PHYSICS EXPERIMENTS — 13210-1
Experiment 10
Adiabatic Compression
PHYSICS EXPERIMENTS — 13210-1
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.
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.
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.
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
p1V1 = p2V2
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).
can be determined from the pressure values in the cycle for each adiabat, using equations 1 and the ideal gas law as:
(eq. 2)
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 0-2 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 p1starts to appear.
•Quickly crush the bottle so the wood rod rests on the wood block: this is the adiabatic 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 Graphmenu choice. Select ExamineAnalyze Data A from the Analyzemenu. 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 difference 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.
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. 120/13