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

Activation Energy As Prerequisite For Activated Complex

There is an *energy hill* all chemical reactions must climb inorder for the reactants in the chemical reaction to produce the desired products. The *activation energy* is the energy required to climb to the peak of this hill. The *peak* is the *activated complex*. It is a short-lived high-energy (excitations due to absorption of activation energy) zone where energetic collisions cause changes in the electron cloud of the colliding molecules and allow bonding rearrangement. Consequently, the reaction is able to slide down the hill as the products are being formed.

(a) Figures 11.1(a) and 11.1(b) are energy diagrams. Which diagram represents an endothermic reaction and which diagram represents an exothermic reaction?

(b) Compare the activation energy required for exothermic reaction with that required for endothermic reaction.

Mechanical processes also need activation energy. Consider figure 11.1(c). *A* is a rectangular prism in a vertical position. Its weight is W and its center of gravity is C_{1} when in a vertical position. Suppose the prism is pushed slightly such that it tilts and its center of gravity changes to C_{2} and thereafter, falls on its own to a horizontal position where its center of gravity is C_{3}. The vertical distance between C_{1} and C_{2} is y_{1}. The vertical distance between C_{1} and C_{3} is y_{2}.

(c) What is the activation energy required by the prism inorder to fall to its horizontal position?

**The strings**:

S_{7}P_{3}A_{32} (Force - Push)
**The math**:

Pj Problem of Interest is of type *force*. Energy is the capacity for work. It is force that is the doer of the work. So energy and work problems are of type *force*. The collisions occuring at the activated complex are *force-pushes*. Also the push that tilts the rectangular prism in fig 11.1(c) is a *force-push*.

(a) The energy diagram in figure 11.1(a) represents an exothermic reaction (energy is released). The energy diagram in figure 11.1(b) represents an endothermic reaction (energy is absorbed).

(b) Generally, an exothermic reaction will require less activation energy than an endothermic reaction. However, there are some chemical reactions expected to be exothermic that require very high activated energy.

(c) Activation energy that must be supplied to the rectangular prism to activate the fall:

= Wy_{1}.

The net energy change = -Wy_{2} (energy is released).

The negative net energy change (energy released) is due to the difference in the gravitational potential energy (G.P.E) of the prism in its vertical position relative to its horizontal position. The prism falls from a *metastable * position at a higher G.P.E to a *stable* position at a lower G.P.E.

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