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

Why Heat Of Vaporization Is Larger Than Heat Of Fusion

Why is heat of vaporization larger than heat of fusion?

**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*. In this instance, the energy is heat energy which is a consequence of kinetic energy. The kinetic energy is due to atom collisions (*force-push*). It is in this sense that the Pj Problem of interest is of type *force*.

**Heat Of Vaporization**: the quantity of heat required to vaporize 1 gram of a liquid substance at its boiling point at constant temperature. In other words, amount of heat needed to change a substance from the liquid phase to a gas phase.
**Heat Of Fusion**: the quantity of heat required to liquefy 1 gram of a solid substance at its melting point at constant temperature. in other words, amount of heat needed to change a substance from the solid phase to the liquid phase.

Vaporization and fusion are phase changes. The volume-increase in a liquid to gas phase change is larger than the volume-increase in a solid to liquid phase change. Since work is the product of pressure and change in volume, more work is required (at constant pressure) for vaporization than for fusion. Hence more energy (heat energy) is required for vaporization than for fusion.

Implicit in the volume increase as a result of the phase changes are the relative molecular distances. The molecules of a substance are so much further apart when the substance is in a gaseous state than when it is in a liquid state. The separation of the molecules of a substance requires energy. This energy is directly proportional to the intermolecular distance realized. In other words, a lager energy is required to keep the molecules of a substance further apart. Consequently, the heat of vaporization is larger than the heat of fusion.

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