PRESSURE-VOLUME
RELATIONSHIPS: BOYLE’S GAS
LAW
Student Learning Objectives. Instruction in this lesson should result in
students achieving the following objectives:
1 Describe the relationship of pressure and volume as it relates to gases.
2 Explain Boyle’s Law.
3 Explain Charles’ Law.
4 Create a mathematical expression describing Boyle’s Law, Charles’ Law and
the Combined Gas Law.
5 Discuss how knowledge of Boyle’s Law and Charles’ Law are applied to do
productive work using pressure, volume, and temperature relationships.
Anticipated Problem: What is the relationship between pressure and volume as it relates
to gases?
I. Matter, including atmospheric gases, consists of tiny particles known as molecules.
Pressure is an application of forces in direct contact. The space an object, such as a gas,
occupies is known as volume.
A. An inverse relationship exists between pressure and volume as they apply to gases. As
volume of a gas decreases, the pressure the gas molecules exert on the walls of the
container increases.
Anticipated Problem: What is Boyle’s Law?
II. An English scientist named Robert Boyle discovered in 1662 that the pressure a gas
exerts could be increased by decreasing its volume while holding its temperature
constant. Gases exert pressure when their molecules collide with the walls of a container
such as the cylinder of an engine.
A. When the volume of a gas is decreased, the gas molecules contact the container sides
more frequently increasing the pressure on the gaseous molecules.
B. The inverse relationships of: 1) increasing volume causing decreasing pressure and 2)
decreasing volume causing increasing pressure were discovered by Robert Boyle and
expressed in Boyle’s Law.
Anticipated Problem: What is Charles’ Law?
III. French scientist Jacques Charles showed that raising the temperature of a gas would
tend to increase the volume of the gas, if the pressure of the gas remained constant.
Raising the temperature of a gas causes the molecules in the gas to move faster. Lowering
the temperature causes the molecules to slow down in movement.
A. The heat that is created upon ignition causes the gases in the engine cylinder to expand
rapidly. Charles’ Law states an increase in the temperature of a gas results in an increase
in the pressure of the gas. This results in expansion of gas molecules within the cylinder
and the subsequent downward movement of the piston.
Anticipated Problem: What mathematical formulas are used to calculate changes in
pressure, volume, and temperature of gases involving Boyle’s Law, Charles’ Law, and
the Combined Gas Law?
IV. The formula for Boyle’s Law demonstrates the inverse relationship that can be
expressed by the following: P1×V1=P2×V2 where P1 is the original pressure of a gas, V1
is the original volume of a gas, P2 is the new pressure of a gas, and V2 is the new volume
of a gas. Mathematically, if the volume of a gas is reduced by one-half, the pressure on
the gas is doubled.
A. Charles’ Law demonstrates a direct relationship between the temperature of a gas and
its pressure. The formula is expressed as P1/P2 = T1/T2 where P1 is the original pressure
on a gas, P2 is the new pressure on a gas, T1 is the original temperature of a gas, and T2
is the new temperature of a gas. If the temperature of a gas doubled, the pressure on the
gas will also double because of the direct proportional relationship.
B. In the Combined Gas Law, Boyle’s, Charles’, and GayLusaac’s Laws can be brought
together to more realistically show that a sample of gas will be under the influence of all
three variables of pressure, temperature, and volume simultaneously. The formula can
be expressed as P1 × V1/ 1 = P2 × V2/T2.
Anticipated Problem: How can knowledge of Boyle’s and Charles’ Gas Laws be
applied to do productive work using air volume/pressure/temperature relationships?
V. The most common example of pressure / volume relationships in agriculture
mechanics is the internal combustion engine. The engine must follow four strokes of
operation in order to produce mechanical energy from chemical energy. The four strokes
are intake, compression, power, and exhaust.
A. Compression is the process of compressing the air/fuel mixture in an internal
combustion engine. Gasoline and Diesel engines differ in how much compression is
necessary to ignite the air/fuel mixture. The ratio between the volume of the cylinder
when the piston is at bottom of the cylinder compared to the volume of the cylinder when
the piston is at the top of the cylinder is known as the compression ratio.
B. Gasoline engines have a lower compression ratio because a spark plug is present to
ignite the air/fuel mixture toward the completion of the compression stroke. Diesel
engines do not contain spark plugs so the compression has to be increased substantially
to ignite the air/fuel mixture on its own. Diesel engines usually have a compression ratio
of 16 to 1 or higher while gasoline engines have a compression ratio of approximately 8
to 1.
C. Volumetric efficiency for an engine is determined by how well the engine can draw
the air / fuel mixture into the cylinder. The efficiency decreases when the engine operates
at high speed because the piston travels too fast to properly draw the mixture into the
cylinder prior to the compression stroke.
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 7
PRESSURE-VOLUME RELATIONSHIPS:
BOYLE’S GAS LAW
Part One: Matching
Instructions: Match the word with the correct definition.
a. Intake
d. Compression
b. Boyle’s Law e. Horsepower
c. Charles’ law f. Power i. 8:1
g. Exhaust
h. 16:1
_______1. The stroke that involves the ignition of the air/fuel mixture in a four-stroke engine.
_______2. Explains the direct relationship between increasing temperature and increasing
pressure of a gas.
_______3. The stroke that involves downward movement of a position drawing the air/fuel
mixture into the cylinder in a four-stroke engine.
_______4. The most common compression ratio of a gasoline engine.
_______5. The stroke that involves the upward movement of the piston to reduce the volume of
air/fuel mixture in the cylinder prior to ignition in a four-stroke engine.
_
Part Two: Fill-in-the-Blank
Instructions: Complete the following statements.
1. According to ________ __________, when the volume of a gas decreases, the pressure of the
gas increases.
2. The volume of air in the cylinder of an engine before compression compared to the volume of
air in the cylinder after compression is known as the __________ _____.
3. If the volume of a gas is reduced by one-fourth, the pressure of the same gas will increase by
_____ times.
4. __________ is the measure of the average kinetic energy or velocity of the molecules of a
substance.
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 8
Part Three: Multiple Choice
Instructions: Write the letter of the correct answer.
_______1. Which of the following terms describes the space occupied by the molecules?
a. Pressure
b. Volume
c. Compression
d. Continuity
_______2. Which of the following terms describes the force of molecules colliding with the
container?
a. Pressure
b. Volume
c. Compression
d. Continuity
_______3. All matter is made up of tiny particles known as __________.
a. DNA
b. Nanophones
c. BTU
d. Molecules
_ Part Four: Short Answer
Instructions: Answer the following questions.
1. What is the relationship between pressure and volume of a gas?
2. What effect does temperature have on a gaseous substance under pressure?
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 9
Assessment
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 26
TS–A
Technical Supplement
PRESSURE-VOLUME
RELATIONSHIPS: BOYLE’S GAS
LAW
1. What is the relationship between gas pressures and volumetric change?
Volumetric efficiency measures how well an engine “breathes” by drawing the airfuel
mixture into the cylinder. Volumetric efficiency is reduced at high engine
speeds because the piston is moving down so rapidly that it travels downward too far
before the air-fuel mixture flows into the cylinder. Factors affecting volumetric efficiency
include: atmospheric pressure, air temperature, air cleaner condition, carburetor
design, intake manifold design, size and number of intake valves, valve timing,
and camshaft design. Larger or a greater number of intake valves result in a high
efficiency.
Cams shaped to allow a greater duration or open size for intake valves result
in improvement in efficiency. A larger air horn carburetor and a larger and straighter
path intake manifold design results in better and faster intake for a high volumetric
efficiency.
2. What is Boyle’s Gas Law?
Boyle’s Gas Law states that as the volume of a container of gas decreases, the pressure
of the gas will increase assuming that there is no change in temperature.
Increasing volume causes a drop in pressure. The pressure of a gas depends upon
how often its particles strike the container’s walls. The smaller the space, the more
often the particles will strike the walls of the container. If the space increases, the
pressure will decrease. In other words, pressure increases proportionately as volume
decreases.
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 27
3. How can knowledge of Boyle’s Gas Law be applied to do productive work
using air/volume relationships?
Pressure/volume relationships are important to understand when measuring engine
performance, especially in an internal combustion engine. The pressure increases
inside the cylinder as the volume decreases due to the upward movement of the piston.
This increased pressure increases the temperature, which makes the air/fuel
mixture easier to ignite. This can be explained in Boyle’s law. The heat that is created
upon ignition causes the gases to expand rapidly in the enclosed cylinder. This
can be explained by Charles’ law. These expanding gases push in all directions and
cause the piston to move.
When a force is applied through a distance, work is accomplished. The pushing or
pulling of one body on another is force. Work can be accomplished in an engine
when the force from the ignition of the air/fuel mixture causes the piston to move
downward.
As the piston reaches bottom dead center (BDC), a port or hole is opened allowing
the burned gases to escape. Remember that bodies in motion tend to stay in motion.
This is referred to as inertia. Inertia causes the piston, which is attached to the crankshaft,
to begin moving upward. During the intake stroke new air-fuel mixture
moves into the cylinder.
The relationship between the total cylinder volume when the piston is at BDC and
the volume remaining when the piston is at top dead center (TDC) is known as the
compression ratio. For example, if at BDC a cylinder’s volume is six cubic inches
and at TDC it is one cubic inch, then the compression ratio of the engine is six to
one. Small gasoline engines have compression ratios of five or six to one. Diesel
engines in tractors usually have a compression ratio of sixteen to one. Diesel engines
in Chevy trucks run twenty-eight to one and Ford trucks run twenty-three to one.
Some motorcycles have a compression ratio of nine or ten to one.
Illinois Physical Science Applications in Agriculture Lesson B4–5 • Page 28