Gases and Pressure

Define atmospheric pressure.
Outline Boyle’s Law for pressure and volume of gases.
Outline the Combined Gas Law for temperature, pressure, and volume of gases.
Perform simple calculations involving temperature, pressure, and volume of gases.
Discuss clinical applications of gases and pressure.
Week 3 Learning Goals 1, 14 - 17.

What is pressure and how is it measured?
- Pressure is defined as the quantity of force per unit area.
- The SI unit of pressure is Pascal (1 Pa = 1 N/m²).
What are fluids?
- A fluid is a substance that does not hold its own shape and can flow.
- Gases are classified as a type of fluid.

The earth’s atmosphere consists of gas molecules that constitute air.
These molecules are held close to the earth due to gravity but are in motion because of their kinetic energy.
Each location in a fluid experiences pressure from the weight of the fluid molecules above it.
Atmospheric pressure is greater at lower altitudes (closer to sea level) due to the increased number of air molecules stacked above.

A vacuum is defined as a space that is not occupied by any mass.
Achieving a vacuum involves constricting space within a container, pushing gas out and then increasing the container size while preventing gas from re-entering, creating a negative pressure relative to the surrounding atmosphere.
The closer the pressure is to absolute zero, the closer it is to an ideal vacuum.
Pumps are devices used to push fluids (liquids or gases) in or out of apparatus, subsequently adjusting pressure as a result.

Gas in an enclosed container is composed of molecules with kinetic energy that move randomly.
Inter-molecular and molecular-container collisions lead to forces being exerted, causing pressure within the container.

What happens to total force exerted on the container if the number of gas molecules increases but the container size is constant?
The total pressure would increase as a result of increased molecular interactions.

What happens when the number of gas molecules remains constant but the container size decreases?
The pressure will increase as the gas molecules are confined to a smaller volume, leading to more frequent collisions with the container walls.

Commonality of Concepts:
- Both scenarios increase the density of the gas.
- Pressure is proportional to density, dependent on the number of molecules or the volume of the container.

Boyle’s Law defines the relationship between pressure and volume while assuming that the quantity of gas (its mass) and temperature remain unchanged.
The mathematical expression of Boyle’s Law is:
- P_1V_1 = P_2V_2
This law indicates that pressure varies inversely with volume: when volume increases, pressure decreases by the same factor to keep their product constant.

A fixed quantity of helium is placed in an adjustable container with an initial volume of 1 m³.
If the volume is reduced to one-tenth of its original size, the increase in pressure inside the container can be predicted using Boyle’s Law.

Given:
- Mass of helium is constant
- Initial volume: 1 m³
- New volume: 0.1 m³
What facts are given directly in the question?
- Fixed mass, initial and new volume of the gas.
Other Facts}:
- Ideal gas behavior can be assumed if mentioned in the problem.
Assumptions:
- Temperature is constant.

Target Variable:
- New pressure of the gas after volume alteration.
Units of Measurement:
- Pressure, measured in Pascals (Pa).
Significant Figure (SD):
- Follow significant figure rules based on initial data provided.
Closing Statement:
- State the relationship explored through Boyle’s Law and its implications on pressure change.

Which physics laws apply here?
- Boyle’s Law as the main governing principle for this scenario.
Broad Predictions:
- As volume decreases, pressure increases.
Symbol Representation:
- Use symbols such as P for pressure and V for volume in equations.
Equations to Utilize:
- Usage of Boyle’s Law equation for calculations.

Simplification:
- Assess the equation for any potential simplifications.
Rearrangement:
- Rearrange to isolate the target variable (pressure).
Substituting Known Values:
- Prepare values for substitution based on definitions in Boyle's Law.

Substitute known values into the equation.
Remember to include units in calculations to verify accuracy across dimensional analysis.

Understand that the calculated pressure is a relative measure, not an absolute one, as pressures are defined relative to atmospheric pressure.

Gases naturally extend to occupy maximum available space and minimize pressure.
If two gas containers are connected and pressure is higher in one, gas will flow into the lower pressure container until there is an equalized pressure (redistribution of gas molecules).
The flow of gases occurs when there exists a pressure gradient (ΔP).

Breathing is a practical illustration of Boyle’s Law and gas flow principles.
To fill the lungs with air, a pressure gradient is necessary to allow external air to flow in.
Atmospheric pressure applies outside, which must be higher than the internal lung pressure.

Volume increase in lungs is achieved through the contraction of intercostal muscles and diaphragm, decreasing pressure within lungs according to Boyle’s Law, resulting in a pressure gradient (ΔP) for inhalation.
Exhaling Requirements:
- Lung volume must decrease for air to flow out, creating the opposite pressure gradient.

Gas molecules are perpetually in random motion, possessing kinetic energy (KE).
The total KE of the gas molecules is dependent on their internal energy (temperature):
- Higher temperatures correspond to more KE and consequently more collisions, increasing force against container walls.

Higher temperatures lead to increased force exerted on container walls, correlating with increased gas pressure.
The relationship is given as pressure being proportional to temperature:
P ext{ is proportional to } T
The ratio of pressure to temperature remains constant if the volume is fixed:
rac{P_1}{T_1} = rac{P_2}{T_2}

Definition:
The Combined Gas Law integrates the relationships among pressure, temperature, and volume.
Combined equations include:
rac{P_1V_1}{T_1} = rac{P_2V_2}{T_2}
Important Note:
Temperature must be expressed in absolute terms (Kelvin).

The interconnectedness of pressure, volume, and temperature is fundamental.
Adjusting one parameter results in changes to at least one of the other factors.
Altering temperature leads to a volume change if the pressure is constant, and changing pressure or volume can induce temperature variations.