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

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Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

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Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

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Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Non-Ideal Gas Behavior

Given that volume = V liters; pressure = P atmosphere; temperature = T Kelvin; Numuber of Moles = n.
**Boyle's Law: V α 1/P (constant n, T)**
**Charle's Law: V α T (constant n, P)**
**Avogadro's Law: V α n (constant P, T)**
**Ideal Gas Equation: V α nT/P ; V = nRT/p (R is proportionality constant = 0.0821 L-atm/mol-K**
**Graham's Law Of Effusion: the effusion rate of a gas is inversely proportional to the square root of its molar mass**.
**van der Waals Equation: (P + n ^{2}a/V^{2})(V - nb) = nRT**

Where a and b are van der Waals constants. The constant b L/mol corrects for the intrinsic volume of 1 mole of a gas molecules while the constant a L

(ii) Identify two reasons why gases behave non-ideally

(iii) How does the ratio PV/RT help to reveal non-ideal behavior of gases?

(i) CCl

(ii) CCl

**The strings**:
S_{7}P_{3}A_{32} (force - push)
**The math**:

The Pj problem of interest is of type force (force - push)
**(ai)** The basic premise of the non-ideal behavior of gases is that at high pressures and low temperatures the ideal gas equation becomes a less accurate determinant of the behavior of gases.
**(aii)** The intrinsic volume of a mole of gas molecules and the attractive forces between the molecules are two reasons why gases deviate from ideal behavior.
**(aiii)** The ratio PV/RT should be constant for a given sample of gas at all combinations of pressure, volume, and temperature. If this is not the case, then the gas sample is behaving non-ideally.
**(b)** van der Waals equation: (P + n^{2}a/V^{2})(V - nb) = nRT

For Ar: a =1.344, b = 0.0322

For CO_{2}: a = 3.57, b = 0.427

So, we expect Ar to behave closer to ideal gas behavior.
**(ci)** Ideal gas equation: PV = nRT

So, CCl_{4} at ideal behavior: P = (1x0.08206x313)/28 = 0.917 atm
**(cii)** van der Waals equation:(P + n^{2}a/V^{2})(V - nb) = nRT

So P = nRT/(V-nb) - n^{2}a/V^{2} = (1x0.08206x313)/(28-0.1383) - 20.4/784

So, P = 25.685/27.862 - 0260 = 0.922 - 0260 = 0.896 atm.

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