gas law in the p-V diagram of
Figure 2 to derive that the squeezed bottle
volume V2 can be calculated from V2 =
(p1V1)/p3. Calculate the volume of the squeezed
bottle.
PHYSICS EXPERIMENTS — 132
10-3
3. Use the ideal gas law in the PV diagram of
Figure 2 to derive that the highest air temperature
T2 can be calculated from T2 = (p2/p3)T1.
Calculate the high temperature. (Watch your
temperature scales!!)
4. Use the ideal gas law in the PV diagram of
Figure 2 to derive that the lowest air temperature
T4 can be calculated from T4 = (p4/p1)T1.
Calculate the low temperature. (Watch your
temperature scales!!)
5. Use your pressure data and your result from
Question 2 to carefully draw the p-V diagram for
the cycle to scale. Use the diagram to estimate
the net work per cycle.
rev. 12/13