[Physics Class Notes] on Rolling Motion Pdf for Exam

You must have seen the motion of a rolling ball or a wheel many times, but do you know the kind of motions that an object and its particles undergo while in rolling motion? A combination of translational and rotational motions happen during the rolling motion of a rigid object. To define rolling motion, we must understand the forces like angular momentum and torque. This article will give you the definition of rolling motion, and you would also learn rolling motion equations here.

Rolling Objects Physics

When there is a rolling motion without slipping,  the object has both rotational and translational movement while the point of contact is instantaneously at rest.

Let us first understand pure translational and pure rotational motions.

  • Pure Translational Motion

An object in pure translational motion has all its points moving with the same velocity as its center of mass i.e. they all have the same speed and direction or V(r) = Vcenter of mass. In the absence of an external force, the object would move in a straight line.

An object in pure rolling motion has all its points moving at right angles to the radius (in a plane that is perpendicular to its rotational axis). The speed of these particles is directly proportional to their distance from the axis of rotation. Here V(r) = r * ω. Here ω is the angular frequency. Since at the axis r is 0 hence particles on the axis of rotation do not move at all whereas points at the outer edge move with the highest speed.

  • The points on either side of the axis of rotation move in opposite directions.

  • Vpoint of contact = 0 i.e. the point of contact is at rest.

  • The velocity of the center of mass is Vcenter of mass = R * ω.

  • The point farthest from the point of contact move with a velocity of

Vopposite the point of contact = 2 * Vcenter of mass = 2 * R * ω.

Heave and Pitch

A ship on the sea has 6 different kinds of motions called:

This is a linear motion along the vertical z-axis.

This is also a linear motion along the transverse Y-axis.

It is again a linear motion along the longitudinal x-axis.

This is a rotational motion around a longitudinal axis.

This is a rotational motion around the transverse axis.

This is a rotational motion around the vertical axis.

Mechanical Energy is Conserved in Rolling Motion

As per the rolling motion definition, a rolling object has rotational kinetic energy and translational kinetic energy. If the system requires it, it might also carry potential energy. If we include the gravitational potential energy also then we get the total mechanical energy of a rolling object as:

Etotal = (½ * m * V2center of mass) + (½ * Icenter of mass * ω2) + (m * g * h).

When there are no nonconservative forces that could take away the energy from the system in the form of heat, an object’s total energy in rolling motion without slipping is constant throughout the motion. When the object is slipping them energy is not conserved since there is a heat production due to kinetic friction and air resistance.

Moment of Inertia

Rotational inertia is a property of rotating objects. It is the tendency of an object to remain in rotational motion unless a torque is applied to it.

If a force F is exerted on a point mass m at a distance r from the pivot point, then the point mass obtains an acceleration equal to F/m in the direction of F. Since F is perpendicular to r in the case above, the torque τ = F * r. The rotational inertia is given by the formula m * r2.

Parallel Axis Theorem

If the rotational axis passes through the center of mass, then the moment of inertia is minimal. Moment of inertia increases as the distance of the axis of rotation from the center of mass increases. As per the parallel axis theorem, the moment of inertia about an axis that is parallel to the axis across the object’s center of mass is given by the below formula:

Iparallel axis = Icenter of mass + M * d2

Where d is the distance of the parallel axis of rotation from the center of mass.

Let us understand this with an example: Let there be a uniform rod of length l having mass m, rotating about an axis through its center and perpendicular to the rod. What is the moment of inertia Icenter of mass?

Solution. Moment of inertia of a rod = ⅓ * m * l2

Distance of the end of the rod from its center = l/2

Hence the parallel axis theorem of the rod = ( ⅓ * m * l2) – m * (l/2)2)

                = ( ⅓ * m * l2) – ( ¼  * m * l2

Icenter of mass = 1/12 * m * l2

[Physics Class Notes] on Schottky Diode Pdf for Exam

What is Schottky Diode? 

A Schottky diode, widely popular as barrier diode, refers to a metal-semiconductor diode that comprises lower voltage drops than usual PN-junction diodes. On top of that, it possesses a fast switching speed. 

Their advantage includes the fact that their forward voltage drop is significantly lower than PN-junction diodes. It is because they constitute a metal electrode that links with N-type semiconductor. Contrarily, a PN-junction diode comprises P-type material and N-type material. 

In this case, a P-type semiconductor refers to an intrinsic or pure semiconductor, such as silicon or germanium. In this case, one has to add a trivalent impurity. These trivalent impurities include Boron (B), Gallium (Ga), Indium (In), and Aluminum (Al). These are also acceptor impurities. 

On the other hand, N-type materials refer to the integration of phosphorus, arsenic, antimony, and bismuth to pure semiconductors. 

How Does a Schottky Diode Function? 

A diode in this category functions as per the Schottky diode theory. It states that an essential factor in its functioning is fast switching rate and considerably lower voltage drop. 

Also, it lacks the propensity to store electrical charges at their diode junctions. One of the reasons that enable its working is the overall lack of a depletion layer. In most cases, when current passes through a diode, the terminals witness a drop in voltage. 

The drop conventionally ranges between 0.15 and 0.45 volts as opposed to an ordinary PN-junction diode. In the case of the latter, the spectrum of voltage drop is 0.6 to 1.7 volts. It happens mainly because current advances in a forward direction

Schottky diode working leverages the low voltage drop to generate a higher efficiency and output. For this to happen, the N-type semiconductor has to function as a cathode. The metal assumes the role of an anode. 

What is Schottky Diode Symbol? 

The following diagram represents the Schottky diode symbol – 

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In the above diagram, the anode section is essentially a metal, such as molybdenum, chromium, tungsten, or platinum. On the other hand, n-type semiconductors such as the integration of silicon and bismuth stand for the cathode section. 

What is Schottky Diode Construction? 

The following figure is a pictorial representation of Schottky diode construction and working –

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In this figure, you can see that a lightly doped n-type semiconductor connects to a metal electrode or the anode. Here, you can refer to the connection as ‘metal-semiconductor junction’. When current flows in a forward direction, electrons travel from the n-type material end to the metal anode. 

The drift of majority charge carriers heavily influences the overall current component passing through this category of a diode. However, such diodes also exhibit the properties of a rectifying diode. 

The primary reason behind this is that diode conduction ceases and blocks the flow of current.  It is due to the absence of p-type semiconductor. As a result, these diodes respond rapidly to reverse bias alterations. 

What are the Characteristics of a Schottky Diode? 

Since you know what is Schottky diode and its construction, it is time to move on to its characteristics. 

Therefore, Schottky diode characteristics are as follows – 

  • When compared with conventional PN-junction diodes, these diodes exhibit significantly lower drops in forward voltage. 

  • Forward voltage drops vary between 0.15 and 0.45 volts, as opposed to 0.6 to 1.7 volts in PN-junction diodes. 

  • Forward drop in these diodes increases with the enhancement of doping concentration of N-type semiconductors. 

  • The drop in forward voltage in a Schottky barrier constitutes semiconductors such as Silicon. 

  • Besides, these also act as a unipolar device owing to the lack of current flow from metals to N-type conductors. 

  • The implemented metals do not undergo charge storage. As a result, these switch considerably quickly with a minimum noise component. 

Furthermore, Schottky diode applications include the following – 

  • Implementation in the electronics industry due to its properties as a general diode rectifier. 

  • Radio Frequency (RF) applications also find broad uses of this technology. 

  • These also find application in signal detection and logic circuits. 

What are the Disadvantages of a Schottky Diode? 

Despite its various uses,there are a few disadvantages of Schottky diodes. This includes – 

Since you are now aware of what is Schottky diode, you should check out related concepts to know a lot more about this subject. You can also download our app to avail a convenient and interactive learning experience. 

[Physics Class Notes] on Semiconductor Diode Pdf for Exam

A semiconductor, as the name mentions, is an element that bears partial conducting ability. A semiconductor does neither fit itself under the category of conductors nor under the category of the insulator. Generally, some impurities are always added to the semiconductor for the best results. This process is commonly termed doping. Based on the type of impurity, semiconductors are further categorized into two types- a) p-type semiconductor (positively charged) and b) n-type semiconductor (negatively charged). P and N-type semiconductors have limited usage when they are used in isolation. But when we make a collaborative usage for both p and n-type semiconductors, it is called a p-n junction.

When a p-n junction is affixed to some external voltage provider, for instance, a battery, the complete set-up will be known as a Semiconductor Diode. Though the entire set-up is bi- terminal, the passage of current is unidirectional.

Types of Semiconductors

Semiconductors are classified under two heads based on the connection used:-

  • Semiconductor Diode Forward Bias: It is a very well-known fact that a battery has two terminals- a positive terminal and the other negative one. So, when the semiconductor’s N and P end is fixed with the negative and positive sides of the battery, respectively, the set-up is coined as Semiconductor Diode forward bias. Since the negative extreme will drive away free electrons in the front of the junction, and the P end of the semiconductor will thrust the holes, they will merge at the junction. But free electrons coming out of the battery will penetrate the N region, and the valence electrons abandon the P region, thus creating a movement of current.

  • Semiconductor Diode Reverse Bias: As the name suggests, it is just the opposite concept of forwarding bias. Now, the semiconductor’s N side is affixed with the positive end of the battery. This entire set-up is known as Semiconductor Diode reverse bias. The electrons that arise from the N side of the semiconductor will be directed along with the positive terminal of the battery. The negative terminal will drive the holes away from the junction. The holes and electrons do never meet at the junction, and there is a clog of current in this setup. As we can see, the majority current does not flow in the reverse bias. Instead, there is a reverse flow of current in this situation due to minority carriers.


Symbol of the Circuit

There are certain symbols used to express an electrical circuit. Following the above discussions, we can create a symbol of the Semiconductor Diode. It is represented as:- 

Semiconductor Diode Characteristics

There is a graphical representation of the voltage and current, as applied in the case of Semiconductor Diode forward bias and Semiconductor Diode reverse bias. When a forward bias is raised, we also observe a rise in current up to a stable voltage called knee voltage in a linear fashion. But after this voltage, the current differs in a non-linear way. 

As we know, reverse current does not depend on the reverse bias. Rather this current depends on the temperature of the junction. It is calculated that the current multiplies to the extent of 7% for every 1-degree rise in temperature.

Zener Breakdown

If the reverse bias is raised to a large extent, the electric field also gets expanded, which in turn creates a huge number of electrons and holes. It is defined as a Zener breakdown.

Dynamic Resistance

It is explained as the ratio of minor changes in the voltage to the ratio of minor changes in the current. It is expressed in the form of rd. Therefore the numerical expression of voltage resistance is rd = [frac {Delta V} {Delta I}]

Numerical:- A diode is made constant in a circuit. The voltage falls by 0.5 V, and the highest power marked is 100 mW. What should be the value of the resistor R, which is attached in series to this diode?

Solution:- Current that flows among the diode the, I = [frac {Power} {Voltage}]

Therefore, I= [frac {(100 times 10^-3)} {0.5V}]

 (as we know 1mW= 10-3 W)

= 0.2 A

Resistance=Net Voltage/Current [frac {Net Voltage} {Current}]

= [frac { (1.5−0.5)} {0.2}]

 = 5 Ohm.

The devices made from semiconductors have very much eased our lives. There are different types of diodes like the Semiconductor Diode that are used in many devices. So, it becomes important for us that we know about these devices in detail. The motive of this article is the same i.e it is meant to give you in-depth detail on the Semiconductor Diode. You will be able to study the definition of Semiconductor Diode, its different characteristics and its symbol.

Diode

A diode is a semiconductor device made up primarily of silicon components. The anode, which is inherently positive and has a lot of holes, is positioned next to the cathode, which is negatively charged and contains a lot of electrons. A depletion area forms at this point, with no holes or electrons. A positive anode voltage causes the depletion region to be small, allowing current to flow; a negative anode voltage causes the depletion region to be big, prohibiting current flow.

A diode is a two-terminal electrical component that conducts electricity mostly in one direction. It has a strong resistance on one end and a low resistance on the other.

To limit the voltage across circuits or to convert AC into DC, diodes are used. They also serve to safeguard the circuits. The most common semiconductors used to manufacture diodes are silicon and germanium. Although they both transport electricity, in the same way, however, how they do so, differs. Diodes are available in a range of shapes and sizes, each with its own set of uses.

Diode Construction

The two semiconductor materials that can be utilized to manufacture diodes are silicon and germanium. When the anode voltage exceeds the cathode voltage and the diode conducts readily with minimum voltage loss, it is said to be forward-biased. When the cathode voltage exceeds the anode voltage, the diode is said to be reverse-biased. The direction of conventional current flow is depicted by the arrow in the symbol.

Diode’s Symbol

The anode and cathode are the two terminals of a diode. The anode is represented by the arrowhead. In the forward-biased condition, the anode represents the traditional current flow direction. The cathode is represented by the vertical bar. 

The following are some of the most commonly used and essential diodes:

Tunnel Diode

Because of the quantum mechanical process known as tunneling, a tunnel diode (also known as an Esaki diode) has essentially zero resistance. In tunnel diodes, the PN junction is heavily doped and about 10 nm wide. The n-side conduction band electron states are more or less aligned with the p-side valence band hole levels, resulting in a broken bandgap.

Zener Diode 

The most valuable sort of diode is the Zener diode, which can provide a constant reference voltage. When a specific voltage is supplied, these are reverse biased and break down. When the current flowing through the resistor is limited, a stable voltage is formed. Zener diodes are often used in power supplies to provide a reference voltage.

LED (Light Emitting Diode)

A photodiode can detect even a little amount of current flow induced by light. Even a small amount of current flow caused by light can be detected by a photodiode. When it comes to detecting light, these are incredibly useful. Photodiodes are reverse bias diodes that are commonly found in solar cells and photometers. They’re even used in the generation of electricity.

[Physics Class Notes] on Diffraction of Light – Young’s Single Slit Experiment Pdf for Exam

Diffraction is the line of study that helped in the development of precise spectrometers, hence helping Astronomy take great leaps. This was possible in the early nineteenth century when two great scientists were struggling in their lives separately in Italy and Germany. These two weak youngsters were still struggling to get educated. Fraunhofer was the son of a maker of decorative glasses and mirrors in Bavaria, while Fresnel was the son of an architect in Normandy.

What is Diffraction of Light? 

Diffraction is the bending of light around the sharp corner of an obstacle. When light is incident on a slit, with a size comparable to the wavelength of light, an alternating dark and bright pattern can be observed. This phenomenon is called the single slit diffraction. According to Huygens’ principle, when light is incident on the slit, secondary wavelets generate from each point. These wavelets start out in phase and propagate in all directions. Each wavelet travels a different distance to reach any point on the screen. Due to the path difference, they arrive with different phases and interfere constructively or destructively.

Diffraction Due to Single Slit

When light is incident on the sharp edge of an obstacle, a faint illumination can be found within the geometrical shadow of the obstacle. This suggests that light bends around a sharp corner. The effect becomes significant when light passes through an aperture having a dimension comparable to the wavelength of light.

If light is incident on a slit having a width comparable to the wavelength of light, an alternating dark and bright pattern can be seen if a screen is placed in front of the slit. This phenomenon is known as single slit diffraction.

Young’s Single Slit Experiment

Thomas Young’s double-slit experiment, performed in 1801, demonstrates the wave nature of light. In this experiment, monochromatic light is shone on two narrow slits. The waves, after passing through each slit, superimpose to give an alternate bright and dark distribution on a distant screen. All the bright fringes have the same intensity and width.

In a single slit experiment, monochromatic light is passed through one slit of finite width and a similar pattern is observed on the screen. Unlike the double-slit diffraction pattern, the width and intensity in the single-slit diffraction pattern reduce as we move away from the central maximum.

Explanation of The Phenomenon and Diffraction Formula

According to Huygens’ principle, when light is incident on the slit, secondary wavelets generate from each point. These wavelets start out in phase and propagate in all directions. Each wavelet travels a different distance to reach any point on the screen. Due to the path difference, they arrive with different phases and interfere constructively or destructively.

If a monochromatic light of wavelength λ falls on a slit of width a, the intensity on a screen at a distance L from the slit can be expressed as a function of θ.

Here, θ is the angle made with the original direction of light. It is given by,

I[left ( theta  right )] = I[_{0}] [frac{sin^{2}alpha }{alpha ^{2}}]

Here, [alpha] = [frac{Pi }{lambda }] sin[theta]   and I₀ is the intensity of the central bright fringe, located at θ =0.

Diffraction Maxima and Minima 

Bright fringes appear at angles,

[theta] [rightarrow] 0,[theta][rightarrow]  sin-1 [left ( pm frac{3lambda }{2} right )], [theta] [rightarrow] sin-1 [left ( pm frac{5lambda }{2} right )]

[theta] [rightarrow] 0 is the central maximum

Dark fringes correspond to the condition,

a sin[theta] = m[lambda] with m = ±1, ±2, ±3…

In a double slit arrangement, diffraction through single slits appears as an envelope over the interference pattern between the two slits.

Fringe width  

The angular distance between the two first order minima (on either side of the center) is called the angular width of central maximum, given by

2[theta] = [frac{2lambda }{a}]

The linear width is as follows,

[Delta] = L.2[theta] = [frac{2Llambda }{a}]

The width of the central maximum in the diffraction formula is inversely proportional to the slit width. If the slit width decreases, the central maximum widens, and if the slit width increases, it narrows down. It can be inferred from this behaviour that light bends more as the dimension of the aperture becomes smaller.

Conditions for Diffraction

Types of Diffraction

  • Fresnel Diffraction: The light source and the screen both are at finite distances from the slit. The incident waves are not parallel. 

  • Fraunhofer Diffraction: The light source and the screen both are infinitely away from the slit such that the incident light rays are parallel.

Solved Examples

1. Fraunhofer diffraction at a single slit is performed using a 700 nm light. If the first dark fringe appears at an angle 30°, find the slit width.

Solution: Using the diffraction formula for a single slit of width a, the nth dark fringe occurs for,

a sin[theta] = nλ

At angle θ=30°, the first dark fringe is located. Using n=1 and

λ = 700 nm=700 X 10⁻⁹m,

a sin 30°=1 X 700 X 10⁻⁹m

a=14 X 10⁻⁷m

a=1400 nm

The slit width is 1400 nm.

2. Find the angular width of central maximum for Fraunhofer diffraction due to a single slit of width 0.1 m, if the frequency of incident light is 5 X 10¹⁴ Hz.

Solution: wavelength of the incident light is,

[lambda] = [frac{c}{nu }]

Here, c=3 X 10⁸m/s is the speed of light in vacuum and =5 X 10¹⁴Hz  is the frequency.

The angular width of the central maximum is,

2[theta] = [frac{2lambda }{a}]

2[theta] = [frac{2c}{nu a}]

Using c = 3×10⁸m/s, = 5×10¹⁴Hz a = 0.1m,

2[theta] = 1.2×10⁻⁴rad

The angular width is 1.210⁻⁴rad

About Fraunhofer and Fresnel

Fraunhofer

Fraunhofer and Fresnel, both kids faced immense hardships in life, partly because of their weak constitutions. At the end of the first decade of the nineteenth century, the building where Fraunhofer lived collapsed. Fraunhofer was the only one who survived. Maximilian IV Joseph, Prince-Elector of Bavaria, who was busy in the rescue efforts, noticed Fraunhofer and decided to take him under his wing. With the entry of Maximilian into his life, Fraunhofer’s life took a turn for the better.

Fresnel

In the neighbouring country of Italy simultaneously, Fresnel was still struggling to read at the age of eight. Surrounded by his three siblings, Fresnel h
ad toys aplenty. At the age of nine, he managed to transform a harmless toy into such a lethal weapon that elders in his society were forced to ban the use of the now-dangerous toy. This caused no end of worry and consternation to his parents and grown-ups, but his genius was finally recognized. 

He was taught by fine tutors and by the age of 16, he was admitted to the École Polytechnique. Here, an eminent mathematician, Adrien-Marie Legendre noticed Fresnel’s answer paper of striking ingenuity. Fresnel was encouraged in his studies of Maths and Science. He then graduated from École des Ponts et Chaussées as an Engineer.

Fraunhofer, The Scientist

Somewhere down a few longitudes, Maximilian took charge of the education of Fraunhofer and put him under the care of Joseph von Utzschneider, an attorney with a unique business mind. In those days industrious Utzschneider was busy partnering with Georg Reichenbach and J. Leibherr to open the Mathematical Mechanical Institute Reichenbach Utzschneider Liebherr. This institute was established to produce surveying instruments with high-quality lenses – incidentally, just the thing that Fraunhofer had a knack for.

After a failed stint at establishing his own business, Fraunhofer was offered a position in the Institute by Utzschneider. Here, under the guidance of expert glassmaker Pierre Guinand, Fraunhofer shined. Within two years he was offered a junior partnership in the Institute. Within a decade, Fraunhofer had turned the Institute around and was producing quality refractor lenses with a diameter of seven inches. This was an achievement in those times and was ably equipped with a decent-sized telescope.

Fresnel, The Scientist

On the other side, Fresnel was following the footsteps of his father, the architect. Having a few false starts mostly because he supported the monarchy that kept changing at that point in history, Fresnel settled as an engineer for the roads of Paris.

By now the careers of both scientists were converging as both were taking a keen interest in optics. By the middle of the second decade, both Fresnel and Fraunhofer were knee-deep in their research, resulting in scintillating findings that are studied in Optics for class 12 and higher classes.

Fraunhofer had a knack for handling glass and optics. A major challenge at his time was accurately polishing spherical surfaces of large glass objects. With his ingenuity, Fraunhofer improved upon and also invented machines that did more accurate grinding and polishing of glass surfaces. This greatly improved the kinds of lenses being manufactured and thus improved the quality of optical instruments being used.

In 1811, he constructed the furnace that would make the perfect large-sized lenses required in larger telescopes. With this new furnace, Fraunhofer created his own crown glass that had no irregular refractive power as larger crown glasses of that time tended to have.

In 1814, Fraunhofer invented the modern spectroscope through a series of experiments. By observing the orange fixed light in the spectrum of fire, he researched the dark lines of the solar spectrum, as well as in several bright stars, thus initiating research in stellar spectroscopy.

In 1821, he invented the diffraction grating and became the first scientist to get line spectra and then measure the wavelengths of spectral lines. His passion always remained practical optics so he kept developing and bettering optical instruments. He also created the Dorpat Refractor ad and Bessel Heliometer.

The most practical and popular invention of Fresnel was Fresnel Lens. He created this for Napoleon. It is used in theatrical and cinematic lighting fixtures and lighthouses to shine a narrow beam in all directions simultaneously. These are made of a lot of complicated wedge-shaped parts. Fresnel lenses magnify a light beam about 150 times and shine it, thus making it very practical in lighthouses in his time. Today these lenses are popular in film-making and theatre.

Did you know?

  • In the diffraction pattern of white light, the central maximum is white but the other maxima becomes colored with red being the farthest away.

  • Diffraction patterns can be obtained for any wave. Subatomic particles like electrons also show similar patterns like light. This observation led to the concept of a particle’s wave nature and it is considered as one of the keystones for the advent of quantum mechanics.

  • The interatomic distances of certain crystals are comparable with the wavelength of X-rays. Using X-ray diffraction patterns, the crystal structures of different materials are studied in condensed matter physics.

[Physics Class Notes] on Solid Deformation Pdf for Exam

Matter has three forms: solids, liquids, and gases. They differ in the way ions, molecules, and atoms are arranged in them. Solid is characterized by tightly packed particles that are not free to move around within the substance. A solid can change its shape when pressure is applied to it. The change might be very little for some structures like a building or very large in objects like a spring. This article will look into what is deformation and what are the different types of deformation that can happen in a solid. Let us first define deformation.

Deformation Definition 

What forces act on a solid object affects the spacing of atoms within the solid to a small extent. This change in spacing changes the external structure or shape and size of the solid, and it is termed as deformation of solids. 

Stress and Its Types

Stress is considered as a force that produces strain when it acts on an object or material. The unit of stress is force/area (for example, lb/in2) since the stress is applied over an area. The pressure is a special type of stress where forces are acting in equal magnitude from all directions. But if the force from all directions is not equal, then we get differential stress. There are mainly three types of stress:

This is also called extensional stress, which causes the material (to which stress is applied) to stretch. An example is the stretching of a rubber band.

This kind of stress results in the object being squeezed or squashed. An example is when you squeeze a ball; you are applying compressive stress.

The deforming stress acts tangentially to the object’s surface and the result in either slippage or translation of the object.

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Features of Deformation in Solids 

  • When stress is applied to a solid, a deformation occurs, which gives rise to internal intermolecular forces in the solid that oppose the forces being applied.

  • If the applied forces are not so strong, then the internal molecular forces can resist the stress, and the object can acquire a new equilibrium state. Once the load is removed, the object then comes back to its original state.

  • If the force is very large, there could be permanent deformation of solids or even a complete structural failure.

  • The type of deformation that a solid undergoes depends on its material, size, geometry, and forces.

Types of Deformation of Solids

A strain is defined as a change in the size, shape, or volume of an object. Strain could also be in the form of any movement of the material, including titling and translation. 

Solids can undergo various types of deformation as described below:

  • Elastic deformation – This kind of deformation is reversible, and the object returns to its original size and shape once the applied force is removed. 

  • Linear elastic deformation is given by Hooke’s law that states that the amount a body extends is directly proportional to the force applied on it provided the elastic limit of the object is not exceeded. The deformation formula according to Hooke’s law is; σ = E * ε, where σ is the force applied, E is the spring or elastic constant (called young’s modulus), and ε is the extension or resulting strain.

  • The elastic constant is measured as force per unit extension, and its unit is N m-1. It is denoted by the gradient of the graph drawn by force against the extension. 

  • When the material reaches its yield strength, its elastic range ends, and plastic deformation begins.

  • Stress = Force/cross-sectional area

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  • Plastic or ductile deformation – This is an irreversible kind of deformation that starts as elastic deformation, and the object can partially return to its original state till this stage. A material like soft thermoplastic has a large plastic deformation range. Some ductile metals like gold, silver, and copper also have a large range of plastic deformation. Materials with minimal plastic deformation ranges are rubber, hard, thermosetting plastics, and ceramics. Plastic deformation can be of different types under tensile stress:

    • Strain hardening region – Due to the movement of atoms, the material becomes harder.

    • Necking region – After the ultimate strength is reached, there is a reduction in the cross-sectional area of the specimen. At this point, the material can no longer tolerate the maximum stress, and there is a rapid increase in the strain in the object.

    • Fracture – This indicates the end of plastic deformation where the material breaks.

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Young’s Modulus

Young’s modulus is a fundamental property of all materials which is unchangeable. However, it is dependent on pressure and temperature. Young’s modulus is also called the elastic modulus, and in simple words, it describes the stiffness of the material, i.e., how easily you can bend or stretch the material. The name “Young’s modulus” comes from 18th-century English physicist and physician Thomas Young. Young’s modulus describes the elastic properties of a material undergoing compression or tension in only one direction. It indicates a material’s ability to withstand length changes when it is undergoing lengthwise compression or tension. Mathematically it is expressed as:

Young’s modulus = stress/strain = (F * L0)/(A * (Ln – L0)) 

Or, F/A = Y * (ΔL/L0)

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Where L0 is the original length, Ln is the new length, F is the force applied, and A is the cross-sectional area of the metal bar.

Young’s modulus is measured in pascal and 1 Pascal = Nm-2

[Physics Class Notes] on Specific Heat of Constant Pressure Pdf for Exam

The heat capacity of a substance, commonly abbreviated as thermal capacity (capital C), is a measure of the amount of heat needed to change the temperature of the substance by a specific amount. Heat capacity is measured in SI units and is referred to as the joules per kelvin (J/K) unit.

 

In a heat capacity calculation, the amount of heat energy transferred to an object (symbol C) is proportional to the amount of temperature increase that results.

[C=QDelta T.C=QDelta T].

A system’s heat capacity scales with its size since it is an extensive property. When a sample contains twice as much substance as another, it takes twice as much heat (Q) to achieve the same temperature change (ΔT). It would take 2,000 J to heat a second iron block with twice the mass of a first iron block if it took 1,000 J to heat a block of iron.

The Measurement of Heat Capacity

It is not always possible to predict the capacity of a system in terms of heat. This depends more on the state variables of the thermodynamic system under discussion. The amount of change in volume or pressure is dependent upon many factors, including the temperature itself, the pressures that are in the system, and how those pressures have changed while the system has been going from one temperature to another. Unlike pressure-volume work done on the system, pressure-volume work done on the system absorbs heat without raising its temperature. This is because pressure-volume work on the system raises its temperature by a mechanism other than heating. It is because of this temperature dependence that a calorie is formally defined as the energy required to heat 1 g of water from 14.5 to 15.5 degrees Celsius instead of generally by just 1 degree Celsius.

 

Therefore, different methods can be used to determine heat capacity, most commonly at constant pressure and volume. To indicate the meaning of the measured value, the subscripts (p and V, respectively) are usually used. Typically, gas and liquid measurements are also based on constant volume. As the temperature increases, the substance expands against the constant pressure as it is measured at constant pressure. Therefore, the constant pressure measurements are greater than those at constant volume. In gases, significantly greater values are typically found under constant pressure than under constant volume, especially for gases at constant pressure.

 

Molar Specific Heat Capacity at Constant Pressure: If the heat transfer to the sample takes place at the same pressure as the sample remains, this method is known as Molar Specific Heat Capacity at Constant Pressure. 

 

Molar Specific Heat Capacity at Constant Volume: If the sample is converted to heat by keeping its volume constant, the actual heat produced by this process is known as Molar Specific Heat Capacity at Constant Volume.

Points to Consider

  • Mass and volume are irrelevant for the specific heat capacity as opposed to the total heat capacity. In order to raise the temperature of a given substance by one degree Celsius, the amount of heat it takes to warm that mass by one degree Celsius. Special heat capacity is measured in J/(kg °C) or equivalently in J/(kg K).

  • C=cm or c=C/m is the relationship between the capacity for heat and the specific heat.

  • The mass m, specific heat c, change in temperature ΔT, and heat added (or subtracted) Q are related by the equation: Q=mc Temperature and phase of substances have an effect on specific heat values. Since they are difficult to calculate, they are measured empirically and available in tables as references.

Key Terms

  • In thermodynamics, specific heat capacity can be defined as the amount of heat needed to raise or lower the temperature of a unit mass of a substance by one degree Celsius. Specifically, it is a property of intensities.