Misunderstood Concept in Physics: Entropy

The Earth receives a certain amount of energy from the sun every day. This energy is vital for sustaining life and driving various processes on our planet. The question arises as to how much of this energy is radiated back into space by the Earth. It is important to understand that energy never really disappears; rather, it transforms from one form to another. Throughout most of Earth's history, the amount of energy received from the sun has been approximately equal to the amount radiated back into space.

Now, let's travel back to the winter of 1813 in France, a period marked by invasions from Austria, Prussia, and Russia. Among the individuals living through this tumultuous time was Sadi Carnot, a 17-year-old student and the son of one of Napoleon's generals. Sadi aspired to join the fight against the invading armies and wrote a letter to Napoleon expressing his desire. Unfortunately, Napoleon, preoccupied with the battles, did not reply to the young student's request.

However, a few months later, when Paris came under attack, Sadi Carnot's wish was granted as he and fellow students defended a chateau near the city. Despite their efforts, they were unable to hold off the advancing armies, and Paris fell within a day of fighting. The defeat and forced retreat left Sadi devastated.

Seven years later, Sadi Carnot visited his father, who had sought refuge in Prussia following Napoleon's downfall. Notably, Sadi's father was not only a general but also a physicist. During their meeting, they delved into discussions about the groundbreaking technology of the time – steam engines. These engines were already being utilized for powering ships, mining ore, and excavating ports. The future prospects of nations, both industrially and militarily, hinged on having the most advanced steam engines. Unfortunately, French designs were lagging behind those of other countries, particularly Britain.

Determined to improve France's position and restore its prominence, Sadi Carnot embarked on a three-year journey to study heat engines. He sought to understand how an ideal heat engine would operate, one without friction or losses to the environment. His insights led him to envision a hypothetical ideal engine consisting of two large metal bars, one hot and one cold. Between them lay a chamber filled with air, through which heat could flow in or out only from the bottom. Within this chamber was a piston connected to a flywheel.

The engine's functioning involved a cyclical process: first, the hot bar was brought into contact with the chamber, causing the air inside to expand and push the piston up, turning the flywheel. Then, the hot bar was removed, and the air continued to expand without heat, lowering its temperature until it matched that of the cold bar. When the cold bar was introduced, the flywheel pushed the piston down, compressing the air and transferring heat into the cold bar. The cycle then repeated, with the hot bar being reconnected.

Sadi Carnot realized that this ideal engine was entirely reversible. If the engine was run in reverse, the same number of cycles could be run backward, and everything would return to its original state without any additional input of energy. However, despite its reversibility, the efficiency of this engine was not 100%. The efficiency could be calculated based on the energy of the flywheel, the heat input from the hot bar, and the temperatures of the hot and cold sides.

Carnot's ideal engine demonstrated that the efficiency of a heat engine does not depend on its materials or design but rather on the temperatures of its hot and cold sides. To achieve 100% efficiency, the hot side would need to have infinite temperature or the cold side absolute zero, both of which are unattainable in practice. Hence, even in an ideal scenario with no friction or losses, it is impossible to create a heat engine with 100% efficiency.

In Carnot's time, high-pressure steam engines could only reach temperatures up to 160 degrees Celsius, limiting their theoretical maximum efficiency to 32%. In reality, these engines operated at around 3% efficiency due to friction, heat dissipation to the environment, and the absence of constant-temperature heat transfer.

Rudolf Clausius later introduced the concept of entropy to measure the spread-out nature of energy. Entropy is associated with the tendency of energy to become more dispersed and less available for work. According to Clausius, the entropy of the universe tends to a maximum over time. This increase in entropy is why energy spreads out and time has a clear direction, known as the arrow of time.

The sun plays a crucial role in maintaining low entropy on Earth. It provides a continuous stream of concentrated energy, which plants capture and use to grow. Animals, in turn, consume plants and convert the energy to maintain their bodies and engage in various activities. This process of energy transformation leads to an increase in entropy, as energy becomes more spread out and less useful.

The universe began with extremely low entropy after the Big Bang. As gravity caused matter to clump together, enormous amounts of potential energy turned into kinetic energy, and entropy increased. Stars, planets, galaxies, and life formed as a result of this increase in entropy.

Black holes, as discovered by Stephen Hawking, also contribute to the universe's entropy. Hawking radiation emitted by black holes is a form of energy loss, which increases their entropy. In fact, almost all the entropy of the universe is tied up in black holes.

Ultimately, the universe's entropy will continue to increase, leading to the heat death of the universe in the distant future. This state represents the maximum spread-out energy, resulting in a lack of interesting structures or processes.

Despite the inevitability of increasing entropy, complexity and interesting phenomena arise in intermediate states where energy is neither fully concentrated nor fully dispersed. Earth's unique position, receiving low entropy from the sun, allows for the existence of complex structures, including life. It is essential to make use of this low entropy while it is available and understand the complexities that arise from it.

In conclusion, the concept of entropy is central to understanding the arrow of time and the behavior of energy in the universe. It governs the spread-out nature of energy and explains why certain processes are irreversible. The continuous increase in entropy contributes to the formation of complex structures and drives the evolution of the universe. As we continue to explore the intricacies of entropy, we gain insights into the fundamental workings of our world and the universe at large.