Understanding Liquid Pressure, Buoyancy, and Expansion
Liquid Pressure and States of Matter
Pressure Exerted by Liquids
Liquids exert pressure in all directions. The pressure (p) at the base of a liquid column with density (d) and height (h) is calculated as: p = d * h * g, where g represents the acceleration due to gravity.
Analysis:
- A) Liquid pressure is independent of the surface area. Larger areas experience a greater total force, but the pressure remains the same.
- B) Torricelli demonstrated that barometric pressure equals the pressure exerted by a 76 cm column of mercury (Hg). Denser liquids (like water, which is 13.6 times denser than mercury) would require a proportionally taller column to match atmospheric pressure.
- C) Bathyspheres and bathyscaphes are spherical steel vessels used for underwater observation. Jacques Piccard reached a depth of 11,000 meters in a bathyscaphe, withstanding immense pressure.
States of Matter
- Bose-Einstein Condensate (BEC): A state of maximum coherence at absolute zero (0K), where matter condenses into a “super-atom.” Atoms occupy the ground state, exhibiting superconductivity (zero electrical resistance) and superfluidity (near-zero viscosity).
- Solid: Molecules are strongly bound, resulting in a definite shape and volume. Friction is present due to the close interaction of molecules.
- Liquid: Molecules have weaker cohesive forces, allowing them to flow freely. Liquids have a definite volume but adapt to the shape of their container.
- Gas: Molecules are far apart with minimal cohesive forces. Gases have neither a definite shape nor volume, expanding to fill their container.
- Plasma: The most abundant state of matter in nature, found at very high temperatures (e.g., the Sun’s surface). Electrons are stripped from atoms, leaving positively charged ions. Examples include fluorescent tubes, lightning, stars, and nebulae.
Cohesion Force
Cohesion refers to the attractive forces between atoms within a molecule. In an atom, the attractive forces between the positively charged protons and negatively charged electrons are dominant due to the proton’s greater mass.
Buoyancy and Flotation
Thrust (Buoyancy)
Thrust is the upward force exerted by a fluid on a submerged object. It arises because the pressure at the bottom of the object is greater than the pressure at the top. Thrust (E) is calculated as: E = Vc * Pf, where Vc is the volume of the submerged portion of the body and Pf is the density of the fluid.
Specific Gravity
Specific gravity is the ratio of a substance’s weight to the weight of an equal volume of water. It can be calculated as: p = P / V or p = d * g, where P is the weight, V is the volume, d is the density, and g is the acceleration due to gravity.
Pascal’s Principle
Pascal’s principle states that pressure applied to a fluid in equilibrium is transmitted equally in all directions. This principle is applied in hydraulic systems like brakes, elevators, and presses.
Archimedes’ Principle and Flotation
A submerged body experiences two opposing forces: weight (downward) and thrust (upward).
- A) If thrust is less than weight, the body sinks.
- B) If thrust equals weight, the body remains suspended in the liquid.
- C) If thrust is greater than weight, the body floats.
Condition of Flotation: A body floats when the weight of the displaced liquid equals the weight of the body.
Floating Bodies
- Boats: Float due to their specific shape, which displaces a large volume of water.
- Buoys: Used to mark navigation hazards.
- Life Preservers: Utilize buoyant materials like cork to keep people afloat.
- Hydrometers: Cylindrical instruments used to measure the specific gravity of liquids. Examples include alcoholmeters and volumeters.
- Icebergs: Large masses of floating ice, with approximately 9/10 of their volume submerged.
- Submarines: Designed to operate submerged, on the surface, or partially submerged. They control buoyancy by adjusting the amount of water in ballast tanks.
Ballooning
Hot air balloons float because the hot air inside is less dense than the surrounding air. The buoyant force (Fasc) is calculated as: Fasc = E – P, where E is the thrust and P is the total weight of the balloon.
Thermal Expansion
Bodies expand when heated and contract when cooled.
- Linear Expansion: The increase in length (L) of a body is given by: ΔL = α * Li * Δt, where α is the coefficient of linear expansion, Li is the initial length, and Δt is the change in temperature.
- Superficial Expansion: The increase in surface area (ΔS) is given by: ΔS = 2α * Si * Δt, where Si is the initial surface area.
- Volumetric Expansion: The increase in volume (ΔV) is given by: ΔV = 3α * Vi * Δt, where Vi is the initial volume.
Applications of Expansion
- Spaces are left between railroad tracks to accommodate expansion due to temperature changes.
- Bridges are often placed on rollers to allow for expansion and contraction.
- Heat-resistant glassware has a low coefficient of expansion, preventing breakage due to rapid temperature changes.