Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Water-Ice Equilibrium And Le Chatelier's Principle

*Water*, like other *matter* exists in three states: solid, liquid and gas. Each of these states has its equilibrium conditions that are affected by changes in their environments (e.g. change in temperature, pressure, concentration, etc). In 1884, Henri Louis Le Chatelier discovered an equilibrium principle that became known as Le Chatelier's Principle
**(a)** State Le Chatelier's Principle.
**(b)** What is implied if liquid water and ice is in equilibrium?
**(c)** Figure 14.7 is the inside of a thermos from a top view. It shows water and ice in equilibrium at 0^{o}C. What will happen to the water-ice equilibrium in the thermos if a 100^{o}C copper penny is dropped into the thermos?
**(d)** What will happen if instead of dropping the hot penny as in (c), a cold penny at -10^{0}C is dropped into the thermos?
**(e)** Why is it difficult to skate in very cold ice (temperature very much below 0^{o}C)?

**The strings**:
S_{7}P_{7}A_{72} (equilibrium-dynamic).
**The math**:

Pj Problem of Interest is of type *equilibrium* (equilibrium-dynamic).

**(a)** *Le Chatelier's Principle: If stress is applied to a system at equilibrium, the system will tend to readjust so that the stress is reduced*.
**(b)** At equilibrium, there is no net change as a consequence of their interaction. H_{2}O (l) <-----> H_{2}O (cr).
**(c)** The hot penny will loose heat and the heat it lost will be absorbed by the water-ice mixture. Some ice will melt until the system (water-ice mixture, penny) is returned to the equilibrium temperature of 0^{o}C. This readjusted equilibrium will have more water and less ice.
**(d)** The cold penny will absorb heat from the water-ice mixture until the system (water-ice mixture, penny) is returned to the equilibrium temperature of 0^{o}C. This readjusted equilibrium will have more ice than water because some of the water became ice.
**(e)**
Easy skating on ice requires a critical range of thickness of the layer of water on the surface of the ice. A thin layer (below the lower bound of the critical thickness range) of water on the surface of the ice causes insufficient *slickness* on the surface of ice. Consequently, friction between the skate and the ice is higher than required for easy skating.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings