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

Fuel Value Of A Substance

(a) Define the term *fuel value*.

(b) Carbohydrates, proteins and fats are foods with fuel values. So, they are sources of energy.

Which is a greater source of energy as food, 5 g of fat or 9 g of carbohydrate.

(c) A serving of a certain food contains 7 g fat, 9 g carbohydrate, and 1 g protein. Estimate the number of Calories in a serving of this food.

(d) The heat of combustion of fructose, c_{6}H_{12}O_{6}, is -2812 kJ/mol. If a delicious apple weighing 120 g contains 16 g of fructose, what caloric content does the fructose contribute to the apple?

**The strings**:
S_{7}P_{6}A_{66} (grouping/interaction - chemical).
**The math**:

Pj Problem of Interest is of type *grouping/interaction* (chemical).
**(a)**: the *fuel value* of a substance is the amount of energy (usually heat) released when 1 g of the substance is combusted.
**(b)**: the fuel values of:

Carbohydrate = 17 kJ/g

Protein = 17 kJ/g

Fat = 38 kJ/g

So, fuel value of 5 g of fat = 5 x 38 = 190 kJ

So, fuel value of 9 g of carbohydrate = 9 x 17 = 153 kJ

So, 5 g of fat is a greater energy source than 9 gram of carbohydrate.
**(c)**: fuel values of:

7 g of fat = 7 x 38 = 266 kJ

9 g of carbohydrate = 9 x 17 = 153 kJ

1 g of protein = 1 x 17 = 17 kJ

So, total fuel value in a serving = 266 + 153 + 17 = 436 kJ

1 calorie = 4.184 J

So, 436 kJ = (436 x 10^{3})/4.184 = 104 kilocalories

1 kilocalorie (kcal) = 1 Calories (Cal)

So, 104 kcal = 104 Cal.

So, the number of Calories in a serving = 104 Cal.
**(d)** Molar mass of c_{6}H_{12}O_{6} = 12x6 + 1x12 + 16x6 = 72 + 12 + 96 = 180 kg

So, heat of combustion/g = -2812/180 = -15.62 kJ/g

So, 16 g of c_{6}H_{12}O_{6} = 16 x -15.62 = -249.92 kJ . Negative sign indicates heat is released.

249.92 kJ = 249.92/4.184 kcalories = 59.73 kcal = 59.73 Calories.

So, the fructose in the apple contributes 59.73 Calories to the apple.

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.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

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

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