# Boyle’s Law

## Inquiry Lab Kit for AP® Physics 2

### Materials Included In Kit

Syringes with plungers, 6
Syringe tip caps, 6
Wooden bases with large (23-mm diameter) predrilled holes, 6
Wooden tops with medium (20-mm diameter) predrilled holes, 6

Books
Ruler

### Safety Precautions

Wear appropriate safety eyewear. Do not aim the pressurized syringe at anyone or anything as the syringe tip cap could shoot off. Check the syringe, plunger and tip cap before using and replace any parts that are damaged or worn.

### Disposal

All materials may be saved and stored for future use.

### Lab Hints

• This laboratory activity can be completed in two 50-minute class periods. It is important to allow time between the Introductory Activity and the Guided-Inquiry Activity for students to discuss and design the guided-inquiry procedures. Also, all student-designed procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day.
• Enough materials are provided in this kit for 24 students working in groups of 4 or for 6 groups of students.
• Any kind of mass or object (e.g., books or reams of paper) can be used as the pressure load for this experiment. Be aware that stacking masses too high or unevenly on the top wooden block may cause the syringe to tip over and necessitate further data collection. If the mass is not marked, make sure students measure the mass of the object using a balance and record this in a data table.
• It may be necessary to grease the plunger prior to each trial to minimize friction in the syringe.
• Volume measurements, in mL and with a ruler, were recorded using the first leading edge of the syringe plunger as a marker. Advise students to be careful when they record the syringe volume because it is easy to record an “upside down” volume.
• Small books were used to apply the measurable force, or pressure, to the syringe plunger. Standard masses, such as those used to calibrate a balance, in the range of 50–200 g, were not sufficient to cause an easily measurable volume change.
• For graphing purposes, remind students that the pressure is not zero when the plunger is in the starting position, rather it is equal to atmospheric pressure. Drawing a free-body diagram, as prescribed by the Prelab Questions, of the prevailing forces may help students realize this.
• The system, without weights added to the top, is in equilibrium. The internal gas pressure exerted on the plunger is equal to the external, atmospheric pressure and so the plunger does not move. With each addition of more mass, the system must be given time to re-equilibrate, that is, for the plunger to come to a stop owing to the internal pressure/atmospheric pressure + mg balance.
• Students might need a reminder on how to recognize a hyperbola: the products of the coordinates at all points should be constant. Rearrange PV = nRT to y = mx + b form. Place P on the y-axis so the equation becomes P = (nRT)/V. Assuming the compression is slow enough so that the temperature doesn’t change, the process is isothermal and a graph of P vs. 1/V is linear with the other gas variables constant.
• Students can use graph paper and count squares to get at the area under the curve. Integral calculus may be done, but is not necessary.
• To calculate pressure in kPa:
• Convert grams to kilograms.
• Convert kilograms to newtons (force) = mass x acceleration due to gravity, mass in kg x 9.8 m/sec2.
• Pressure = force/area and is expressed in units of newtons/m2. Area is the area of the syringe opening (use A = πr2, r = 7.5 x 10–3 m).
• Convert to kPa.
• Add to each the standard atmospheric pressure; 101.33 kPa.

### Teacher Tips

• The guided-inquiry design and procedure section was developed to subtly lead students through the experimental design process. You may decide to provide less or more information than is included, as long as the students are challenged to think critically.
• This laboratory provides a unique opportunity to demonstrate the interdisciplinary nature of science. The ability of the distinct disciplines, chemistry and physics, to inform each other is particularly pronounced in this investigation.

### Further Extensions

Opportunities for Inquiry

Explore Charles’s law, the relationship between absolute temperature and volume. Or explore the lesser-known Amonton’s law, which describes the relationship between temperature and pressure. A hole may be drilled in the syringe and a temperature probe inserted to measure temperature as gas is compressed.

Alignment to the Curriculum Framework for AP® Physics 2

Enduring Understandings and Essential Knowledge
The energy of a system is conserved. (5B)
5B5: Energy can be transferred by an external force exerted on an object or system that moves the object or system through a distance. This process is called doing work on a system. The amount of energy transferred by this mechanical process is called work. Energy transfer in mechanical or electrical systems may occur at different rates. Power is defined as the rate of energy transfer into, out of, or within a system. (A piston filled with gas getting compressed or expanded is treated in Physics 2 as part of thermodynamics.)
5B7: The first law of thermodynamics is a specific case of the law of conservation of energy involving the internal energy of a system and the possible transfer of energy through work and/or heat. Examples should include P–V diagrams—isovolumetric processes, isothermal processes, isobaric processes, and adiabatic processes. No calculations of internal energy change from temperature change are required; in this course, examples of these relationships are qualitative and/ or semiquantitative.

Learning Objectives
5B5.4: The student is able to make claims about the interaction between a system and its environment in which the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic energy plus potential energy).
5B5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance.
5B5.6: The student is able to design an experiment and analyze graphical data in which interpretations of the area under a pressure-volume curve are needed to determine the work done on or by the object or system.
5B7.1: The student is able to predict qualitative changes in the internal energy of a thermodynamic system involving transfer of energy due to heat or work done and justify those predictions in terms of conservation of energy principles.
5B7.2: The student is able to create a plot of pressure versus volume for a thermodynamic process from given data.
5B7.3: The student is able to use a plot of pressure versus volume for a thermodynamic process to make calculations of internal energy changes, heat, or work, based upon conservation of energy principles (i.e., the first law of thermodynamics).

Science Practices
1.1 The student can create representations and models of natural or man-made phenomena and systems in the domain.
1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively.
2.2 The student can apply mathematical routines to quantities that describe natural phenomena.
4.2 The student can design a plan for collecting data to answer a particular scientific question.
4.3 The student can collect data to answer a particular scientific question.
5.1 The student can analyze data to identify patterns or relationships.
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.

### Science & Engineering Practices

Developing and using models
Planning and carrying out investigations
Analyzing and interpreting data
Using mathematics and computational thinking
Obtaining, evaluation, and communicating information
Engaging in argument from evidence

### Disciplinary Core Ideas

MS-PS3.C: Relationship between Energy and Forces
HS-PS3.C: Relationship between Energy and Forces

### Crosscutting Concepts

Patterns
Stability and change
Cause and effect
Scale, proportion, and quantity
Systems and system models

### Performance Expectations

MS-PS3-5. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.
HS-PS3-1. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.
HS-PS3-2. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motion of particles (objects) and energy associated with the relative position of particles (objects).

1. When you use a bicycle pump to inflate a bicycle tire, are you doing work on the gas or is the gas doing work on the environment? Explain.

You are doing work on the gas. In order to compress the gas, you must exert a force to move the bicycle pump over a distance.

2. If you inflate a bicycle tire to near-bursting using a bicycle pump, and then release the pump handle, the handle will rise against gravity.

In this case, is work done on or by the gas? In this case, work is done by the gas on the bicycle pump handle. The internal pressure exerted by the gas molecules in the pump is greater than the external atmospheric pressure and exerts a force against gravity over a distance.

3. One summer saw gasoline prices fall significantly from the previous summer. The falling gas prices were attributed, in part, to a glut, or huge supply of oil on the market. In this simplified model, is the relationship between oil supply and gas prices an inverse or direct relationship? Explain.

This model describes an inverse relationship between oil supply and gas prices. That is, as one increases, the other decreases.

4. Explain why the pressure exerted by gas molecules against their container walls increases as the container size, or volume, decreases.

According to the kinetic molecular theory of gases, gas molecules exhibit constant, random motion. Gas molecules exert pressure by bumping into, or colliding with, their container walls. If the container size is decreased while the number of gas molecules stays the same, then the number of collisions between the gas molecules and container walls will increase, and so too will the pressure.

5. The apparatus used in this experiment consists of a plunger inserted in a syringe held upright by two wooden blocks. Mass is added to the top wooden block and resulting volume changes are measured. What prevents the plunger from rising up and out of the syringe housing, when no books or masses are kept on top of it?

Atmospheric pressure, or the force air molecules exert in their collisions with the plunger, prevent it from rising in the absence of an additional external force. When the plunger is static, the internal pressure of the gas molecules must be equal to the external, atmospheric pressure.

6. Given your answer to Question 5, how will this impact your calculation of the pressure, or, the first point on a PV graph?

The first point on the PV graph will have a pressure value equal to atmospheric pressure. As books are added to the top of the plunger, new pressures attributable to the addition of new mass will be calculated and added to the atmospheric pressure.

7. Draw a free-body diagram of the forces on the piston to show that the total force on the top block (mg + atm) is in direct opposition to the internal pressure of the gas in the syringe.
8. Calculation of the amount of work done on or by a gas requires integral calculus, or graphical analysis. Describe how you might use graphical analysis to determine the area under a curve like the one shown in Figure 1 by using graph paper composed of small squares or blocks.

If graph paper composed of small squares is used, the area of one square may be calculated by measuring the side length and squaring to determine the area of a single square. The squares under the curve can then be counted. The total number of squares multiplied by the area of one square will provide an estimate of the area under the curve. Some squares will have only a portion of their areas fall under the curve, so some level of approximation is required. Alternatively, a triangle can be outlined (as best as possible) under the curve and the sides measured to enable calculation of the triangle’s area using the formula A = ½ x base x height.

### Sample Data

Discussion for Introductory Activity
As the plunger is depressed, the volume of the container, or syringe, decreases. Since the syringe is capped, the amount of gas in the syringe remains constant. Therefore, as the volume decreases, the pressure of the gas inside the syringe increases because the number of collision between the gas molecules and their container walls increases. As the plunger is depressed, the gas is being worked upon. It takes a force (i.e., the push of your hand) to move the plunger over a distance. When you release your hand from the plunger, it rises as the gas expands to fill a larger volume. In this case, the gas is performing work on the plunger by moving it over a distance.

Analyze the Results

• How do your measured values describing the volume changes with pressure changes compare to the theoretical, calculated values? Account for differences.

Recall that Boyle’s law can be expressed as P1V1 = P2V2 to convey the fact that as volume decreases, pressure must necessarily increase to keep the product PV constant. You may use atmospheric pressure and the initial syringe volume to calculate the constant PV product. As mass is added to the syringe, the pressure exerted may be calculated and plugged into the equation P1V1 = P2V2, which may be rearranged to solve for a theoretical V2 value. The theoretical V2 value may be compared to the experimental V2 value, or the volume change attributable to the addition of increased mass.

Remember we are assuming that the gas inside the syringe is ideal and thus has negligible volume and molecules that do not attract each other. As the volume decreases, we would expect deviations from ideal behavior to become more pronounced because the gas molecules assume more significant volumes relative to the container volume and their proximity increases the strength of the attractive forces the experience amongst themselves.

• The process by which data is manipulated and graphed to yield a straight line, as opposed to a curve, is called linearization. How can you manipulate your PV data to convert your curve into a straight line?

This can be done by taking the inverse of all volume measurements, that is, by dividing the measured volumes into 1. This has been done and the results reported in the sample data.

The linearization of the PV data is based on rearrangement of the ideal gas law so that pressure and volume are on opposite sides of the equation: P = nRT/V. The term nRT is a constant and can be omitted from the equation to yield the direct relationship P = 1/V.

{14009_Data_Table_1}
Example Calculation of Pressure

P = F/A
P = mg/πr2
P = (0.9117 kg x 9.8 m/s2)/[π x (0.0103m)2]
P = 26830.81 Pa
P = 26.83 kPa (the atmospheric pressure, 101.33 kPa, must be added to this value: 26.83 kPa + 101.33 kPa = 128.16 kPa)

{14009_Data_Figure_2}

Discussion for Guided-Inquiry Activity

1. Design an experiment that uses the apparatus provided to derive the mathematical relationship between a gas’s pressure and the volume of the container in which it is held. Use the following questions to guide you as you design your experiment.
• Gather several (5–8) objects of approximately equal or uniform mass. These may be copies of the same textbook, reams of paper, or other heavy objects of equal weight.
• Prepare a data table to record the volume of air in the syringe versus the number of masses added to the apparatus. Note: Create enough columns to record three trials, plus a column for the average volume.
• Before beginning, record the first data point by reading the initial volume of air in the syringe with no masses on the apparatus.
• Stack the first mass on the top block of the apparatus and record the volume of air (in cc) as indicated on the scale of the syringe.
• Continue stacking masses on top of the apparatus, recording the air volume each time. If time allows, repeat the procedure 1–2 times.
• Average the volume data and record in a data table.
•  Plot the data on a sheet of graph paper.
• Use P = F/A = mg/πr2 to calculate pressure on the plunger as mass is added, where r is the plunger radius.
1. What are the two gas variables you will be measuring, and plotting on a graph?

Pressure and volume.

2. How can you apply a measurable pressure, or rather calculate the pressure, applied to the syringe plunger?

Objects with mass significant enough to move the plunger in the downward direction—to compress the internal gas—must be selected. Prior to the placement of each object on top of the plunger, or top wooden block, the object should be massed on a top-loading balance with a high (appr. 1,000 g) capacity. The measured mass can be used with the formula P = mg/πr2, to calculate the pressure applied to the syringe plunger.

3. How can the experimental volume change be measured as the pressure exerted on the plunger changes?

The experimental volume change can be measured directly by observation using the mL markings on the syringe. It is recommended that the leading edge of the syringe be used to most closely approximate the true volume of gas in the syringe. The conical tip of the syringe takes up space, but it does not occupy a significant volume relative to that occupied by the gas.

4. According to the kinetic molecular theory of gases very fast compressions of a gas from large volumes to small volumes cause significant temperature changes. Why then, for the purpose of this experiment—to determine the mathematical relationship between the gas variables pressure and volume—is it necessary to compress the gas in the syringe slowly?

We are attempting to derive a relationship between the two variables, pressure and volume. Therefore, we want to control the experiment such that the effects of one of those variables on the other are the only effects we observe. In other words, we want to avoid causing significant temperature changes because if significant temperature changes occur red in conjunction with the pressure and volume changes, it would be difficult to determine how much of the volume change could be attributed to the pressure change and how much of the volume change could be attributed to the temperature change. If we want to measure the effects of one variable on the other, we have to control any external variables such as temperature and moles. In other words, we want to hold those constant. Experiments in which temperature is held constant can be called isothermal with respect to each other.

2. Construct a graph of pressure (y-axis) versus volume (x-axis).
1. How many data points are necessary?

To some degree, this is a matter of subjectivity on the part of the experimentalist. Two data points can be used to define a line but should not be relied upon as confirmation of a relationship, either direct or indirect, between two variables. The experiment is limited in the sense that only so much mass can be placed on the top wooden block before the syringe is fully compressed. Moreover, objects with masses in the range of approximately 500 g to 1,000 g are needed to cause measurable volume changes. We found that using five small books in this mass range yielded good, reproducible data. Between four and seven data points is recommended as necessary and practical, given the limitations of the apparatus.

2. Describe qualitatively what happens to gas pressure as the volume of its container decreases and how this relationship is reflected in your graph.

With respect to a gas held in a container of alterable volume, as the container volume decreases, the gas molecules’ motion is confined to a smaller space, and so the number of collisions between the gas molecules and container walls increases. In turn, the pressure the gas molecules collectively exert against their container walls increases. The graph of our sample data, given below, bears out this relationship. You can see that as volume (x-axis) increases pressure (y-axis) decreases in a non-linear fashion.

3. Recall the introductory demonstration in which you were asked whether the compression of the gas in the syringe entailed doing work on the gas. Did you perform work on the gas when you compressed it or did the gas perform work on the plunger, and your hand indirectly?

Compressing the bicycle pump entailed the exertion of a force over a distance. In other words, you had to use mechanical energy to push down the pump handle. In other words, you performed work to compress the gas.

4. Calculate the amount of woek done on or by the gas in your experiment. Hint: The area under a pressure–volume curve is equal to the work done on or by the gas.

The method(s) described in the answer to Prelab Question 8 may be used to determine the amount of work done on or by the gas:

Review Questions for AP® Physics 2
1. Why is it necessary to account for atmospheric pressure when carrying out your experiment?

The atmospheric pressure at sea level on any given day is typically about 101.33 kPa. Comparatively, the applied pressure (by the addition of masses such as books) to the syringe plunger necessary to compress the internal gas by an observable volume is calculated to fall approximately in the range of 10–30 kPa. Because pressures in this range are in fact lower than the atmospheric pressure, the atmospheric pressure cannot be considered negligible, but must be considered significant.

Prior to placing an external, non-atmospheric pressure on the syringe plunger, the plunger is kept in a static position (it does not rise or fall) because the internal pressure of the gas is equal to the external atmospheric pressure. The two pressures are said to be in equilibrium, in other words.

2. You may or may not have lubricated the syringe prior to carrying out your experiment. How would adding a lubricant, to promote easier movement of the plunger, impact your results?

Any friction between the syringe plunger and the syringe itself must be overcome by the external applied pressure to move the plunger in a downward direction against the internal gas pressure. Of course, the syringe plunger’s rising in the upward direction would also be impeded by friction. It would be difficult to quantify the effects, but it is likely that larger volume changes would be observed as friction decreases, that is, when the system is lubricated.

3. Describe two sources of error and the effects each had or may have had on your experimental data.

The system may not be entirely closed. That is, some gas may escape with compression. In this case, the plunger would move further into the syringe and the experimental volume change would be overestimated. Also, there is some random error inherent to reading the volume. Finally, if compression occurred too quickly the internal gas temperature may be raised and the internal pressure raised in direct proportion. As a result, the plunger would not move as far into the syringe and the volume change for a given application of pressure would be underestimated.

4. Is it reasonable to neglect the mass of the plunger and top wooden blocks in the calculation of the external pressure, or force, applied to the syringe plunger? Explain.

In order to make this determination, weigh the plunger and calculate the pressure it can exert based on that weight. If the pressure is small compared to the atmospheric pressure and the pressure exerted by the books it can be neglected.

5. Explain how you might derive theoretical numbers, or data, to which you can compare your experimental results?

You are applying a pressure and experimentally measuring the volume change. In order to derive theoretical volume changes you must plug the calculated pressure into the simple gas law equation P1V1 = P2V2, with the understanding that the P1V1 product must remain constant if temperature and the number of moles of gas are held constant. The difference in the volumes V1 and V2 can be compared to the experimental volume change measured using the syringe.

6. How does the assumption that the air in the syringe is an ideal gas impact this experiment?

The kinetic molecular theory assumes that ideal gas molecules have negligible volume relative to their containers and also do not experience intermolecular forces. As container volume increases, gases tend to deviate from ideal behavior because their volume becomes increasingly significant relative to their container and they are able to exert attract forces on each other owing to increased proximity. However, the volume does not become exceedingly small in this experiment and so the deviations from ideal behavior are likely negligible.

### References

AP® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

# Boyle’s Law

## Inquiry Lab Kit for AP® Physics 2

### Introduction

Physics and chemistry often overlap, perhaps most significantly in their ability to form joint explanations for the behavior of gases. The four variables used to describe a gas—pressure, volume, temperature and moles—are closely related. As one or more change, one or more of the others also change, in direct or inverse relation. This advanced inquiry investigation explores the relationship between a gas’s pressure and the volume of the container in which it is held as well as how a gas performs work or is worked upon.

### Concepts

• Boyle’s law
• Linearization
• Isothermal processes
• Graphical analysis
• Work

### Background

The kinetic molecular theory describes the particles in a gas as being far apart and in rapid, random motion. Gas molecules in a closed container move rapidly in unpredictable paths and frequently collide with container walls. Each collision gives rise to pressure, a force per unit area measured in millimeters of mercury (mmHg), atmospheres (atm), torr, pounds per square inch (psi), and Pascals (Pa), to name several pressure units. Much of what follows concerning the behavior of gases can be derived from this very basic premise.

For example, when molecules speed up, they bounce off container walls more frequently, and with more force… and so pressure increases. A variety of conditions can be altered, with respect to a gas, to increase or decrease the number and force of collisions of gas molecules with container walls—and thereby increase or decrease a gas’s pressure. The simple gas laws describe two-variable relationships: what happens to one variable when another is changed. These simple gas laws make intuitive sense if thought of in the context of gas molecules exerting pressure against their container walls by colliding with them.

When the volume of a container holding gas molecules decreases, the molecules have less space to move in and so more collisions with container walls occur and pressure increases. The relationship between gas pressure and volume, described by Boyle’s law, is inverse. As one increases the other decreases.

{14009_Background_Equation_1}
Boyle’s law assumes temperature and amount (number of gas moles) are constant. From this idea we can write the equation P1V1 = P2V2 to convey the fact that as volume decreases, pressure must necessarily increase to keep the product PV constant.

To derive this relationship, Boyle built a simple apparatus to measure the relationship between the pressure and volume of air. The apparatus consisted of a J-shaped tube that was sealed at one end and open to the atmosphere at the other end. A sample of air was trapped in the sealed end by pouring mercury into the tube. In the beginning of the experiment, the height of the mercury column was equal in the two sides of the tube. The pressure of the air trapped in the sealed end was equal to that of the surrounding air, equivalent to 29.9 inches (760 mm) of mercury. When Boyle added more mercury to the open end of the tube, the air trapped in the sealed end was compressed into a smaller volume. The difference in height of the two columns of mercury (Δh) was due to the additional pressure exerted by the compressed air compared to the surrounding air. Boyle found that when the volume of trapped air was reduced to one half its original volume, the additional height of the column of mercury in the open end of the tube measured 29.9 inches. The pressure exerted by the compressed air was twice as great as atmospheric pressure. The mathematical relationship between the volume of air and the pressure it exerts was confirmed through a series of measurements. This advanced inquiry investigation asks students to explore Boyle’s law in the context of physics, particularly how a gas performs work or is worked upon.

### Experiment Overview

The purpose of this advanced inquiry investigation is to derive a mathematical equation describing the relationship between the pressure and volume of a gas at constant temperature. The mathematical relationship will be determined via graphical analysis, which will also be used to determine the amount of work done on or by a fixed amount of gas. In the introductory part of the experiment, a special apparatus will be set up in order to quantify the amount of applied force needed to compress a sample of gas a measurable amount. In the guided inquiry portion of the experiment, the relationship between pressure and volume will be derived by constructing graphs, which must be further interpreted to determine the amount of work done on or by the gas.

### Materials

Syringe with plunger
Syringe tip cap
Wooden base with large (23-mm diameter) predrilled hole
Wooden top with medium (20-mm diameter) predrilled hole

### Prelab Questions

1. When you use a bicycle pump to inflate a bicycle tire, are you doing work on the gas or is the gas doing work on the environment? Explain.
2. If you inflate a bicycle tire to near-bursting using a bicycle pump, and then release the pump handle, the handle will rise against gravity. In this case, is work done on or by the gas?
3. One summer saw gasoline prices fall significantly from the previous summer. The falling gas prices were attributed, in part, to a glut, or huge supply of oil on the market. In this simplified model, is the relationship between oil supply and gas prices an inverse or direct relationship? Explain.
4. Explain why the pressure exerted by gas molecules against their container walls increases as the container size, or volume, decreases.
5. The apparatus used in this experiment consists of a plunger inserted in a syringe held upright by two wooden blocks. Mass is added to the top wooden block and resulting volume changes are measured. What prevents the plunger from rising up and out of the syringe housing, when no books or masses are kept on top of it?
6. Given your answer to Question 5, how will this impact your calculation of the pressure, or, the first point on a PV graph?
7. Draw a free-body diagram of the forces on the apparatus to show that the total force on the top block (mg + atm) is in direct opposition to the internal pressure of the gas in the syringe.
8. Calculation of the amount of work done on or by a gas can require integral calculus, or graphical analysis. Describe how you might use graphical analysis to determine the area under a curve like the one shown in Figure 1 by using graph paper composed of small squares or blocks.
{14009_PreLab_Figure_1}

### Safety Precautions

Wear appropriate safety eyewear. Do not aim the pressurized syringe at anyone or anything as the syringe tip cap could shoot off. Check the syringe, plunger and tip cap before using and replace any parts that are damaged or worn.

### Procedure

Introductory Activity

Class Demonstration

1. Participate in the demonstration of the assembly and operation of the apparatus. Consider how the apparatus could be used to gather pressure versus volume data and to derive a mathematical relationship between the two variables. The following steps are necessary to set up and use the apparatus:
1. Remove the syringe tip cap from the syringe and take the plunger out of the syringe.
2. Locate the wooden top piece (it has a medium, 20-mm diameter hole) and set it on a flat surface with the hole upward.
3. Press the top end of the plunger firmly into the hole in the wooden top.
4. Replace the syringe onto the plunger, set the plunger to the desired volume of air (maximum volume = 30 cc), and then replace the syringe tip cap on the syringe.
5. Locate the wooden base piece (it has a larger, 23-mm diameter hole) and set it on a flat surface with the hole facing upward.
6. Press the syringe/plunger/wooden top setup into the hole in the wooden base.
7. Before beginning the experiment, test the assembled apparatus by pressing down on the wooden top piece. Release the pressure and read the air volume as indicated on the scale of the syringe. If the air volume does not return to close to 30 cc when released, then remove the syringe from the base, remove the tip cap, and draw more air into the cylinder. Recap the end and replace the syringe onto the base. The entire side wall of the black rubber plunger may need to be lubricated with silicone grease or petroleum jelly.
2. Capping the syringe outlet to prevent air from escaping and then pressing down on the plunger compresses the air inside the pump. What happens to the pressure of the gas? Is the plunger doing work on the gas or is the gas doing work on the plunger?
3. Release the applied pressure from the syringe plunger and notice how the plunger rises. Is gas doing work or being worked upon?
Guided-Inquiry Design and Procedure
1. Design an experiment that uses the apparatus provided to derive the mathematical relationship between a gas’s pressure and the volume of the container in which it is held. Use the following questions to guide you as you design your experiment.
1. What are the two gas variables you will be measuring and plotting on a graph?
2. How can you apply a measurable pressure, or calculate the pressure, applied to the syringe plunger?
3. How can the experimental volume change be measured as the pressure exerted on the plunger changes?
4. According to the kinetic molecular theory of gases, very fast compressions of a gas from large volumes to small volumes cause significant temperature changes. Why then, for the purpose of this experiment—to determine the mathematical relationship between the gas variables pressure and volume—is it necessary to compress the gas in the syringe slowly?
2. Construct a graph of pressure (y-axis) versus volume (x-axis).
1. How many data points are necessary?
2. Describe qualitatively what happens to gas pressure as the volume of its container decreases and how this relationship is reflected in your graph.
3. Recall the introductory demonstration in which you were asked whether the compression of the gas in the syringe entailed doing work on the gas. Did you perform work on the gas when you compressed it or did the gas perform work on the plunger, and your hand indirectly?
4. Calculate the amount of work done on or by the gas in your experiment. Hint: The area under a pressure–volume curve for a gas is equal to the work done on or by the gas.
Analyze the Results
• How do your measured values describing the volume changes with pressure changes compare to the theoretical, calculated values? Account for differences.
• The process by which data is manipulated and graphed to yield a straight line, as opposed to a curve, is called linearization. How can you manipulate your PV data to convert your curve into a straight line?

### Student Worksheet PDF

14009_Student1.pdf

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