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May25

Temperature, Entropy and Quantum Mechanics: Why Zero Kelvin is Not Possible?

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What Is Temperature?

A Modern Understanding of Temperature

Temperature is something we experience every day. We say that tea is hot, ice is cold, and the weather is warm or cool. But in physics, temperature is much deeper than just the feeling of “hotness” or “coldness.”

Modern science tells us that temperature is related to the motion and energy of tiny particles such as atoms and molecules.

Temperature and Particle Motion

All matter is made of particles that are always moving.

  • In hot objects, particles move faster.
  • In cold objects, particles move slower.

For an ideal gas, the average kinetic energy of particles is:

E = (3/2) × k × T

where:

  • E = average kinetic energy
  • k = Boltzmann constant
  • T = temperature in kelvin

This means temperature is connected to the average energy of random particle motion.

Temperature Is a Collective Property

A single molecule does not have a temperature.

Temperature appears only when a very large number of particles are considered together.

So, temperature is a “collective” or “statistical” property of matter.

Temperature and Entropy

Modern physics also connects temperature with a very important idea called entropy.

Entropy measures the amount of disorder or the number of possible microscopic arrangements inside a system.

  • Higher temperature generally means particles can arrange themselves in more possible ways.
  • Lower temperature means fewer possible arrangements.

The deep thermodynamic relation is:

1/T = dS/dE

where:

  • T = temperature
  • S = entropy
  • E = energy

This equation shows that temperature is deeply connected to how energy and disorder are related in Nature.

The Kelvin Scale and Absolute Zero

Scientists use the kelvin scale for temperature.

  • 0 K is called absolute zero.
  • 0 K = −273.15°C

At absolute zero, particles have the minimum possible thermal energy.

Why Zero Kelvin Cannot Be Reached

According to modern physics, reaching exactly 0 K is impossible.

There are two major reasons.

1. Heisenberg’s Uncertainty Principle

Quantum mechanics tells us that particles can never become perfectly motionless.

According to the Heisenberg Uncertainty Principle:

Δx × Δp ≥ h/(4π)

where:

  • Δx = uncertainty in position
  • Δp = uncertainty in momentum
  • h = Planck’s constant

This means we cannot know both the exact position and exact momentum of a particle at the same time.

If a particle became completely motionless at 0 K, its momentum would become exactly zero, which would violate quantum mechanics.

Therefore, even near absolute zero, particles still possess a tiny unavoidable motion called:

Zero-point energy

So Nature never becomes completely still.

2. Cooling Becomes Harder and Harder

As temperature decreases:

  • particles lose energy,
  • but removing the remaining energy becomes increasingly difficult.

Scientists can get extremely close to 0 K, but they can never reach it exactly.

This idea is part of the Third Law of Thermodynamics.

The Coldest Temperatures Ever Created

Using advanced techniques like laser cooling, scientists have cooled matter to temperatures only a tiny fraction above absolute zero.

At such temperatures, strange quantum effects appear, including:

  • superconductivity,
  • superfluidity,
  • Bose–Einstein condensates.

These states help scientists study the quantum world.

Modern Understanding of Temperature

Today, physicists understand temperature as:

  • a measure of the average energy of particles,
  • a statistical property of many particles together,
  • a quantity deeply connected with entropy,
  • and a concept linked with quantum mechanics.

Temperature is therefore not just about “hot” and “cold.”
It is one of the fundamental ideas that helps us understand the microscopic behavior of matter and the deeper laws of the universe.

May20

What is Temperature? and Why Absolute Zero is not possible?

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What Is Temperature?

Temperature is one of the most familiar quantities in physics, yet its true meaning is remarkably profound.

At the microscopic level, temperature measures the average random kinetic energy of particles in a system. In simpler terms:

The faster the particles move randomly, the higher the temperature.

In gases, particles move freely in all directions. In solids, atoms vibrate about fixed positions. As thermal motion increases, temperature rises.

Thus, temperature is fundamentally connected to microscopic motion.

What Happens When Temperature Decreases?

When a body cools:

  • particle motion decreases,
  • vibrations become weaker,
  • and the average kinetic energy reduces.

This naturally leads to an important question:

Can particle motion become completely zero?

If that were possible, the system would reach the lowest possible temperature: 0 K, called absolute zero.

Classically, one might imagine that at 0 K all particles become perfectly motionless.

Quantum mechanics, however, forbids this possibility.

Heisenberg’s Uncertainty Principle

One of the foundational principles of quantum mechanics is Heisenberg’s uncertainty principle:

This principle states that a particle cannot simultaneously possess:

  • perfectly definite position,
  • and perfectly definite momentum.

This is not a limitation of measurement instruments. It is a fundamental law of nature.

Why Absolute Zero Is Impossible

Suppose a particle inside a solid reaches absolute zero.

Hence a particle cannot simultaneously have:

  • zero momentum,
  • and a definite position inside matter.

Some residual momentum uncertainty must always remain.

As a result, particles retain a minimum unavoidable motion even at extremely low temperatures.

This residual energy is called zero-point energy.

Zero-Point Energy

Even near 0 K:

  • atoms in a crystal continue to vibrate slightly,
  • electrons retain quantum motion,
  • and complete stillness never occurs.

Nature permits minimum motion, but never perfect stillness.

Thus:

Absolute zero can be approached indefinitely, but never perfectly reached.

Final Conclusion

Temperature is a measure of microscopic random motion. As temperature decreases, this motion reduces, but quantum mechanics prevents it from becoming exactly zero.

Heisenberg’s uncertainty principle ensures that particles can never possess both perfectly definite position and zero momentum simultaneously.

Therefore:

0 K is Fundamentally Unattainable.

Absolute zero is not merely technologically difficult — it is forbidden by the quantum structure of nature itself.

May19

IIT JEE Advanced AIR 56, IJSO Gold, and World Rank 10 in SIN: Vasu Vijay’s Gratitude towards Devansh Sir

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Very few academic journeys reflect excellence across so many of the world’s most prestigious examinations and Olympiads at such a young age. From securing an extraordinary AIR 56 in IIT-JEE Advanced, to winning a Gold Medal with International Rank 8 at the International Junior Science Olympiad (IJSO) 2022 in Bogotá, Colombia, to achieving International Rank 10 along with Distinction in the prestigious Sir Isaac Newton (SIN) Exam conducted by the University of Waterloo, Vasu Vijay’s accomplishments stand as a remarkable testament to intellectual depth, discipline, and conceptual mastery.

What makes his story especially meaningful to me, however, is not merely the scale of these achievements, but the transformation behind them.

As Vasu himself shares in this testimonial, there was a time when Physics felt difficult and unintuitive to him. Over the years, through a learning approach centered around intuition, conceptual understanding, analytical thinking, and scientific imagination, he gradually developed not only mastery over the subject, but also a genuine love for it.

His words beautifully reflect a philosophy I have always believed in deeply — that true excellence in Physics does not emerge from memorizing formulas or mechanically solving thousands of problems, but from learning how to think clearly, understand concepts fundamentally, and approach challenges with calmness and intelligence.

One of the most touching parts of Vasu’s testimonial is his gratitude toward the way he was taught to approach both Physics and examinations themselves — not with fear or pressure, but with curiosity, strategy, and confidence. To know that this mindset contributed meaningfully to his Olympiad journey, his international success, and his IIT-JEE performance is profoundly fulfilling as a teacher.

Vasu’s journey is not merely a story of ranks and medals. It is a story of transformation — from confusion to clarity, from hesitation to confidence, and from learning formulas to truly understanding the beauty of Physics.

I feel immensely proud to have been part of his journey and deeply grateful for the sincerity and warmth with which he has expressed his appreciation.

Respected Devansh Sir,

I remember that at the beginning of Class 9, Physics was the subject I struggled with the most. Even the basic concepts often felt unclear to me, and I never really enjoyed studying the subject. However, the way you taught Physics completely changed how I viewed it. Your emphasis on intuition and conceptual understanding helped me develop genuine interest in the subject.

What impacted me the most was that your teaching was never limited to memorizing formulas or blindly applying methods. Instead, you always encouraged us to understand the idea behind every concept and every question. Because of this, whenever I now encounter a Physics problem, my first instinct is to understand the concept deeply before attempting to solve it. The questions discussed in class were themselves more than sufficient to develop a strong understanding, without the need to solve hundreds of questions from multiple books.

Apart from academics, your guidance regarding examination pressure and mindset also helped me immensely. I still remember your idea of treating an exam like a puzzle, where the objective is to optimize marks, calmly and intelligently. That approach proved to be extremely effective for me and positively influenced my performance in every major examination thereafter.

This way of learning and approaching Physics helped me throughout my entire Junior Science Olympiad journey, from NSEJS and INJSO to the OCSC selection camp at HBCSE, eventually culminating in a Gold Medal and an International Rank 8 in IJSO 2022 held in Bogotá, Colombia. The same approach and mindset later continued to help me in other examinations as well, including JEE Advanced, where I secured AIR 56, and the Sir Isaac Newton (SIN) Exam, where I secured an International Rank 10 along with a Distinction.

I will always remain grateful to you not just for teaching Physics so beautifully, but also for changing the way I approach learning and problem solving as a whole. Thank you for making Physics so intuitive and enjoyable for me!

Vasu Vijay

May17

Carnot Engine: Proof of Carnot Theorem…

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“It is impossible for any heat engine to be more efficient than a Carnot engine when operating between two given temperatures”.

The Carnot engine is a conceptual engine that achieves the most efficient conversion of heat to work permitted by Kelvin’s statement. In general, efficiency is defined as the ratio of work out to heat in:

For a Carnot engine, the efficiency is found in terms of the temperature of the reservoirs the engine operates between:

Carnot’s Theorem

It is impossible for any heat engine to be more efficient than a Carnot engine when operating between two given temperatures:

Consider a heat engine drawing heat Q1 from a heat reservoir at temperature T1​, delivering work W and dumping heat Q2​ into a heat sink at temperature T2.

The heat engine operates in cycles, that is, it takes in heat Q1, does work W, dumps heat Q2, and in the end returns back to its original unchanged state.

Consider the net change in entropy ΔS of the universe:

The heat reservoir releases a heat Q1 at a constant temperature T1. Thus the change in its entropy is

The heat sink accepts heat Q2 at a constant temperature T2. Thus the change in its entropy is

Thus the net change in entropy of the universe is

Using the second law of thermodynamics, ΔS≥0, which implies

Since the left-hand side represents the efficiency of the given heat engine (η) and the right-hand side is the efficiency of a Carnot engine,

Hence proved!

May17

Pressure is Isotopic: It Has No Preferred Direction

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Pressure Is Isotropic

Why Pressure in a Fluid Acts Equally in All Directions

One of the most fundamental results in fluid mechanics is:

At a given point inside a stationary fluid, pressure acts equally in all directions.

This property is called the isotropy of pressure.

At first glance, the statement appears intuitive. Yet it emerges from a deep physical requirement: a fluid at rest cannot sustain shear stress.

The Core Physical Idea

Unlike solids, fluids cannot resist continuous tangential deformation. If unequal directional stresses existed at a point inside a stationary fluid, the fluid element would experience a net turning or shearing effect.

The element would then deform and begin to flow.

But a stationary fluid, by definition, is in equilibrium.

Therefore:

No directional imbalance can exist inside a fluid at rest.

Pressure must therefore act equally in every direction.

The Conceptual Proof

Consider an extremely small fluid element inside a liquid at rest.

Suppose pressure along one direction were greater than pressure along another direction.

The larger pressure would produce a greater force on one face of the element, generating an unbalanced shear tendency. Since fluids cannot sustain shear stress in static equilibrium, motion would immediately begin.

This contradicts the assumption that the fluid is stationary.

Hence the only possible equilibrium condition is:

Thus, pressure at a point in a static fluid is isotropic.

An Important Consequence

Because pressure has no preferred direction:

  • fluids exert force perpendicular to surfaces,
  • Pascal’s law becomes possible,
  • and hydraulic systems function efficiently.

From ocean depths to hydraulic lifts, isotropic pressure governs the behavior of fluids everywhere.

Final Conclusion

Pressure in a stationary fluid is isotropic because any directional inequality in pressure would create shear forces and destroy equilibrium. Nature preserves stillness inside fluids by ensuring perfect directional balance.

May13

AIR 1 JEE Advanced 2025 Rajit Gupta’s Heartfelt Testimonial for Devansh Sir

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Some journeys begin with talent. Others begin with the right guidance at the right time.

Rajit Gupta first joined my NSEJS batch as a young student in 9th grade with curiosity, sincerity, and a willingness to learn deeply. Over the years, that curiosity evolved into extraordinary achievement — culminating in an exceptional academic journey that includes AIR 1 in Joint Entrance Examination – Advanced, 100 percentile in JEE Mains, selection in multiple prestigious Olympiad camps, qualification for International Physics Olympiad, and selection for APhO twice.

What makes Rajit’s journey especially meaningful to me is not only the scale of his achievements, but the depth of understanding and intellectual maturity he developed along the way. His testimonial beautifully reflects the philosophy I have always believed in — that true Physics education is not about memorization, but about intuition, clarity, imagination, and genuine curiosity.

I am deeply proud of Rajit and grateful to have witnessed his remarkable journey from a young Olympiad student to one of the finest performers in the country.

Respected Devansh Sir,

I am Rajit Gupta. I was your student in NSEJS batch in 9th grade. This year I appeared in JEE and I have got Rank 1 in JEE Advanced, 100 Percentile in JEE Mains, and very good scores in NSEP and NSEA.

I wish to express my deepest gratitude for the immense impact you have had on my journey.

When I started learning physics in your classes, it was completely new to me. But instead of just making me memorize concepts, you motivated me to truly understand them. Your guidance not only helped me build strong intuition but also sparked a genuine interest in the subject.

What sets you apart is the effort and dedication you put into each of your students. Your well-thought-out resources, insightful suggestions, and constant encouragement played a crucial role in my growth. Thanks to your support, I was selected for the Junior Science OCSC, Astronomy OCSC and later for the Physics OCSC twice. I qualified for IPhO this year and also got selected for APhO two times (although I wasn’t able to attend the event this year due to my JEE).

Looking back, I realize that without the strong foundation you gave me, none of this would have been possible. You gave me the perfect kickstart, and for that, I will always be grateful.

Thank you very much, Sir!

Best regards,
Rajit Gupta

May13

“Physics Started Making Sense” — A Heartfelt IIT Bombay Student Testimonial

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Sometimes, even a few months of the right guidance can completely transform a student’s confidence and way of thinking. Palak Sanadhya joined my classes only a short time before JEE Advanced, yet her sincerity, hard work, and deep commitment toward conceptual understanding helped her secure admission to Indian Institute of Technology Bombay in Chemical Engineering.

What makes her testimonial especially meaningful to me is that it reflects the very philosophy with which I teach Physics — not as a collection of formulas to memorize, but as a subject to be visualized, understood intuitively, and appreciated deeply. I am grateful to have played a small role in her remarkable journey.

Securing admission to Chemical Engineering at Indian Institute of Technology Bombay after clearing one of the most competitive examinations in the country was a dream come true for me. And although I studied under Mr. Devansh Mittal for only around three months before JEE Advanced, the impact of his teaching during that short period was truly remarkable.

What immediately stood out to me in his classes was the way he approached Physics — not as a subject to be memorized, but as something to be deeply understood and mentally visualized. In an environment where students often focus only on speed and formulas, his teaching emphasized imagination, intuition, and conceptual clarity.

Whether it was Mechanics, Thermodynamics, Waves & Oscillations, Electrodynamics, Optics, or Modern Physics, he explained every topic with extraordinary precision and simplicity. Even concepts that had previously felt confusing became intuitive after his explanations. His ability to connect physical understanding with mathematical problem-solving made a tremendous difference in my preparation.

One of the most unique aspects of his teaching was his belief, inspired by Albert Einstein, that imagination and intuition are just as important as logic in learning Physics. Instead of encouraging rote methods, he trained us to think independently and understand the deeper meaning behind every concept. That approach not only improved my problem-solving ability, but also gave me confidence while attempting challenging JEE Advanced questions.

Beyond academics, I was deeply touched by the sincerity and honesty with which he guided his students. He genuinely cared about our progress, regularly communicated with parents, and ensured that students remained disciplined, motivated, and mentally focused during such an important phase of preparation.

Despite the limited time I spent under his mentorship, his guidance had a lasting impact on my understanding of Physics and my confidence as a student.

Mr. Devansh Mittal is far more than an excellent teacher — he is a mentor who inspires students to think deeply, learn sincerely, and believe in their own potential.

I will always remain grateful for his support and guidance during one of the most important phases of my academic journey.

— Palak Sanadhya

May13

“I Have Not Seen Such High-Quality Lectures Before”: An IIT Delhi Professor’s Remarkable Testimonial

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There are moments in a teacher’s journey that become deeply meaningful — not merely because of praise, but because of the source from which that appreciation comes.

Receiving a heartfelt testimonial from Prof. Saif Khan Mohammed of Indian Institute of Technology Delhi was one such moment for me.

Prof. Saif is not only a distinguished academician from the Department of Electrical Engineering at IIT Delhi, but also someone who himself secured an under-100 rank in IIT-JEE during his student years. His deep understanding of Physics, analytical thinking, and exposure to high-level technical education make his words especially valuable and humbling.

What touched me most was not simply his appreciation of my lectures, but his recognition of the philosophy behind my teaching — beginning from first principles, developing intuition step by step, and helping students gradually build the confidence to solve highly challenging problems, including advanced problems from the legendary book by I. E. Irodov.

As educators, we often strive not merely to teach formulas, but to cultivate curiosity, clarity of thought, and genuine understanding. To know that these efforts resonated with a respected IIT Delhi professor and benefited his daughter deeply is something I will always cherish.

I am sharing his words below with immense gratitude and humility.

Dear Shri Devansh

I am Prof. Saif Khan Mohammed, Dept. Electrical Engineering l.I.T. Delhi. My daughter is enrolled in your online course. I have been personally viewing your physics video lectures and I must say that I have not seen such high quality lectures before. My daughter has seen other online lectures, but none of them are as good as yours. After seeing your lectures she was able to solve difficult problems in Mechanics from the book by I. E. Irodov. The way you start any topic from basics and gradually increase complexity is what makes it easy for students to learn physics with so much ease. I thank you for your great contribution to education and I am sure you will make even greater contribution in the years to come.

Prof. Saif

IIT Delhi

—

Prof. Saif is a learned professor at IIT Delhi. He himself had under 100 Rank in IIT-JEE when he appeared into it.

https://iitd.irins.org/profile/70117

May9

MIT, Stanford, Oxford & Beyond — Rudra Pethani’s Gratitude for Devansh Sir

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Rudra Pethani is one of the most exceptional young students I have had the privilege to teach. His remarkable journey reflects not only extraordinary intelligence and hard work, but also deep curiosity, discipline, and a genuine passion for learning.

Rudra represented India at the 20th International Junior Science Olympiad (IJSO) held in Thailand and brought immense pride to the nation by winning a Gold Medal. Over the years, he has consistently demonstrated outstanding academic excellence and an exceptional ability to think deeply and intuitively about science and problem solving.

Today, his achievements have earned him acceptance into some of the finest universities in the world — including MIT, Stanford University, Oxford University, and Imperial College London — an accomplishment that very few students across the globe achieve.

What makes Rudra truly special is not only his brilliance, but also his humility, sincerity, and relentless desire to understand concepts at their deepest level.

Below is a heartfelt testimonial written by Rudra about his learning journey and experience with my physics mentorship.

My name is Rudra Pethani, and I am studying in Allen Career Institute.  

I came in contact with Devansh Sir in January 2024 for the INJSO Online Workshop, and I have been his student ever since. He has a completely different and unique approach to physics that I had never seen before. His clear and concise manner of speaking makes each and every student understand what he is trying to convey to us. Moreover, his systematic and methodical approach towards problem solving and concept building has really helped me get a strong grasp on the entirety of physics. The emphasis given to intuitive learning of all the various topics has helped me gain confidence and given me the ability to solve even the toughest of problems. 

I would like to thank Devansh Sir for imparting his vast knowledge to me. Without his guidance, I do not think I would have been able to get this wonderful achievement. 

Nov17

Ford vs Ferrari: Truly Exhilarating Cinematic Experience…

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Ford vs Ferrari is the Incredible, Spectacular, Big-Budget, Star-Powered, Thrill Ride from Bale and Damon with stunning visual racing scenes is a must watch on the big screen. The movie doesn’t even let you lean on your recliner, keeps you straight up with excitement and finally gives you the perfect Movie-Gasm multiple times in its course, the pulsating effect of which continues for a few hours even after you exit from the movie theatre. Even if you are not a motorhead, you will certainly be thrilled by this high-velocity bromance, powered by zealous acting and Mangold’s fastidious direction.

It is pulse-pounding and propulsive, despite a two-and-a-half-hour runtime. The racing sequences are so authentically mounted that you can almost smell the gasoline and burning rubber as the squealing tyres pierce your soul and your seats shudder every time a car roars across the screen.

In the mid-’60s, Ferrari is dominating the racing world, effortlessly winning prize after prize. So Henry Ford II (Tracy Letts) orders his underlings to construct a car that will have Ferrari drivers choking on fumes. Enter Carroll Shelby (Matt Damon) and Ken Miles (Christian Bale), two mavericks who might just be able to pull it off.

The title Ford vs Ferrari is not a perfect title for the film, as it is not primarily about Ford vs Ferrari, but Obsessions vs Egos. It is primarily a battle between The Makers and The Managers at Ford. The movie shows how in a corporate style, hierarchical system, what ultimately may matter is not the perfection, but the perception!

Ford v Ferrari works as an entertainment for dozens of reasons, not least of which are the performances. It simply won’t be an enjoyable experience at home, and in that regard, Ford vs Ferrari, certainly demands a drive and not a walk to the theatre. You cannot afford to miss it. Watch it late at night, because the chances are, the pulsating hangover of the movie will compel you to extremely fast drive on the tracks, which otherwise you may regret later on a crowded day time road!

My Rating: 4.5 / 5.