Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

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Energy

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Sound

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COHN - Natures Engineering Of The Human Body

The Human-Body Systems

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Differential Calculus

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Painting

Photons Required To Heat Coffee In A Microwave Oven

Microwave ovens use microwave radiation to heat food. Moisture in the food absorbs microwaves. Food becomes hotter as moisture in food becomes hotter.

How many photons must a microwave radiation with a wavelength of 11.2 cm produce, in order to heat 200 mL of coffee in a microwave oven, from 23^{o} C to 60^{o} C?

**The strings**:

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

Pj Problem of Interest is of type *force* (push). Energy is the capacity to do work which is actualize by *force*. Light energy can do a *pull* or *push* work. The *push* work is more common. In this problems the photons are being *pushed* out. Hence the Pj Problem of Interest here is of type *force-push*.

Energy in one photon = E = hν-----------(1).

Where E is the energy of one photon; h is Planck's constant (0.66252 x 10^{-33} Js) and ν is the frequency of the microwave.

ν = (velocity of light)/(wavelength of light)

= (3 x 10^{8})/(11.2 x 10^{-2}) = 26.79 x 10^{8} Hz Hertz cycles per second).

So, Energy of one photon of microwave with wavelength 11.2 cm is:

= hν = (0.66252 x 10^{-33})(26.79 x 10^{8}) = 17.75 x 10^{-25} J.

Specific heat of water = 4.184 J.

Density of water = 1gm/mL

Assuming coffee is dilute aqueous solution

So, specific heat of coffee = specific heat of water.

So, Energy required to heat 200 mL of coffee from 23^{o} C to 60^{o} C

= 4.184 x 200 x (60 -23) = 4.184 x 200 x 37 = 30.961 x 10^{3}.

So, number of photons required to heat coffee in the microwave oven from 23^{o} to 60^{o} when the wavelength of the microwave radiation is 11.2 cm is:

(30.961 x 10^{3})/(17.75 x 10^{-25}) = 1.7 x 10^{28}

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