PSAA Curriculum Unit Physical Science Systems

Problem Area Energy and Power Systems

Pressure – Volume Relationships: Boyle’s Gas Law Lesson

Can we boil water at room temperature? Fill a 60cc syringe with 20cc of water. Fill a 60cc syringe with 20cc of water. Remove air bubbles. Remove air bubbles. Cap the tip of the syringe so that no air can enter or leave the syringe. Cap the tip of the syringe so that no air can enter or leave the syringe. Pull the plunger as fast as you can. Pull the plunger as fast as you can. What happens???? What happens????

Learning Objectives Describe the relationship of pressure and volume as it relates to gases. Explain Boyle’s Law. Explain Charles’ Law.

Learning Objectives (cont.) Create a mathematical expression describing Boyle’s Law, Charles’ Law and the Combined Gas Law. Discuss how knowledge of Boyle’s Law and Charles’ Law are applied to do productive work using pressure, volume, and temperature relationships.

Terms Boyle’s Law Charles’ Law Combined Gas Law Compression Compression ratio Molecules Pressure Volume Volumetric efficiency

What is the relationship between pressure and volume as it relates to gases? 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.

What is the relationship between pressure and volume as it relates to gases? 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.

What is Boyle’s Law? 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.

Boyle’s Law When the volume of a gas is decreased, the gas molecules contact the container sides more frequently increasing the pressure on the gaseous molecules. 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.

The Pressure and Volume Relationship of a Gas

What is Charles’ Law? 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.

Charles’ Law 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.

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?

The formula for Boyle’s Law 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.

The formula for Charles’ Law 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.

The Combined Gas Law 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.

Sample Problem #1

Answer #1

Sample Problem #2

Answer #2

How can knowledge of Boyle’s and Charles’ Gas Laws be applied to do productive work using air volume/pressure/temperature relationships?

Internal Combustion Engine and pressure/volume relationships 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.

Internal Combustion Engine and pressure/volume relationships 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.

Internal Combustion Engine and pressure/volume relationships 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.

Internal Combustion Engine and pressure/volume relationships 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.

Review/Summary What is the relationship between pressure and volume as it relates to gases? What is the relationship between pressure and volume as it relates to gases? What is Boyle’s Law? What is Boyle’s Law? What is Charles’ Law? What is Charles’ Law?

Review/Summary 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? 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? How can knowledge of Boyle’s and Charles’ Gas Laws be applied to do productive work using air volume/pressure/temperature relationships? How can knowledge of Boyle’s and Charles’ Gas Laws be applied to do productive work using air volume/pressure/temperature relationships?