Its All about Pj Problem Strings (SiPjAjk) - 7 Spaces Of Interest (Si) and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (Ajk)

WiseBites - Chew And Swallow

My Brain Is Stringed - Iremisan Adegiga : I became a TECian (a person or any other being that sees the Universe through the TECTechnics Prism) about two years ago after ... more

The Risk View Of Loss Risk, the probability or chance of loss is an existential reality. Risk lurks in the existence of all entities. Consequently, its absolute elimination is ... more

Rest - I. Adegiga: Rest is simply a break from work and a time to rejuvenate the body, mind and spirit. The duration of rest may... more

While Africa Slumbered - O. A. Asemota: The African Story to date, is bittersweet. Volumes have been written about the first continent. Also, there have been many movies (fictions and nonfictions) about Africa. The Black Panther is an example of a recent fictional movie about Africa. I saw the movie, The Black Panther. The cinematography, costumes and cast are excellent. However, after all the pageantry, I was reminded that... more

Jealousy The Green-Eyed Monster - Iremisan Adegiga : Human imperfection with respect to existential living is an existential reality. As humans live day by day, they fall short of the marks they set for themselves, or that societies set for them; or that their religion set for them; etc. I am definitely a member of the group of imperfect humans. However, there is .. more

The Simplicity Of Nature's Infinite Intelligence: Nature has dual meanings in this presentation: (a) the totality of the being of the physical Universe ... more

Why Greatness Eludes Nigeria - O.A. Asemota: While contemplating the title of this article, two thoughts came to mind ... more

The Animal In Humans: the domestication of humans began centuries ago as humans became smarter than their fellow animals in the jungle. Civilization after... more

Great Concepts From Africa: Africans established human existence on Earth. There is no human accomplishment greater than this. In addition to pioneering human existence on Earth, Africans gave humanity the following great concepts ... more

Hi-story - Iremisan Adegiga: I called my parents at the end of my freshman year in college to inform them about my decision to major in history instead of economics as... more

Political Thieves Within Nigeria: The Implication - O. A. Asemota: Stealing is the taking of property without permission from the owner of the property. A thief is one who steals... more

A Grain Of Faith In The Scientific Method...more

Genesis Chapter One (KJV) -Reconciling Creation With Facts: Belief in the creation account in Genesis Chapter one, is mostly faith-based. Nonetheless, there is...more

War. Lessons Unlearned: Cognitive beings defend being and space when faced with existential threats ...more

Denatured Conquest: The ability to conquer (defeat or overwhelm) was incorporated into the being of cognitive beings at their creation because ...more

Many Kingdoms Within Nigeria's Democracy - O. A. Asemota: There were sophisticated political systems in the space now called Nigeria prior to the coming of the white men... more

Bloom - Kimberlee June Benart: My momma said to me, ďDonít hide your light under ... more

Leaders And Leaders-Makers: Human political systems did not fall from the sky. They are consequences of gradual political evolutions that... more

Policing The Pursuit Of Knowledge : Policing is the enforcement of the system of laws of a space. The police are ... more

Spiritual But Not Religious - Kimberlee J. Benart : I saw the title of the blog and took the time to read it, but how it saddened me to see it full of harsh unkindness ... more

Mis-Information As A Weapon - The Larger Issue: Information is shared knowledge. The knowledge shared does not have to be accurate...more

I Charlie - A Farmer At Heart: From growing up on a farm in America to pioneering and working in Africa...more

One Nation Under What?: A nation is a group of individuals with different identities... more

Selective Freedom: Freedom is the condition of not being controlled by another. The implication here is not that a person is ... more

Ultimate Reality: the awareness of being establishes reality ... more

All is Mathematics: Nature only speaks mathematics within the context of 7 universal concepts (Pj problems). This language is uniform everywhere in the Universe and is ... more

Good Walls Bad Walls: A wall is a barrier that encloses a space. A wall does not have to be visible to the naked eye. The structure of a wall... more

Expressions Of Pj Problems

"I have reduced physics to mathematics" - Descartes.
Strings (SiPjAjk) reduce all knowledge to mathematics.

Gibbs Free Energy As Predictor Of Chemical Reaction Spontaneity

Gibb's Free Energy As Predictor Of Chemical Reaction Spontaneity

When deviations from generally accepted rules occur, smart humans want to know why.
Generally, an exothermic reaction involves an increase in disorder. So, an exothermic reaction that involves a decrease in disorder (increase in order) is a deviation from expectation.
Generally an endothermic reaction involves a decrease in disorder. So, an endothermic reaction that involves an increase in disorder (decrease in order) is a deviation from expectation.
Theoretical physicist and chemist J. Willard Gibbs (A.D. 1839 - 1903) was one of the people who wanted to know why the deviations stated above exist. The answer he developed, introduced a quantity called free energy (now called Gibbs Free Energy in his honor).

(a) State Rudolf Clausius' mathematical definition of entropy
(b)Relate change in Gibbs Free Energy to Change in enthalpy, temperature and change in entropy
(c) Relate change in Gibbs free energy to chemical equilibrium constant
(d) Relate change in Gibbs free energy to standard cell potentials through the Nernst equation
)e) Explain the spontaneity of the reaction of the combustion of 2 moles of hydrogen gas despite the decrease in entropy.
(f) State Ludwig Boltzmann's mathematical definition of entropy.
                → Solution: the strings and the math.

Thermodynamic Stability As A Function Of Enthalpy Of Formation

Thermodynamic Stability As A Function Of Enthalpy Of Formation

Synthesis and decomposition reactions are two important chemical reactions. For example, the combustion of carbon (as coal) and the decomposition of the carbon dioxide that is the product of the combustion are synthesis reaction and decomposition reaction respectively (figure 11.2).
In general, a systhesis reaction has the following form:
element or compound + element or compound -------> compound
In general, a decomposition reaction has the following form:
compound -------> two or more elements or compounds Thermodynamic stability is the non-spontaneity of the decomposition of the product of a synthesis chemical reaction.

(a)What is enthalpy of formation?
(b) Show that the carbon dioxide that is the product of the combustion of carbon (as coal) is thermodynamically stable.
                → Solution: the strings and the math.

Activation Energy As Prerequisite For Activated Complex

Activated 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?

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 C1 when in a vertical position. Suppose the prism is pushed slightly such that it tilts and its center of gravity changes to C2 and thereafter, falls on its own to a horizontal position where its center of gravity is C3. The vertical distance between C1 and C2 is y1. The vertical distance between C1 and C3 is y2.

(c) What is the activation energy required by the prism inorder to fall to its horizontal position?
                → Solution: the strings and the math.

Energy In A Mole Of Crystalline Solid

Crystalline Scandium
The above photo is of a sample of crystalline scandium (Sc, atomic number 21).
The atoms and molecules of a solid are in constant motion at ordinary temperatures eventhough there is equilibrium spacing between them. Thermal agitation due to heat causes the atoms and molecules to oscillate about their equilibrium positions oftentimes at very high frequency. The resulting kinetic energy acquired by the atoms and molecules constitute the thermal energy of the substance.
Consequently, both kinetic energy (thermal) and potential energy (structure) consitute the total energy in solids and liquids (this potential energy is not in gases).

(a) Suppose an individual atom of a crystalline solid behaves as a point mass. Calculate the total energy of the atom at 25oC.

(b) Calculate the total energy in one mole of the crystalline solid at 25oC.
                → Solution: the strings and the math.

Potential Energy Between Atoms As A Function Of Nucleic Spacing

Potential Energy Between Atoms
The bonding force F, between atoms may be expressed approximately as follows:

F(r) = A/rM - B/rN (N > M) -----------(1)
Where r, is the center-to-center spacing between atoms and A, B, M, and N are constants that vary according to the type of bond.
A/rM represents the attractive force while B/rN represents the repulsive force.

In general, the potential energy, U(r) between atoms is defined as the work capacity of interatomic forces for a given reference frame.

Hence, U(r) = ∫F(r)dr = ∫(A/rM - B/rN)dr -----------(2)

(a) Determine the expression for U(r) by integrating equation (2).
(b) Show that the curve U(r) in figure 10.8 has a minimum at equilibrium spacing, r0.
(c) What is the significance of U(ro)?
(d) Explain the meaning of the area under the curve U(r) from r0 to infinity.
                → Solution: the strings and the math.

Interatomic Force As A Function Of Nucleic Spacing

Interatomic Force
The bonding force F, between atoms may be expressed approximately as follows:

F(r) = A/rM - B/rN (N > M) -----------(1)
Where r, is the center-to-center spacing between atoms and A, B, M, and N are constants that vary according to the type of bond.
A/rM represents the attractive force while B/rN represents the repulsive force.

(a) Express the equilibrium spacing r0 in terms of A, B, M, and N.
(b) Derive another form for F(r) in which the only constants are r0, A, M, and N.
(c) From the equation for F(r) derived in (b) calculate the following:
(i) The spacing r1 for which F is maximum
(ii) The value of the maximum force Fmax.
                → Solution: the strings and the math.

Maximum Charge In Coulombs On A Bismuth Ion

Maximum Charge Of Bismuth Ion In Coulombs
The above photo is of a sample of Bismuth. The atomic number of Bismuth is 83 and its electron configuration is as follows:
1s22s22p63s23p6 4s23d104p65s24d105p66s24f145d106p3
Determine in Coulombs the maximum charge on a bismuth ion.
                → Solution: the strings and the math.

Properties Of Elements Due to Valence-Shell Electrons

Similar Valence Shell Electrons Similar Chemical properties
The electron configurations of seven elements of the Periodic Table are shown in Table 10.1. Which of the elements should have similar physical and chemical properties?
                → Solution: the strings and the math.

Electron Residency In Atomic Orbitals

Periodic Table Showing Sub-Shells That Are Filling
Figure 9.16 shows the order in which the electrons of atoms fill their orbitals. Use this information to determine the electron configuration of the following elements:
(a) Iron (b) Aluminum (c) Bismuth
                → Solution: the strings and the math.

Volume Of A Barrel

The Volume Of A Barrel
Determine the approximate volume of the barrel in figure 5.1, if the sides are bent to the arc of a parabola and D = 60 inches, d= 50 inches, and h = 120 inches
                → Solution: the strings and the math.

The Grocer And His Fruits

The Grocer And His Fruits
Suppose a grocer sells 2 apples for 5 cents and 3 oranges for 5 cents. He surmises that the simple arithmetic of selling 5 fruits for 10 cents results in the same average price. In other words, according to him, a sale of 2 apples and 3 oranges have the same average price as a sale of any 5 pieces of fruits for 10 cents.
Is the grocer right? What is the correct average price ?
                → Solution: the strings and the math.

Time Population A Equals Population B

The population of town A is 10,0000 and is increasing by 600 each year. The population of town B is 20,000 and is increasing by 400 each year. After how many years will the two towns have the same population?
                → Solution: the strings and the math.

Break-Even Point Of A Publisher

Love Royal And True
A publisher finds that the cost of preparing a book for printing and of making the plates is $5000. Each set of 1000 printed copies costs $1000. He can sell the books at $5 per copy. How many copies must he sell to at least recover his costs?
                → Solution: the strings and the math.

Circle Test For Deductive Reasoning

Circle Test For Deductive Reasoning
Radeen examined figure 1.1 and posited the following premises and deductive conclusion:
All college students are clever. All young boys are clever. Therefore All college students are young boys.
Evadin examined figure 1.1 and posited the following premises and deductive conclusion:
All college students are clever. All young boys are clever. Some clever college students are young boys.
Who has the correct deductive conclusion base on figure 1.1. Radeen or Evadin?
                → Solution: the strings and the math.

Conditional River Crossing With Wolf, Goat And Cabbage

Wolf, Goat, Cabbage
A wolf, a goat, and a cabbage are to be rowed across a river in a boat holding only one of these three objects besides the oarsman. How should he carry them across so that the goat should not eat the cabbage or the wolf devour the goat?
                → Solution: the strings and the math.

Select A Fruit

Select A Fruit
Container A, contains 7 apples. Container B, contains 7 peaches. You are asked to select a fruit from each of the following spaces formed by containers A and B:
(a) A ∪ (A ∩ B)
(b) A ∩ (A ∪ B)
(c) (A - B) ∪ B
What is the maximum number of apples you can select? What is the maximum number of peaches you can select?
Hint: simplify expressions before selecting. A ∪ B (fig. 7.87a) means the set of elements in A or in B or in both (if in both, counted only once). A ∩ B ( fig. 7.87b) means the set of elements in A and in B (elements common to both A and B). A - B (fig. 7.87c) means the set of elements in A but not in B.
                → Solution: the strings and the math.

Average Rate Of Work - Two Ditch Diggers

Average Rate Of Work - Two Ditch Diggers
A ditch-digger can dig a ditch in 2 days and another ditch-digger can dig the same ditch in 3 days. What is their average rate of ditch-digging per day?
                → Solution: the strings and the math.

Energy Stored In A Magnetic Field And Incremental Inductance

Energy Stored In A Magnetic Field And Incremental Inductance
Figure 16.2 shows the i - λ characteristics of an iron-core inductor:
(a) Calculate the energy and incremental inductance for i = 1 A.
(b) Given that the sinusoidal current i(t) = 0.5sin2πt and coil resistance is 2Ω, calculate the voltage across the terminals of the inductor.
                → Solution: the strings and the math.

Induced Voltage Of Coil In A Magnetic Field

Induced Voltage Of Coil In A Magnetic Field
A coil having 100 turns is immersed in a magnetic field that is varing uniformly from 80 mWb (milliWeber) to 30 mWb in 2 seconds. Determine the induced voltage in the coil.
                → Solution: the strings and the math.

Charge Moving In A Constant Magnetic Flux

Charge Moving In A Constant Magnetic Field
Figure 1.2 shows a charge q moving with velocity u (a vector) in a magnetic field with magnetic flux density B (a vector). Assuming that the field is a scalar field (i.e, it is spatially unidirectional).
(a) Express the vector force f in terms of the charge q, and the vectors u and B.
(b) What is the magnitude of f If u makes an angle θ with the magnetic field?
(c) Suppose the magnetic flux lines are perpendicular to a cross sectional area A (fig1.3). Express the magnetic flux ψ, of the field in terms of the flux density B.
Magnetic Flux Perpendicular To A Cross Sectional Area
(d) State Faraday's Law that relate magnetic flux φ to eletromotive force (emf), e.
                → Solution: the strings and the math.

3 Phase Power

3 Phase Power
Figure 8.56 is a Wye (or Y) configuration of a Balanced three phase AC circuit. Show that:
(a) The magnitude of the line voltages is equal to √3 times the magnitude of the phase voltages.
(b) No conducting wire is needed to connect nodes n and n'.
(c) If the 3 balanced load impedances are replaced with 3 equal resistances R, the total instantaneous power delivered to the balanced load by the 3-phase generator is constant.
                → Solution: the strings and the math.

AC Power Triangle

AC Power Triangle Figure 8.14 shows a simple AC circuit. Figure 8.14(a) is the time domain circuit while figure 8.14(b) is its power triangle. Given that v(t) = 16cosωt; i(t) = 4cos(ωt - π/6); and ω 377 rad/sec. Determine:
(a) The power factor, pf.
(b) The values of the real power P, the reactive power Q and the apparent power S of the power triangle.
                → Solution: the strings and the math.

Average AC Power

Average AC Power
Figure 8.7 shows a simple AC circuit. Figure 8.7(a) is the time domain circuit while figure 8.7(b) is its phasor form.
Given that the sinusoidal voltage and current of the circuit are as follows:
v(t) = Vcos(ωt); i(t) = Icos(ωt - θ); Determine:
(a) The average power of the circuit in the time domain
(b) The average power of the circuit in the frequency domain.
                → Solution: the strings and the math.

Center Tapped Transformer

Center Tapped Transformer
Figure 8.42 shows a center-tapped Transformer. The following information is given about the transformer:
Voltages and current are rms values.
Primary voltage = 4,800 V
Secondary voltage of 240 V is split (because transformer is center tap) into two voltages:
V2 = 120 V; V3 = 120 V.
Three resistive loads (R1, R2, R3) are connected to the transformer (connection not shown in figure 8.42).
R1 is connected to the 240 V line.
R2 and R3 are connected to each of the 120 V lines.
Determine the power absorbed by each of the loads, if:
Power absorbed by R2 = P2
Power absorbed by R1 = 5P2
Power absorbed by R3 = 1.5P2
Ccurrent through primary coil, I1 = 1.5625 A.
                → Solution: the strings and the math.

Ideal Transformer

Ideal Transformer
Figure 8.35 shows an Ideal Transformer. Show that: The apparent power of the primary coil equals the apparent power of the secondary coil.
                → Solution: the strings and the math.

Band Pass Filter

Frequency Response Of Band Pass Filter
Figure 7.56 shows a circuit of a simple RLC filter. Determine:
(a) The frequency response of the RLC filter in terms of the natural or resonant frequency.
(b) The bandwidth in terms of the natural or resonant frequency and the quality factor.
                → Solution: the strings and the math.

High Pass Filter

Frequency Response Of High Pass Filter
Figure 7.50 shows a circuit of a simple RC filter. Determine:
(a) The phasor form of the frequency response, H(jω) in terms of ω, R and C.
(b) The cutoff frequency of the RC filter.
                → Solution: the strings and the math.

Low Pass Filter

Frequency Response Of Low Pass Filter
Figure 7.49 shows a circuit of a simple RC filter. Determine:
(a) The phasor form of the frequency response, H(jω) in terms of ω, R and C.
(b) The cutoff frequency of the RC filter.
                → Solution: the strings and the math.

Phasor Form Of Periodic Signals

Phasor Form Of A Periodic Signal
Figure 8.25 shows the sum Vs(t) of the sinusoidal voltage signals V1(t) and V2(t).
Determine the phasor form of Vs given the following information:
V1(t): amplitude = 15; frequency = 377; phase angle = 45o.
V1(t): amplitude = 15; frequency = 377; phase angle = 30o.
                → Solution: the strings and the math.

Frequency Response Of Output Voltage At High And Low Frequency

Frequency Response
Figure 6.11 shows a circuit of the given elements. Determine the behavior of the frequency response of the voltage V0 at extremely high and low frequencies.
                → Solution: the strings and the math.

Random Signals

The signal v(t) from a voltage source is a binary waveform: it is either 0.5 V or -0.5 V.
The sign change has a 50-50 chance of occurrence within the interval of 1 μs. In other words, v(t) has an equal chance for positive or negative values within this interval.
What is the average and effective values of v(t) over a period of 5 secs?
                → Solution: the strings and the math.

Periodic Signals

Signaling is a ubiquitious phenomenon in the societies of cognitive beings.
(a) What is a signal?
(b) What is a periodic signal?
(c) Identify the following periodic waveforms:
(i) Sinusoids
(ii) Periodic Pulse
(iii) Sawtooth Waveform
                → Solution: the strings and the math.

Even Functions - Odd Functions

Even And Odd Functions
Figure 7.13 shows two periodic signals (blue and red). Which of the signals is an even function and which is an odd function.
                → Solution: the strings and the math.

Mind Warm Ups

The Universe is composed of matter and radiant energy. Matter is any mass-energy that travels with velocities less than the velocity of light. Radiant energy is any mass-energy that travels with the velocity of light.

The Point

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.
Functions
Conics
Ordinary Differential Equations (ODEs)
Vector Spaces
Real Numbers

More Strings (SiPjAjk)


Rocket Work Take That Load Up
Cable Work Bring That Load Up
Friction Work Bring That Moving Object To Stop
Escape Velocity
Signals From Mars
Speed Of A Satellite In An Orbit
Acceleration Of Object In Circular Motion With Constant Speed
Object Thrown Up From The Roof
Maximum Height Of A Projectile
Maximum Range Of A Projectile
Direction Of A Projectile
Difference Between Matter And Radiant Energy
Difference Between Mass And Weight
Einsteins Energy Formula Applied To Uranium-235 Detonation
Water At Bottom Of A Water Fall Warmer Than Water At Top
Air Plane In Flight-Head Wind Tail Wind
Couples In Equilibrium
Sound Travel In An Iron
Shell Fired At An Angle
Range Of A Projectile
How Deep Is The Well
Slow And Steady Average Speed Of Auto
Kings An Aces
Inclined Plane
Car Choices
Free Falling Pebble-2
Free Falling Pebble
Meridian Travel
Row Your Boat
Composition Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Structure Of Matter
Bond Length Bond Angle
Valence Shell Electron Pair Repulsion
Molecular Shape Orbital Hybridization
Sigma Bonds Pi Bonds
Non ABn Molecules
Molecular Orbital Theory

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time
What is Space?
Newton On Space
Space Governance
Leaders
Imperfect Leaders
Essence Of Mathematics
Toolness Of Mathematics
The Number Line
Variables
Equations
Functions
The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being
Forgiveness

Blessed are they that have not seen, and yet have believed. John 20:29

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