Category: Physics Notes PPT

A wave that generally travels continuously in a medium of the same direction without the change in its amplitude is known as a traveling wave or a progressive wave.

 

Let us consider the example of a progressive wave on a string. Here, we will describe the relationship.  

 

In the subjects of Maths and Physics, we will see that this topic is very much related. A propagating dynamic disturbance is known as the waves of one or even more than one quantity. We will discover further about the waves and its progressiveness in this article.

 

What is Progressive Wave

An equation generally can be formed to represent generally the displacement of a particle that is vibrating in a medium through which a wave passes. Thus, we can see that each particle of a progressive wave executes simple harmonic motion of the same period and amplitude differing in phase from each other.

 

Let us now assume that a wave that is progressive generally travels from the origin O along the positive direction of the X-axis from left to right. The displacement of a particle at a given instant is as follows: 

 

y = a sin ωt            …… (1)

 

where we can see that a is the amplitude of the vibration of the particle and then ω = 2πn.

 

The displacement of the particle denoted by letter P at a distance x from O at a given instant is given by,

 

y = a sin (ωt – φ)           …… (2)

 

If two particles are said to be separated by a distance by symbol λ they will differ by a phase of 2π. Therefore we can say that the phase denoted by symbol φ of the particle P at a distance

 

x is  φ = 2π/λ x

 

y = a sin *ωt – 2πx/λ          …… (3)

 

Since we see that the symbol ω = 2πn = 2π (v/λ), the equation is given by

 

y = a sin

 

(2πvt/λ)−(2πx/λ)

 

(2πvt/λ)−(2πx/λ) 

 

y =  a sin 2π/λ (vt – x)               …… (4)

 

Since ω = 2π/T we see that the equation (3) can also be written as,

 

y = a sin 2π *t/T – x/λ)            …… (5)

 

If the wave that generally travels in the direction which is opposite the equation generally becomes

 

y = a sin 2π (t/T + x/λ)             …… (6)

 

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Progressive Wave – Important Points

• Each particle that is present in the medium executes the vibration which is about its mean position. The disturbance that progresses is from one particle to another.

• The particles of the medium vibrate with the same amplitude about their mean positions.

• Each particle or we can say that the successive particle of the medium performs a motion similar to that of its predecessor along the direction of the propagation of the wave, but later in time.

• The phase of every particle changes from 0 to 2π.

• No particle generally remains permanently at the position which is at rest. Twice during each vibration, the particles are momentarily at rest at extreme positions. The particles which are different attain the position at different times.

• The transverse progression of the waves is characterized by crests and troughs. The waves which are longitudinal are characterized by compressions and rarefactions.

• There is an energy transfer as well which is across the medium in the direction of propagation of progressive waves.

• All the particles generally have the same maximum velocity when they pass through the mean position.

• The displacement of the velocity and acceleration as well of the particle separated by the equation that is mλ are the same, where m is an integer. 

 

The Intensity of Progressive Wave

If we generally hear the sound which is produced by violin and the instrument flute or harmonium, we get a pleasing sensation in the ear whereas the sound which is produced by a gun, horn, a motor car, etc., generally produces unpleasant sensation in the ear.

 

The loudness that is generated by the sound depends on the intensity of the sound wave and the sensitivity of the ear.

 

The intensity is generally defined as the amount of energy that is crossing per unit area per unit time that is perpendicular to the direction with respect to the propagation of the wave.

 

Intensity is measured in the W m–2.

 

Types of Progressive waves 

Progressive waves are also known as traveling waves. It reveals continuously. The main characteristic of a progressive wave is that it travels in continuity without a stop or change in its amplitude or direction. If there is one or even more than one quantity, then it is known as a propagating dynamic disturbance.

 

Progressive waves are further classified into two types. One: transverse wave and the second: longitudinal beam. To see how transverse waves are formed, first take a long rope and attach one end to a peg on a wall, stretch it and set it to oscillate up and down at the free end. A bump is formed on the rope which travels in the forward direction. These waves are called transverse waves. 

 

Here, in a transverse progressive wave, the displacement of particles of a medium are at right angles to the direction of the propagation of the wave. When a stone is dropped and still, the water surrounding it moves up and down, therefore right causing circular peaks a circular depression is formed around its circular peak. Thus alternate peaks and depressions are formed with an increasing radius; the peaks are called crest and the depressions are called trough. A crest and a trough make up a wave. 

 

A longitudinal wave is another type of progressive wave. When the displacement of particles of the medium is parallel to the direction of propagation of the wave, the wave is said to be a longitudinal progressive wave. When a spring-mass system oscillates, a longitudinal progressive wave travels along its length in the form of compression and rarefaction. 

A Physicist named Murray Gell-Mann introduced the term ‘quark.’ Here, quark is a type of fundamental particle and a constituent of matter. The interaction between quarks is possible by a subatomic particle or a glue called a gluon.

Now, talking about chromodynamics, the aforementioned statement about the QCD discusses the strong interaction in terms of an interaction between quarks mediated or transmitted by gluons, where both quarks and gluons are assigned a quantum number called ‘colour.’

On this page, we will understand QCD quantum chromodynamics, and lattice quantum chromodynamics in detail.

Quantum Chromodynamics Definition

A quantum field talks of the following two theoretical theories:

Quantum electrodynamics talks about the electric charge; however, quantum chromodynamics classifies the interaction between quarks and gluon in terms of colour. It means QCD Quantum Chromodynamics is analogous to QED Quantum Electrodynamics.

In the nutshell, theoretical Physics talks a lot about QCD or quantum chromodynamics. QCD is the interaction between quarks and gluon. Quarks and gluons make up the composite particles, like protons, neutrons, and pions. Therefore, the interaction between these particles is allocated a quantum number, known as colour.

Point to Note:

In QCD, gluons evolve the theory all around, as it the force carrier of QCD, like photons are for the electromagnetic force in QED theory. 

History of Quantum Chromodynamics

In 1973 the concept of colour because the source of a “strong field” was developed into the idea of QCD by European physicists Harald Fritzsch and Heinrich Leutwyler, alongside American physicist Gell-Mann. 

They used a general field theory developed by Chen Ning Yang and Mills in the 1950s when the carrier particles of a force could themselves radiate further carrier particles.

Properties of Quantum Chromodynamics

Quantum Chromodynamics for dummies is extensively expressed in the two following properties:

• Colour confinement, and

• Asymptotic freedom

Colour Confinement

This property is seen as a consequence of the constant force transfer between two coloured electric charges during their separation: A large amount of energy is required to increase the separation between two quarks within a hadron, as they are very tightly bound in their lattice.

Since we discussed the “lattice,” thing here. It indicates that quarks are fixed in their lattice points, and we need excess energy to set two quarks apart. In the nutshell, QCD is called lattice quantum chromodynamics.

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So, what happens further is, this energy added to the system intensifies on spontaneously producing a quark-antiquark pair, turns the initial hadron into a pair of hadrons rather than producing an isolated coloured charge. 

Do you know?

Though the above analysis on colour confinement is just theoretical; however, this theory is well established from lattice QCD calculations and decades of experiments. 

This is the mere reason, we call the above analysis as lattice quantum chromodynamics.

Asymptotic Freedom

Asymptotic meaning is a straight line that recurrently reaches a given curve but hardly meets the curve at a finite distance.

The asymptotic freedom property of QCD describes a steady decrease in the magnitude of interactions between quarks and gluons, as the energy scale of those interactions increases with the decrease in the scale length.

Point to Note:

Asymptotic freedom is the second property of quantum chromodynamics. It was discovered in 1973 by two American theoretical physicists named David Jonathan Gross and Frank Wilczek, and independently by another American theoretical physicist Hugh David Politzer in the same year. For this work, all three shared the 2004 Physics Nobel Prize.

Point to Note:

In the nutshell, asymptotic freedom is large energy that corresponds to short distances – it infers that there is no interaction between the particles. 

Do You Know?

Every particle physics theory is affirmed on certain natural symmetries whose existence is deduced from observations. These are often called local and global symmetries, the definition of these are as follows:

However, QCD may be a non-abelian gauge theory (or Yang-Mills theory) of the SU(3) gauge group that was obtained by taking the colour charge to define an area symmetry.

Here, non-abelian is sometimes called non-commutative during which there exists a minimum of one pair of elements: a and b of a group (G, *), such a ∗ b ≠ b ∗ a.

Since the strong force cannot differentiate among various flavours of quark, QCD has approximate flavour symmetry, which is broken by the differing quark masses.

Unsolved Problems in Quantum Chromodynamics

There are the two following questions, each on the property of QCD that need to be answered:

1. Confinement

The QCD equations are yet unsolvable at energy scales relevant for describing atomic nuclei. 

A query comes across that how does QCD produce the physics of nuclei and nuclear constituents?

2. Quark Matter

The equations of QCD assume that plasma/soup of quarks and gluons should be formed at heat and density. 

But the properties of matter at this phase still creates a big question mark.

What is a Rainbow?

Rainbow is one of the well-known optical effects that are related to weather, and one of nature’s most glorious masterpieces which result from the refraction of sunlight from falling water droplets plus the reflection of the light from the back of the droplet.

It’s an excellent demonstration of the dispersion of light and proof that visible light is composed of a spectrum of wavelengths, each associated with a distinguishing color.

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You will be surprised to know that you can even see it on sunny days when you are near the waterfalls or fountains.

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             Rainbow in waterfalls                                               Rainbow in fountains

What Are the Rainbow Colors?

We know that rainbows are made by the dispersion of white light by the water droplets.

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Rainbow has seven primary colors in the order of ROYGBIV, i.e., red, orange, yellow, green, blue, indigo, and violet.

What Makes a Rainbow?

We can see anything because the light falling on our eyes, enables us to view them.

Similarly, the red light coming from the upper part of the rainbow reaches our eyes enabling us to see it.

When we look at this color, we would wonder where this light is coming from?

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Let’s consider a single droplet in the red color region, a ray of white light incidents on the surface of it, will reflect some light in the boundary and refract some of it.

The reflected light is white again, and it goes away from our eyes, so we ignore this as this light doesn’t help in forming rainbows.

We know that the white light of the sun is composed of seven colors which are VIBGYOR.

When this white light is passed through the prism, it breaks this white light into its constituent seven colors.

The water droplets during rainfall behave exactly like a prism.

They disperse the white sunlight at the entry point, then this dispersed light falls onto the rare side of the droplet and each light color is again refracted by different angles.

If you observe, this light gets refracted in the same medium.

Here, you can see the light didn’t pass from the water droplet to the air.

Well, this happens because of an optical phenomenon known as the total internal reflection.

Generally, when the light passes from denser to rarer medium, it bends away from the normal.

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However, in the case of total internal reflection, there is an angle called critical angle, ic, the angle at which the refracted ray becomes perpendicular to the normal.

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If you further increase the angle of incidence, the refracted ray remains in an incident medium.

Here, you can notice that a ray of light gets reflected in the same medium.

The same thing happens with the water droplet as well, this angle of incidence at this surface for each colored light is such that they all bend in the same medium, so these different colored light rays are now at the air-water interface again for the third time. However, at this time, the total internal reflection doesn’t occur and these rays bend in the air but now these rays are separated by some amount.

This is because the three refractions created a larger gap between these colors, so all the water droplets in the red region of the rainbow behave in the same manner.

You can see the red color only while all other light colors got refracted.

This is because only the red color from this region reaches our eyes while all other colors are refracted at such a large angle that they don’t reach our eyes on the ground. Similarly, it happens for the region of other colors as well.

This is how rainbows form in the sky.

How to Make a Rainbow?

Things required to make rainbows are:

1. Granulated sugar

2. Coloring tablets or food coloring water

3. Straw

4. Six glasses

5. Measuring spoon

Instructions

Fill each glass with water and add different amounts of sugar in each glass numbered from 1 to 5.

1. Add 0 tablespoon of sugar and red color to it.

2.  Add one tablespoon of sugar and orange food color to it.

3.  Add two tablespoons of sugar and yellow food color to it.

4.  Add three tablespoons of sugar and green food color to it.

5. Add four tablespoons of sugar and blue food color to it.

6. Add five tablespoons of sugar and food color to it.

Stir these glasses until the sugar is dissolved.

Now, transfer about half of the blue into the empty glass, slowly add green water of the same amount on the top of the blue water, and do the same for the next colors.

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You can see a beautiful rainbow. 

How to Create a Rainbow?

Materials Required

1. Water 

2. Sunlight

Tools

1. Prism

2. Whiteboard

Method 

1. Place a whiteboard on the ground under the sunlight.

2. Place the prism above the whiteboard.

3. Now, rotate the prism at certain angles until you get a rainbow.

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Refraction is the bending of light as it passes through a transparent substance. Water, sound, and other waves do it too. This bending had allowed the creation of magnifying glasses, prisms, lenses, etc. 

Here, the degree to which refraction occurs relies on the light’s wavelength. Each light wave has a range or set of wavelengths and will so deviate in a different direction. 

Key Features of Refraction

• Refraction is important in the lens, eye, sound, water, and focal length formation. 

• In a slower medium, the wavelength is also shortened.

• The Index of Refraction describes how light in a medium is divided by light in a vacuum. The formula is n=c/v, where n is the index of refraction, c the vacuum velocity, and v the medium velocity.

Types of Refraction 

Diffuse refraction of light – It scatters light in a variety of directions.

Specular refraction – The angle at which light strikes a specular surface is the same as the angle at which the light strikes the surface.

Glossy refraction – A glossy surface has micro-surfaces angled to the surface plane.

Light is refracted when:

• No change in frequency of the refracted beam.

• Partially reflected and absorbed light at the contact reduces the strength of refracted rays.

• Light deviates when it crosses a border between two mediums. Light’s wavelength and speed vary during refraction.

Refractive Index

The refractive index of the material medium is the ratio of the speed of light in a vacuum to the speed of light in the material medium.

How much of a wave has been refracted is determined by the difference in speed and the initial direction of propagation relative to the direction of speed change.

Dispersion of Light

When light passes through a transparent medium, dispersion is defined as the splitting of the light beam into its seven constituent colours.

Sir Isaac Newton described this occurrence in 1666 A.D. When sunlight passes through a glass prism, he discovered that white light is made up of seven distinct hues.

A rainbow against a dark stormy sky is a sight to behold. How does sunlight on clean raindrops create the rainbow of colours we see? A clear glass prism or a diamond employ the same method to colourize white light.

What causes this to happen? This is due to a phenomenon known as ‘Dispersion of Light,’ which occurs in conjunction with refraction.

The spreading of white light into its complete spectrum of wavelengths is known as dispersion. The spectrum of colours are:

• Violet

• Indigo

• Blue

• Green

• Yellow

• Orange 

• Red

“Spectrum” refers to a ring of brightly coloured lights.

An illustration of light dispersion via a glass prism can help comprehend it better.

Glass Prism – Dispersion of Light

The prism is a five-sided solid with two triangle bases and three rectangular surfaces that are angled inwards.

One of the rectangular faces sends light into the prism, which enters through one of the other rectangular faces and exits through the other rectangle face. The refractive index of different hues of light varies because they travel at different speeds. As a result, when white light passes through the prism’s refracting surface, its constituents bend at different angles, splitting the single beam of light. Because of the refraction induced by the second rectangular surface, the distinct colours of light bend again.

When white light passes through a glass prism, it is split into its component colours. The sole reason for this is Refraction.

After polychromatic light enters from a less dense medium to a large dense medium, refraction causes each colour of light to take a separate path.

Causes of Dispersion of Light 

The cause of dispersion of light through the prism is that white light has a range array of seven colours, and each of those has a subsequent angle of deviation. As such, when light passes through a prism, different colours deviate from different angles. Therefore, those colours get separated and form a series of bands called a spectrum. Out of those seven colours, the red one deviates the least and has got the position on top of the spectrum. Whereas the violet colour deviates most, that is why it has got the position at the bottom of the spectrum.

Here, the sole cause of dispersion of light is refraction.

Because of refraction, every colour of light takes a different path after polychromatic light enters from the less dense medium to a large dense medium. This happens as per Snell’s law. It states that sin()/sin(r) is different for a different colour of light and medium where it travels. Therefore, the split light represents the component of the original incident light.

The above-mentioned explanation shows how dispersion occurs. One thing to be noted here is that in the case of normal incidence, dispersion and refraction doesn’t occur.

Fun facts- Have you ever seen the rainbow and got mesmerized by its natural beauty? They are the perfect phenomenon that occurs and is the best example to bring light for “dispersion of light” alongside refraction. This is the reason you can see rainbow-like occurrences in both crystals and prisms. 

What is Dispersion of White Light?

Dispersion of White Light by a Prism is shown here below:

Wavelength is inversely proportional to the deviation where the light travels. Here, the prism only acts as a medium for dispersion made of seven different colours. Further, refraction occurs when light rays fall on it, and depending on that, the frequency and wavelength deviate differently at a different angle because of the difference in their velocities. The colour deviates the least because it has a maximum wavelength, and the violet colour deviates the most because of its lesser wavelength.

The reason for light dispersion through prisms is because white light has a range of seven hues, each with its angle of deviation.

Light passing through a prism deviates from one colour to another. So the colours divide into a spectrum of bands. 

Red is the colour that deviates the least from the others and is, therefore, the most dominant. 

Light dispersion is caused only by refraction.

After polychromatic light enters a big thick medium, refraction causes each colour to take a separate route. Snell’s law dictates this. It states that sin(i)/sin(r) varies with light colour and medium. So the split light is the original incident light component.

Types of Dispersion

There are several types of dispersion, each of which functions in a unique way, but the three most common are detailed below:

1. Material dispersion (chromatic dispersion)

Rather than a single narrow wavelength, both lasers and LEDs create a variety of optical wavelengths (a band of light).

At different wavelengths, the fibre has varied refractive index characteristics, hence each wavelength travels at a different speed in the fibre.

As a result, some wavelengths arrive ahead of others, causing a signal pulse to disperse (or smears out).

2. Mode dispersion (intermodal dispersion):

When light travels through a multimode fibre, it can take many different routes or “modes” as it travels through the fibre.

Each mode’s distance travelled by light differs from the distance travelled by other modes.

Parts of a pulse (rays or quanta) can adopt several distinct modes when it is transmitted (usually all available modes).

As a result, some pulse components will arrive before others. As the distance between the fastest and slowest modes of light increases, the difference in their arrival times increases.

3. Dispersion of the waveguide

The form and index profile of the fibre core generate waveguide dispersion, which is a very complex phenomenon. However, the proper design can manage this, and waveguide dispersion can even be utilised to counteract material dispersion.

Different fibres’ dispersion:

Waveguide dispersion > mode dispersion > material dispersion

The equilibrium constant, k, is a number that describes the relationship between the number of products and reactants present at equilibrium in a reversible chemical reaction at a given temperature.

K_p and K_c are equilibrium constants of ideal gas mixtures considered under reversible reactions. K_p is an equilibrium constant written with respect to the atmospheric pressure and the Kc is the equilibrium constant used with respect to the concentrations expressed in molarity. The K_p K_c relation can be derived by understanding what are K_p and K_c. 

Let’s consider the general equilibrium equation:

A + B  ⇌ C + D

According to the law of mass action,

The rate at which A reacts ∝ [A]

The rate at which B reacts ∝ [B]

∴ The rate at which A and B react together ∝ [A][B]

So, the rate of the forward reaction = kf [A][B]

Where kf is the velocity constant for the forward reaction.

Now, the rate at which C and D react together ∝ [C][D] 

So, the rate of the backward reaction = k_b [C][D] 

k_b = velocity constant for the backward reaction.

At equilibrium, the rate of the forward reaction = rate of the backward reaction.

  kf [A][B] = kb [C][D]

  [frac{[C][D]}{[A][B]}=frac{kf}{kb}]

At constant temperature k_f and k_b are constant, therefore,[frac{kf}{kb}]=k is also constant at a constant temperature.

Here, k is called the Equilibrium constant.

Equilibrium Constant kc

Let us consider a general reversible reaction:

aA + bB ⇌ uU + vV

Applying the law of mass action here:

[frac{[U]^{u}[V]^{v}}{[A]^{a}[B]^{b}}]= k or kc

In terms of expression of concentrations, k is written as kc.

This mathematical expression is called the law of chemical equilibrium.

Equilibrium Constant Definition

At a constant temperature, the equilibrium constant is the ratio of the product of the molar concentrations of the products, each raised to the power equal to its stoichiometric coefficient and the product of molar concentrations of the reactants, each raised to the power equal to its stoichiometric coefficient.

Do you know how to find equilibrium constant k_p for the reaction?

Let’s derive the equilibrium constant formula for gas-phase reactions:

The Equilibrium Constant k_p for the Reaction

When both reactants and products are in gaseous states, then we express equilibrium constant either in terms of concentration in moles per liter or partial pressures of the reactants and the products. 

Derivation:

The relation between Kp and Kc is given by the following simple derivation. To derive the relation between Kp and Kc, consider the following reversible reaction:

‘a’ mole of reactant A is reacted with ‘b’ mole of reactant B to give ‘c’ moles of product C and ‘d’ moles of product D, 

aA + bB ⇌ cC + dD

Where a,b,c, and d are the Stoichiometric coefficients of reactants A, B and products C, D.

What is kc? 

kc is the equilibrium constant for a reversible reaction and it is given by,

[kc=frac{C^{c}.D^{d}}{A^{a}.B^{b}}]

Where,

C – The molar concentration of product ‘C’

D – The molar concentration of product ‘D’

A – The molar concentration of reactant ‘A’

B – The molar concentration of reactant ‘B’

Where,

PC – Partial pressure of product ‘C’

PD – Partial pressure of product ‘D’

PA – Partial pressure of reactant ‘A’

PB – Partial pressure of reactant ‘B’

Similarly,  Kp is the equilibrium constant in terms of atmospheric pressure and is given by the expression:

                aA + bB ⇌ cC+ dD

 Then, equilibrium constant formula for 

Where pv, px, py, and pz are the partial pressures of V, X, Y, and Z, respectively.

The partial pressures are taken in the following units:

1. Atm

2. Bar

3. Pascal

Relation between  Kp and Kc

To derive a relation between  Kp and Kc, consider the ideal gas equation,

PV = nRT

Where,

P – Pressure of the ideal gas

V – Volume of the ideal gas

n – Number of moles

R – Universal gas constant

T – Temperature

On rearranging the above equation for P,

P = nRT/V…………..(3)

We know that the ratio number of moles per unit volume is the molar concentration of the substance, hence we can write the pressure equation as:

P = molar concentration RT ………………..(4)

Therefore the partial pressures of A, B, C, and D can be calculated by using equation (4):

⇒ PA = A RT

⇒ PB = B RT

⇒ PC = C RT

⇒ PD = D RT

Let us consider a general reversible reaction equation:

                         aA + bB ⇌ cC + dD

Substituting the above values in equation (a), and simplify:

[kp=frac{C^{c}.D^{d}RT^{c+d}}{A^{a}.B^{b}.RT^{a+b}}]

Also, we may write equilibrium constant  (kc)  in terms of molar concentrations as;

So, from eq 

[kp=frac{C^{c}.D^{d}RT^{c+d}}{A^{a}.B^{b}.RT^{a+b}}]

[kp=kc ast RT^{(c+d)-(a+b)}]

Where,

c + d – Number of moles of product = np

a + b – Number of moles of reactant = nr

Therefore, 

(c + d) – (a + b) = np – nr = Δng

Thus we get the relation between Kp and Kc,

kp = kc [(RT)^{Delta n}]

Where,

Δng – Change in gaseous moles of reactant and the product.

This is the required expression that gives the relation between the two equilibrium constants. The relation between Kp and Kc Pdf can be downloaded. Depending on the change in the number of moles of gas molecules, Kp and Kc relation will be changing.

In other terms, we have kc in molar concentration in the following manner:

[kc=frac{CC^{c}.CD^{d}}{CA^{a}.CB^{b}.}]….(b) 

Ca, Cb, Cc, and Cd express the molar concentrations of A, B, C, and D, respectively. 

If we consider the gas as an ideal, then we can apply the ideal gas equation, that is:

pV = nRT or p = [frac{n}{v}]RT = CRT

∵ [frac{n}{v}] =[frac{text{Number of moles}}{text{Litre}}]= C (Molar concentration)

∴ For the gases V, X, Y, and Z, we may write the equation (1) and (2) as;

            pa  = CaRT …(a)

            pb  = CbRT …(b)

            pc  = CcRT …(c)

            pd  = CdRT …(d)

Now, putting values of equations (a), (b), (c), and (d) in equation (2):

             kp  = [frac{(CcRT)^{c}.(CdRT)^{d}}{(CaRT)^{a}.(CbRT)^{a}}]

                  = [frac{CC^{c}.CD^{d}.(RT)^{c+d}}{CA^{a}.CB^{b}.(RT)^{a+b}}]

                  = [frac{CC^{c}.CD^{d}}{CA^{a}.CB^{b}}(RT)^{(c+d)-(a+b)}]  

                  =  kc [(RT)^{Delta n}]

 Where kc =[frac{CC^{c}.CD^{d}}{CA^{a}.CB^{b}}]from equation (2), and

 Δn = (c + d) – (a + b) 

       = No. of moles of products – No. of moles of reactants

       = Change in the number of moles

Hence,             

Where R is the Universal Gas Constant whose value is 0.821 liter-atm per degree kelvin-mole, and

T = Temperature in degree Kelvin (°K).   

Here, Δng – Change in gaseous moles of reactant and the product.

This is the required expression that gives the relation between the two equilibrium constants. The relation between kp and kc Pdf can be downloaded. Depending on the change in the number of moles of gas molecules, Kp and Kc relation will be changing.

Case-1:

If Δng = 0, i.e., if the change in the number of moles gas molecules in the equation is zero.

Then Kp = Kc

Case-2:

If the change in the number of moles of gas molecules is positive, i.e., if Δng > 0 then,

Kp > Kc

Case-3:

If the change in the number of moles of gas molecules is negative, i.e., if Δng < 0 then,

Kp < Kc

Equilibrium Constant Units     

For the general reaction: aA + bB ⇌ cC + dD               

kc =[frac{CC^{c}.CD^{d}}{CA^{a}.CB^{b}.}] = [frac{(MolL^{-1})^{c+d}}{Mol L^{-1})^{a+b}}] = [(Mol L^{-1})^{(c+d)-(a+b)}=(Mol L^{-1})^{Delta n}]

So, the unit of kc is[Mol L^{-1}], and

kp = [frac{PC^{c}.PD^{d}}{PA^{a}.CP}]=  [frac{(atm)^{(c+d)}}{(atm)^{(a+b)}}]= [(atm or bar)^{(c+d)-(a+d)} or (atm or bar)^{Delta n}]

So, the unit of kp = atm or bar.

Application of Equilibrium Constant

One of the applications of the equilibrium constant is to predict the extent of reaction. 

The magnitude of the equilibrium constant gives an idea of the relative amounts of the reactants and products.

For example, consider the following reversible equation and hence calculate Kp and Kc and derive the relationship between Kp and Kc:

                H2 (g) + Br2 (g) ⇌ 2 HBr(g) (kp = 3 x 1019)

                H2 (g) + Cl2 (g) ⇌ 2 HCl(g) (kp = 5 x 1029)

Here, values of kp are very high, i.e., reactions go almost to completion. 

Another Example:

  H2  + I2   ⇌ 2 HI

Solution:

Given the reversible equation,

  H2  + I2   ⇌ 2 HI

The change in the number of moles of gas molecules for the given equation is,

⇒ Δn = number of moles of product – number of moles of reactant

⇒ Δn = 2 – 2 = 0

Therefore, Kp = Kc

Then, Kp and Kc of the equation is calculated as follows,

 [kc= frac{HI^{2}}{H^{2}I^{2}}]

Solved Examples on Kp and Kc

Example 1: For the reaction,

N2O4(g) ⇌ 2 NO2(g) 

The concentration of the equilibrium mixture at 293 K of N2O4 is 5 x 10-8mol/L, and of NO2 is 2 x 10-6mol/L. Find the value of the equilibrium constant.

Applying the formula, k =[frac{[NO]^{2}}{[N2O4]}]

Taking the concentrations w.r.t. standard state concentration of 1 mol/L:

k =[frac{(2×10^{-6})^{2}}{5×10^{-8}}=8×10^{-5}]

Example 2: For the reaction,

N2 (g) + 3H2 (g) ⇌ 2 NH3(g)

If pN2 = 0.30 atm, pH2 =  0.20 atm, and pNH3 = 0.40 atm, then what is the value of kp?

Using the formula, kp =[frac{pNH3^{2}}{pN2.pN2^{2}}]

=[frac{(0.4)^{2}}{(0.3).(0.2)^{2}}]= 13.3 atm

In Physics, every physical entity can be measured in different ways. Every unit can be related to one another by performing unit conversions without violating the laws of physics and laws of nature. 

 

Newton is the SI unit of force and kg is the unit of mass. According to Newton’s Second law of motion, force is directly proportional to the mass of the object on which force has been exerted. Thus we can say Newton and Kg are also directly proportional to each other, thus if we encounter any change in the unit of force in Newton it will result in a change in the unit of mass in Kg keeping the acceleration constant.

 

To arrive at a mathematical description for the relation between Kg and Newton, let us discuss the definition of Kg and Newton respectively. In this article, we try to explain to students the concept with great simplicity and clarity making the students grasp the knowledge with ease. 

 

Table of Content – 

• Introduction

• Meaning of KG

• Meaning of Newton

• Derivation

• Examples 

• Learning from the topic 

• Benefits of referring the notes 

• Frequently asked questions 

 

What is Kg?

There are seven fundamental units in physics, Kg is one of them. (Fundamental units are the units that are independent quantities, all other units are derived from them). The Abbreviation of Kilogram is Kg.

 

1 Kilogram is nearly equal to 1000grams. The kilogram is one of the basic units of metric systems.

 

What is Newton?

Newton is the SI unit of Force. It is defined as the force required to accelerate an object of the mass of 1 kilogram (1kg) by 1m/s² in the direction of applied force. In the CGS system, 1N is equal to 10⁵ Dyne. Dyne is the unit of Force in the CGS system.

 

Derivation

Mathematically we can describe one Newton by using Newton’s second law of motion,

I.e.,

 

⇒ F = ma

 

⇒ 1 Newton = 1Kg x 1m/s²

 

From the above expression, Newton is directly proportional to Kg. Therefore,

• If the object under consideration is having negligible mass or considerably less mass then the force required in Newton will also be very less.

• If the object an action-heavy, then the force required will also be more.

1N is Equal to How Many Kg?

We can not convert Kg to Newton, because Newton is a unit of Force whereas Kg is the unit of mass respectively. Conversion of units can be done for two identical scales but not for two different physical scales. So, we can give a relation for the two units, saying conversion of them will be the wrong term.  

 

When an object is dropped from a certain height above the ground level, it will experience a force purely due to the acceleration due to gravity. While free fall the object will experience a force and the force experienced is known as Weight of the body/object and mathematically is given by:

 

W = mg ……..(1)

 

Now we can give a relation between newton and kg by analyzing how many Kg in one Newton. Let us assume that a 1Kg mass is dropped from a height above ground level with an initial velocity zero then the force experienced by the object is,

 

W = 1Kg x 9.81 m/s² = 9.81 N

 

From the discussion of the relation between Kg and Newton, we have concluded that they are directly proportional to each other. Therefore, we write:

 

1Kg=9.81N

 

Therefore, 1 newton is equal to how much Kg or 1 kg how many newtons? The answer is 9.81N.

 

Similarly, If the question demands for 1 kg wt is equal to how many newtons? (Which is in terms of gravitational force) Then also the answer is either 9.8N or 9.81N or 10N because the value of acceleration due to gravity is considered depending upon the convenience.

 

Example

1. The mass in Kg of an object that Weighs about 40N.

Ans: Given that weight of the object is 40N.

We are asked to find the mass of the object.

From the relation between Kg and Newton we have,

⇒ 1Kg = 9.81N

⇒ 1N = 0.102Kg

Thus,

⇒ 40 N = 40 x 0.102Kg = 4.077Kg

Therefore, the mass in kg of an object that weighs about 40N is 4.077.

An alternative method for calculating the mass of an object whose weight is given is as follows:

We know that,

⇒ 1N = 1Kgm/s²

Therefore,

⇒40N = 40Kgm/s²

We want to convert 40N into Kg, to do that divide the above expression by acceleration due to gravity, i.e., divide by 9.81 m/s²

⇒ 40N = 40Kgms−2/9.81 ms⁻²

⇒ 40N = 4.077kg

This is the required answer.

 

2. How many Newtons is 5Kg?

Ans: We know that 1kg = 9.81N, then:

⇒ 5Kg = 5 x 9.81 N = 49.05N

therefore,49.05N is 5Kg.

 

Learning From the Topic – 

• Every object has a unit of measurement, which measure in different ways and forms 

• Kg and Newton are also forms of units of measurement 

• Kg is the unit of a mass where kg equals 1000 grams of mass of an object

• Newton is the unit to measure the force required to accelerate an object of 1kg of mass.

• Newton’s second law of motion is used to derive one newton. The second law says the rate of change of linear momentum of a body is directly proportional to the external force applied to the body in the direction of applied force. 

• Therefore, 1 Newton = 1Kg x 1m/s²

Read the full article to understand more about the concepts and try t
o solve a few practical questions to evaluate your level of understanding of the topic. 

 

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