Category: Physics Notes PPT

Here we must understand what the definition of an ideal gas is, what do we mean by a closed system and the relationship of the word temperature. A theoretical gas made up of lots of arbitrarily moving point particles whose only interactions are completely elastic collisions is known as an ideal gas. The ideal gas theory is useful because it obeys the ideal gas law, a simplified equation of state, and is modifiable to analysis under statistical mechanics.

 

But, this relationship between pressure and volume was first documented by Richard Townley and Henry Power in the 17th century. Robert Boyle conducted many experiments compiled and confirmed their data and published the results. Robert Hooke, who was Boyle’s assistant built the experimental apparatus as opined by Robert Gunther and other authorities.

This law is based on experiments with air, which Boyle assumed to be a fluid of fine particles which are at rest in between small invisible springs. The common belief in those times was that Air was one of the four elements, but Boyle was not in alliance with this concept. Boyle’s firmly believed that air was an essential element of life; and, he published works on the growth of plants without air.

 

Using a closed J-shaped tube and Boyle poured mercury from one side, and thus he forced the air, on the other hand, to contract under the pressure of mercury. He repeated this procedure of the experiment several times and using different amounts of mercury, and after several iterations, he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it.

 

Edge Mariotte (1620–1684) the French physicist discovered the same law independently of Boyle in 1679, but Boyle had already published it in 1662. Mariotte did, however, discover one different fact that the volume of air changes with temperature. This is the reason why this law is sometimes referred to as Mariotte’s law or the Boyle–Mariotte law.

 

Newton in the year 1687 published it in the Philosophiæ Naturalis Principia Mathematica, wherein he showed and proved mathematically that in an elastic fluid consisting of particles which are at rest, and between which are repulsive forces inversely proportional to their distance, the density would be directly proportional to the pressure, But this mathematical treatise is not the physical explanation for the observed relationship. Instead of static theory, a kinetic theory was needed, which was provided two centuries later when Maxwell and Boltzmann came up with proof of theories.

 

Boyle’s law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities.

 

Boyle’s law can be expressed mathematically as

P α 1/V, i.e. to say the Pressure is inversely proportional to the volume

OR

P x V = k which is to say that if we multiply the pressure by the volume, we get a constant

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

 

The equation states that if the temperature is constant, the product of pressure and volume is a constant for a given mass of confined gas and this holds.

 

Now, for comparing the same substance under two different sets of conditions, the law can be usefully expressed as

P1V1 = P2V2

 

The expression shows that, when the volume increases, the pressure of the gas decreases in proportion. Similarly, as the volume decreases, the pressure of the gas increases. Robert Boyle published the original law in 1662 and hence the law was named after him.

 

This expression means that if the temperature remains constant the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will stay constant. since the pressure is derived as a perpendicular applied force and the probabilistic likelihood of collisions with other particles using collision theory, the application of power to a surface might not be infinitely constant for such values of v but will have a limit when differentiating such values over a given time. Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure p should decrease proportionally. In other words, to put it conversely, reducing the volume of the gas increases the pressure. Boyle’s law is used to forecast the consequence of introducing a change, only in pressure and volume, to the initial state of a fixed quantity of gas.

 

This is the principle utilized and applied in our daily lives even when we cook food using a pressure cooker. The food says rice gets cooked when the water boils. We all live on the planet Earth under atmospheric pressure which is taken as the weight of 13mm of Mercury, Water to cook the rice boils only at 100 Degrees Celsius at atmospheric pressure. Now using this principle water is a heavy thick metal pressure cooker is made to boil at a higher temperature by increasing the weight or causing the pressure inside the cooking vessel to build up quickly. This, in turn, causes the water to attain a boiling point Higher than 100Degree Celsius quickly, and the rice also gets cooked in a much shorter time than in an open vessel.

 

We are creating a closed pressure system when we lock the lid onto the cooker because we are sealing the pot shut. Going back to the Ideal Gas Law and the equation PV=nRT, where P = pressure, V= volume and T = temperature (for completeness, n= the number of moles and R = is the gas constant, but they will not change in this case so we can ignore them, and the volume of the metal pot also will not really change, we will ignore this too). Hence this equation applies to a closed system, and this is the state inside the pressure cooker.

 

So basically here, we have an equation of P=T. If you increase the pressure, the temperature will also increase, and vice versa.

In an open or uncovered pot which is not tightly closed, water boils at 100ºC (212ºF) because it is exposed to the atmospheric pressure. The steam that evaporates from this pot is also at 100ºC (212ºF). Irrespective of the heat supplied to the water, it will remain at 100ºC (212ºF). If the cover is put on the pot to seal it tight and trap the steam inside the vessel, the pressure inside the pot goes up. As the pressure rises, the steam inside the pressurized pot and the temperature of the water also increases over the normal 100ºC (212ºF) boiling point temperature.

 

So, when we begin heating the cooker, the internal pressure will increase, and as the pressure increases, the internal temperature also rises. This will continue to increase until it reaches the trigger pressure of the safety valves, about double the psi (Pressure reading) at sea level. Generally, for most chemical reactions, for every 10 deg C increase, the rate of reaction is doubled, which allows us to reduce the cook time in half. By raising the pressure by ~15 psi, you can braise your food at ~250 deg F (121 deg C) and cut your cook time to a quarter of the standard time. However, you also must factor in the time it will take to come up to pressure as well as the cooldown time, so it ends up being about one third the original time, still a huge reduction. This is the reason why pressure cookers cook the food very quickly.

The capacitor is a device that has the ability or “power” to store energy in the form of an electrical charge that creates a potential difference (Static Voltage) through its plates, much like a small rechargeable battery. There are many types of capacitors available from very small capacitor beads that use resonance circuits to large power factor correction capacitors, but they all do the same, they store charge. In other words, the capacitor is an electronic component whose function is to store electrical charges. It is made of two conductors separated by a dielectric film. These plates accumulate electrical charges when connected to a power source. 

They are often storage sites for analogue signals and digital data. In general, comparisons between the different types of capacitors are made concerning the dielectric used between the plates. Some capacitors look like tubes, small capacitors are often made from ceramic materials and then dipped into an epoxy resin to seal them. Below are some of the more common types of capacitors available.

Capacitor Types 

The types of capacitors available range from very small, delicate trimming capacitors used in oscillators or radio circuits, to large-scale metal-type capacitors used in high-voltage power correction and smoothing circuits. 

The comparison between the different types of capacitors is generally made concerning the dielectric used between the plates. Unlike resistors, there are also various types of capacitors that allow us to vary their capacitance value for use in radio or “frequency tuning” style circuits.

 

Some of the capacitors appear like tubes since the metal foil plates are rolled up into a circle to make a small bundle with the insulating dielectric layer sandwiched between them.

Small capacitors are often made from ceramic materials and then immersed in epoxy resins to seal them. Either way, capacitors play an important role in electronic circuits, so here are some of the more “common” types of capacitors available.

Applications of Capacitors

Capacitors have been used in both physical and electronic devices. They are used in filter applications, energy storage systems, engine starters, and signal processing equipment.

Four Types of Capacitors

1. Film Capacitors:

Film capacitors are the most widely prepared of a variety of types of capacitors, consisting of a relatively expansive category of capacitors defining their dielectric properties. They are available in almost any weight and voltages up to 1500 volts. They vary in any tolerance from 10% to 0.01%. In addition, film capacitors come in a variety of shapes and case types. There are two types of film capacitors, the type of radial lead and the type of axial lead. The film capacitor electrodes may be metallic aluminum or zinc, mounted on one or both sides of the plastic film, resulting in metallic film capacitors called film capacitors. The film capacitor is shown in the following figure:

2. Ceramic Capacitors:

Ceramic capacitors are used in high-frequency circuits such as RF audio. They are also the best alternative for high-frequency compensation for audio circuits. These capacitors are also called disk capacitors. Ceramic capacitors are made by coating two sides of small silver porcelain or ceramic disk and then stacked together to make a capacitor. Low capacitance and high capacitance in ceramic capacitors can be achieved by changing the thickness of the ceramic disk used.

3. Electrolytic Capacitors:

These are the most widely used capacitors with a wide tolerance capacity. Electrolytic capacitors are obtainable with working voltages of up to 500V, although high capacitance values are not accessible at high voltage and higher temperature units are not normal. Two types of electrolytic capacitors, Tantalum, and Aluminum are common. Electrolytic capacitors are categorized based on their dielectric.

• Aluminum electrolytic capacitors – aluminum oxide ( dielectric).

• Tantalum electrolytic capacitors – tantalum pentoxide (dielectric).

• Niobium electrolytic capacitors – niobium pentoxide ( dielectric).

4. Variable Capacitors: 

Among the different types of capacitors are a Variable Capacitor, which is one whose capacity can be changed mechanically intentionally, and repeatedly. This type of capacitor was used to set the resonance frequency in LC circuits, e.g. to adjust the radio for impedance matching in antenna tuner devices.

What are Common Capacitors?

Capacitors are mainly divided into two mechanical groups:

• Fixed capacitors

• Variable capacitors

Some common capacitors and their names are mentioned in the table below.

Capacitor Types and Use

The easiest design of the capacitor is the use of two parallel metal plates separated by an insulation layer called a dielectric.

How Capacitor Works

To begin, we can see that a metal contains an equal number of positively and negatively charged particles, indicating that it is electrically neutral. When we connect a power source or a battery to the capacitor’s metal plates, a current or electrons will attempt to travel from the plate connected to the positive lead of the battery to the plate connected to the negative lead of the battery. However, because of the dielectric between the plates, electrons will not be able to travel through the capacitor and will begin to accumulate on the plate. Because of the repulsion of those electronics that are already on the plate, the battery will have insufficient energy to push any more electronics into the plate once a certain number of electronics have collected on the plate. The capacitor is fully charged at this stage. The first plate has generated a net negative charge, and the second plate has produced an equal net positive charge, resulting in an electric field with an attractive office between them that maintains the capacitor’s charge. 

Main Functions of Capacitor

A capacitor is an electrical component that stores and releases electricity in a circuit. It frequently sends alternating current instead of direct current. As a fundamental component of electrical equipment, a capacitor is usually always present in electronic circuits. The capaci
tor’s fundamental function is to store electrostatic energy in an electric field and, if feasible, to supply this energy to the circuit. To avoid a fatal circuit failure, they allow the AC to flow but restrict the DC from flowing. A capacitor can store electric energy when connected to its charging circuit. When unplugged from its charging circuit, it will discharge the collected energy, allowing it to be used like a temporary battery. The most typical application for capacitors is energy storage. Other uses include power condition, signal coupling or decoupling, electrical noise filtering, and remote sensing. Because of their numerous applications, capacitors are employed in a wide range of sec optics and have become an essential part of daily life.

There is always a line of separation when it comes to a bang and a whimper. In the case of stars, these lines are known as Chandrasekhar Limit. In other words, this is the difference between dying supernaturally and going out in a slow fading on the verge of extinction. Here, in the universe, this line gives rise to a different cosmos formation where stars sow the seeds of life.

Chandrasekhar Limit Definition

A white dwarf star with the utmost mass limit that remains stable is known as the Chandrasekhar limit. EC Stone and Willhelm mentioned the discoveries on how to improve the preciseness of computation in papers. They named it after an Indian astrophysicist Subrahmanyan Chandrasekhar.

History of Chandrasekhar Limit

A decade before Chandrasekhar started his journey to England, i.e., by 1920, the astronomers had realised that Sirius B, a white dwarf companion to the bright star Sirius, had a million times more density than the Sun. This density could only be acquired by an object if the atoms forming the star were so firmly compressed that they were no longer separate entities. The gravitational pressures would compress the atoms so much that the star would consist of positively charged ions surrounded by a sea of electrons.

Before discovering quantum mechanics, physics didn’t understand the force capable of supporting any star against such gravitational force. But a new way was suggested by quantum mechanics, for a star to hold against gravity. As per the quantum mechanics rule, no two electrons can be in the same state. 

Explanation

With the help of thermonuclear fusion, a star is characterised, hydrogen merges to helium, helium merges to carbon, and so on, forming more massive and heavier elements. Still, thermonuclear fusion cannot create an element heavier than iron. Copper, gold, silver, and trace elements are created only by a supernova explosion, which is important for the process of life.

Oxygen, carbon, and nitrogen, which are lighter elements are also essential to life, but these elements will remain locked forever up in stars until a supernova explosion occurs. Similar to the iron-on earth that is locked up in the core, being heavier hydrogen and helium, which comprise most of the initial mass of the stars, they deposit to form the central core of the star.

If stars are destined to become white dwarfs, as Eddington believed, the elements will remain confined to the glamorous interior at best to be provided in minute quantities to the universe as a whole via solar winds. Rocky planet is required to form life as we know, and there is no simple method in which a large quantity of rock can be made available in the universe unless the stars can deliver the material in wholesale quantities, but supernovae can provide that.

Therefore, the Chandrasekhar limit is not just the upper limit for the maximum mass for an ideal white dwarf, but also the threshold. A star can no longer hoard its precious cargo of heavy elements once it crosses the threshold. As an alternative, it delivers them to the universe at large in a supernova. This allows the possibility of the existence of life but marks its death.

Chandrasekhar Limit Derivation

The value for the calculation of the limit depends on the nuclear composition of the mass. For an ideal Fermi gas, Chandrasekhar limit has provided the following expression which is based on the equation of the state: Chandrasekhar limit equation given as: 

[M_{limit} = frac{omega_{3}^{0} sqrt{3 pi}}{2} (frac{hbar c}{G})^{frac{3}{2}} frac{1}{( mu_{0} m_{H})^{2}}]

Where:

• ħ is reduced Planck constant

• c is the speed of light 

• G is gravitational constant

• μe is the average molecular weight per electron. This solely depends on the chemical composition of the star.

• mH is the hydrogen atom mass. 

• ω0

• 3 ≈ 2.018236 is a constant link with a solution to the Lane–Emden equation. 

As √ħc/G is Planck mass, the threshold is of the order of :

[frac{M_{Pl}^{3}}{m_{H}^{2}}]

This simple model requires adjustment for a variety of factors, including electrostatic interactions between electrons and nuclei and effects caused at nonzero temperature, for a more accurate value than a given range. Lieb and Yau give the thorough derivative of the limit from the relative multi-particle Schrödinger equation.

Fun Facts

In the beginning, the scientist community ignored this limit as it would mean legitimising the existence of a black hole. This was considered unrealistic at that time because the white dwarf stars oppose the gravitational collapse from the pressure of electron degeneration.

The Chandrasekhar limit is when the mass of the pressure from the degeneration of electrons is unable to balance the gravitational field’s self-attraction of 1.39 M☉limit.

The Chandrasekhar limit was found in 1930 by Subrahmanyan Chandrasekhar, an Indian astrophysicist and he used Albert Einstein’s special theory of relativity along with the principles of quantum physics to further prove his theory. 

Fossil fuels are non-renewable energy sources(which are present in a limited quantity). They are exhaustible, and will not last for a long period of time if not used judiciously. Although fossil fuels are continually formed by natural processes, they are classified as non-renewable resources because they take millions of years to form. Fossil fuels were formed by the remains of terrestrial and marine flora and fauna that decayed millions of years ago and got buried in layers under huge amounts of pressure and heat. These sources are responsible for pollution to the environment because carbon is the main element present in fossil fuels such as coal and petroleum.

Coal – Description

Coal is a black coloured rock-like fuel in which the content of carbon can vary between 70-90%. It is formed by the decomposition of vegetation under heat and pressure. The process of formation of coal is called carbonisation and the time period during which this process takes place is called the carboniferous age. Coal is one of the most important fossil fuels used to generate electricity. Coal is taken out from the earth by the process of underground mining or surface mining. We burn coal to get energy. Coal is mostly used as a domestic fuel to make food in rural areas. When coal is burnt, it releases harmful smoke. Coal is formed when the buried vegetation is subjected to extremities of heat and pressure. The formation of coal takes place in four stages which are peat, lignite, bituminous, and anthracite. Coal mainly contains carbon, hydrogen, and oxygen.

Types of Coal

1. Lignite 

Lignite is the lowest rank of coal in terms of carbon content(60-70%). It is the youngest type of coal deposit. It is soft and ranges in color from black to shades of brown. As a result, lignite coal is sometimes called brown coal. Lignite is not used on a large scale because other types of coal are superior to it in terms of handling and storage stability. Lignite is used to generate electricity, synthetic natural gas, and to create fertilizer products like anhydrous ammonia and ammonium sulphate.

2. Sub-bituminous  

When lignite is subjected to continued high temperature and pressure for millions of years, the oxygen and hydrogen content gets decreased and the carbon content increases up to 75%. This type of coal burns cleaner than the lignite variety, producing less greenhouse gas emissions.  Sub-bituminous coal is also used in electricity generation and in industrial processes.

3. Bituminous

Bituminous coal is blacker and harder than sub-bituminous coal. It contains a tar-like substance called bitumen. Hence, its name is bituminous. It has a carbon content of up to 85%. It accounts for a majority of the coal industry. Bituminous coal is used in energy generation and for heating purposes also. It is also used in the manufacturing of cement and other industrial uses. 

4. Anthracite

Anthracite is the most superior form of coal or most mature form of coal deposit i.e it contains the highest carbon content (more than 85%). It is harder than bituminous. It is used to provide energy. It burns as a smokeless fuel in furnaces.

 

Petrol – Description

Petroleum is a black coloured liquid fossil fuel composed of a variety of hydrocarbons. It is highly viscous. It is a very useful energy source. However, the petroleum extracted from oil wells is not in a directly usable form. It is impure and, therefore, called crude oil.

Through a process called fractional distillation, this crude oil is refined where different hydrocarbons separate to form different fractions. Petrol, kerosene, paraffin, diesel are some of its fractions. Petrol is used as fuel in vehicles. The fractions obtained by the refining of crude oil are used not just for transportation but also for the manufacture of a variety of products such as plastics, tires, and synthetic materials such as polyester. It is a dependable and portable source of energy. 

However, petroleum has some advantages as compared to coal. These are as follows:

1. It is a high-density fuel.

2. Petroleum is easy to extract.

3. Petroleum can be stored, shipped, and piped over long distances.

4. Petroleum can be used in a wide variety of ways.

5. Petroleum provides a stable energy resource.

However, the combustion of both coal and petroleum is detrimental to the environment.

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Difference between Coal and Petroleum – Tabular Form

Conservation of Coal and Petroleum

As we already know, coal and petroleum are exhaustible sources of energy. If they are not used judiciously, they will not last for more than a few decades. Since they are widely used as sources of energy throughout the world, it is of utmost importance to think about their conservation. Conservation is the process of using a resource in a more careful way so that it can be made to last for a longer period of time. We can conserve coal and petroleum by switching to alternative or renewable sources of energy, such as hydel power, wind energy, geothermal energy, tidal energy, etc. 

In the coming times, the alternatives to fossil fuels like coal and petroleum will provide us more environmentally friendly options for sustainable development, but they will also help in delaying the energy crisis that the world is about to face very shortly.

When force is applied to an elastic band it stretches and when it does stretch it tends to undergo stress during the stretching. When the stress on the elastic band has reached its limit it tends to break and hence releasing the stress that was held by the elastic band. This stress is one of the factors that give it a shape. However, not every object is elastic in nature. Some are rigid and hence cannot be easily malleated even after providing an ample amount of stress to the material. One of the typical examples is a ping-pong ball which is quite brittle as it is made of plastic. Under stress, it tends to break and now holds a shape.

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Compressive stress is the restoring strain developed because of pressure or force applied on a material to deform it, thereby causing a reduction of its volume. This capability of materials to withstand such compression is known as compressive strength. Here, we will discuss these two essential terminologies in detail. 

What Is Compressive Stress?

It is the measure of restoring stress developed in a body as a result of force applied on a material for the intention of deforming it. The maximum force at which materials deform and their volume is reduced, is known as compressive stress. The value of stress may differ from one element to another. Let us understand this by taking two scenarios –

1. In case this force is applied to brittle materials, the material breakdowns into smaller particles because of the sudden release of energy. 

2. In case the material is ductile, it can be compressed easily. 

What is Compressive Strength?

It is the measure of the capacity of a material to withstand the external force applied to it with an intention to deform it. Once the compressive strength limit of a substance is attained, it may fracture or deform. 

Therefore, as per compressive strength meaning, brittle materials are more likely to have higher compressive strength than ductile ones. 

Kinds of Stress

One can deform a solid by applying external force. However, it is possible by only three ways as mentioned below. 

1. Tensile Stress – It is the equal force applied on a body perpendicular to its cross-sectional area to deform it. 

2. Compressive Stress Definition – The solid is compressed by applying an external force. In response, the restoring force is produced in the body, which is known for compressive stress. 

3. Shearing Stress – A tangential force developed in the solid body because of the application of two equal & opposite external forces parallel to its cross-sectional area is known as the shearing stress. 

Formula 

The compressive stress formula can be written as 

σ = F/A 

Where, 

• σ is compressive stress. 

• A is the unit area of a solid body. 

• F is a compressive force. 

This can also be used as the compressive strength formula as it is the limit at which the solid material deforms. 

Units and Dimensions 

SI units for compressive stress or compressive strength units can be expressed as Nm-2 or Pascal (Pa). 

The dimensional formula for the same will be [M L-1 T-2].

Tensile Stress vs Compressive Stress

The significance of constants in Physics is that throughout all of the formulations of the basic theories of Physics and the application to the real world, physical constants appear as fundamental invariant quantities, and they have specific and universally used symbols, that are of such importance that they must be known to as high an accuracy as is possible.

The physical constant also called the fundamental constant or the universal constant is a physical quantity that is believed to be universal in nature and has a constant value at all times.

Fundamental Constants in Physics

Speed of light in vacuum = c

Planck’s constant = h

The electric constant = ε0

The elementary charge = e

Constant Value in Physics

In physics, we deal with various dimensions, and to set the dimensions of an entity, the time length of an event, or the density of the fluid we need to compare them with other entities,  we use as a reference. These entities are the constants of physics, such as the speed of light (c), the charge of the electron(e) or mass (mp) of a proton, Rydberg constant, and so on.

For example, the value of Avogadro’s number is 6.02214 x 10²³ mol⁻¹ remains the same everywhere.

Important Physical Constants

There are various fundamental constants to describe the universe as completely as possible; a few are listed below:

Table: List of All Constants in Physics

All physics constants

Table: All Constant Values in Physics 

 

Famous Constants in Physics

There are so many constants besides those I mentioned above, but some constants in physics are recognized widely.

Constant values in physics that are most popular among all the physical constants are as follows:

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The physical constant is a complex concept that is taught in class 11 physics. This is based on the curriculum set by the Central Board of secondary education and physical constants or Constance of Physics holds a significant weightage in the examination and therefore are extremely important to understand. The concept of physical constants can be studied in depth in the study notes that I provided by Vedanta, these notes are repaired by Vedanta’s export research team who are well-versed in research and curating study notes for students, ’s exports have extensive experience and have done thorough research in the duration of these study notes. The notes provided by Vedanta are based on the latest CBSE curriculum and are therefore up to date.

Physical constants are known by different titles such as fundamental constant, universal constant, Constance of physics. It is extremely important to have an accurate evaluation of the physical constants as their accuracy will help to check how up to the mark the theories are, as they form the basis of Physics their accuracy allows useful applications that can be made based on certain theories. 

Physical constants are a set of fundamental quantities that appear in the basic theoretical equations of physics.

For example, a universal constant of nature is the speed of light in a vacuum (c). The speed of light can be studied in both electromagnetic theory and in relativity theory; in relativity theory, it relies on energy to Mass whose equation can be written as E =mc². The value of the speed of light never changes and it does not depend on any experimental conditions like the speed of a sound wave changes in some cases therefore, the speed of light is a universal constant

Table Representing Some Important Physical Constants