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Gas

Gas can be single atoms or molecules.

Pressure

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Pressure = Force / Area

Temperature

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Thermal motion = Kinetic energy

  • Higher temperature, higher kinetic energy, faster motion, more force, greater pressure

Density

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More particles hitting the box, higher pressure.

Ideal Gas Law

  • Equation: PV = nRT
    • P = Pressure
    • V = Volume
    • n = number of moles
    • R = Constant (often referred to as the "fudge factor" or ideal gas constant)
    • T = Temperature
  • Alternate Formulation:
    • P = number density x R x T
  • Pressure and Temperature Relationship:
    • Pressure is proportional to the density of particles and the temperature.
    • More particles result in higher pressure.
    • Higher temperature results in higher pressure.

Atmosphere

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If there are \(N\) boxes on top, then

  • \(F_b = (N+1) \times F_g\) (force at the bottom)
  • \(F_t = (N) \times F_g\) (force at the top)
    • Air is not accelerating so forces cancel out

What does Pressure really mean?

  • Atmospheric pressure at sea level:
    • 100,000 newtons per square meter
    • 100,000 pascals (Pa)
    • Approximately 10,000 kg per square meter or 14.7 pounds per square inch (psi)
  • Pressure at Denver:
    • 83,000 Pa (12.2 psi)
  • Pressure at Mount Everest:
    • 33,000 Pa (4.9 psi)
  • Analogy for Sea Level Pressure:
    • Equivalent to a bus on top of you or 1 ton per square foot
  • Pressure difference between top and bottom of a wing:
    • 2,000 Pa (1/3 psi)

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Buoyancy

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  • Definition: An object partially or wholly immersed in a fluid is acted upon by an upward buoyant force equal to the weight of the fluid it displaces.
  • Force Dynamics:
    • Total Force Calculation: Total Force = force up - force down - force of gravity = 0
    • This is considered when part of the fluid is analyzed to understand buoyancy.
  • Impact of Different Masses:
    • If the object has a different mass, the force of gravity varies:
      • Greater Mass than the Fluid: Total force is negative, object falls.
      • Less Mass than the Fluid: Total force is positive, object rises.
      • Equal Mass to the Fluid: Total force is zero, object stays where it is.

Hot Air Balloon

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  • Pressure Equilibrium: Pressure inside the balloon equals the pressure outside.
  • Relationship Between Pressure, Density, and Temperature:
    • Pressure is proportional to the product of density and temperature.
    • Hot air, having a higher temperature and the same pressure as the surrounding air, results in a lower density.
  • Resulting Buoyancy:
    • The lower density of the hot air inside the balloon compared to the colder outside air means the overall weight of the balloon is less than the air it displaces.
    • Consequently, the balloon rises.

Regular Balloon

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  • Increased Internal Pressure:
    • The pressure inside the balloon is greater than the pressure outside.
    • This differential is necessary to stretch the balloon material, allowing it to expand.

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  • Tension on Balloon:
    • The tension on the balloon produces an inward force.
  • Pressure Inside Balloon:
    • The pressure of the balloon provides an outward force to balance the tension.

Helium Ballon

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  • Force Due to Gravity:
    • The force due to gravity on a balloon is equal to the weight of the balloon plus the weight of the helium inside it.
  • Weight Comparison:
    • If the weight of the helium is less than the weight of an equivalent volume of air (which it is), and
    • The combined weight of the helium and the balloon is less than the weight of the air displaced by the balloon,
    • Then the balloon will rise.

Bubbles

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Pressure inside is almost the same as pressure outside, but a little bit higher.

Note

❗

ChatGPT said:

Surfactants are molecules that have a unique ability to interact with both water and oil, which is why they are so effective in cleaning processes. Here’s a breakdown of the diagram and its components:

Components of the Surfactant Molecule

  1. Head (Hydrophilic): The head of a surfactant molecule is "water-loving" (hydrophilic). This part of the molecule is attracted to water and tends to dissolve in it. It is usually made up of polar groups such as sulfates or phosphates.
  2. Tail (Hydrophobic): The tail of the molecule is "oil-loving" (hydrophobic) and avoids water but will readily dissolve in oils. These tails are typically long chains of carbon and hydrogen atoms that are non-polar.

Behavior and Functions

  • In Water: When surfactant molecules are placed in water, they orient themselves so that their hydrophilic heads are in contact with the water, while their hydrophobic tails stick out away from the water. This arrangement can reduce the surface tension of water, making it easier to spread and mingle with oils and dirt.
  • Micelle Formation: A key feature shown in the diagram is the formation of micelles. In water, when the concentration of surfactant molecules is high enough, they can form spherical structures known as micelles. In these micelles, the hydrophobic tails are turned inward to form a core that can encapsulate oily particles, while the hydrophilic heads point outward, interacting with the surrounding water. This arrangement effectively captures oily dirt, which can then be rinsed away.
  • Bilayer Formation: The diagram also shows a bilayer formation, which occurs when surfactant molecules align themselves into two layers. In this configuration, the hydrophobic tails face each other, forming a barrier that can trap substances between the two layers of heads. This structure is similar to the lipid bilayers found in cell membranes.

Applications

  • Cleaning: The ability to form micelles and emulsify oils makes surfactants excellent for cleaning applications, as they can effectively remove oils and debris from surfaces and fabrics.
  • Emulsification: Surfactants are also used to stabilize mixtures of oil and water by reducing the surface tension at the interface of the two liquids, which is critical in products like mayonnaise, creams, and sauces.

Structure of a Bubble

  • Soap and Water Layers: The soap film of a bubble has three layers: a thin layer of water sandwiched between two layers of soap molecules. The soap molecules have a hydrophilic (water-attracting) head and a hydrophobic (water-repelling) tail. The heads face inward toward the water, while the tails face outward, forming a stable layer.
  • Surface Tension: Surface tension pulls the molecules of the soap film tightly together, creating a smooth, round shape. Since a sphere has the least surface area for a given volume, bubbles naturally form into spherical shapes to minimize energy.

Forces Acting on a Bubble

  1. Air Pressure Inside and Outside: The air pressure inside the bubble pushes outward, while the surface tension of the soap film pulls inward. These forces balance to keep the bubble intact.
  2. Evaporation: Over time, water in the soap film begins to evaporate, thinning the bubble wall. When the film becomes too thin to maintain the balance of forces, the bubble pops.

The air pressure inside the bubble will always be larger than the air pressure from the outside.