“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,
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.
The Intuitive Physicist 