What is Entropy?- An introduction to the second law of thermodynamics

Have you ever wondered why your hot food eventually becomes cold 😅? In this blog post, we embark on an interesting journey to understand the fundamental principles underlying this phenomenon. While I'll touch on some technical terms, my aim is to make these concepts accessible to everyone by minimizing the use of mathematical equations.

The First Law of Thermodynamics

Before we dive in, let's take a moment to understand what thermodynamics actually means. It is the branch of science that studies how heat and energy move around. It's basically about understanding how energy flows from one object to another.

The first law of thermodynamics (FLoT), also known as the law of conservation of energy, explains that energy cannot be created or destroyed. Instead, it can only change form or move from one place to another within a system. It is useful for understanding energy conversions, but the problem with it is that, it doesn't address the practical limitations of energy conversions. What this means is that even though energy is always conserved, not all of it can be used the way we want.

A quick question

Picture a scenario where a heated object comes into contact with a cooler object, and over time, you notice that the hot object has gotten even hotter while the cold one has become even colder. Does this scenario look like something that can actually happen?

Answer

Surprisingly, according to the first law, this scenario is actually possible as long as we can account for the heat involved. But we don't observe this in our daily lives because something prevents this from happening. And that leads us to the concept of entropy.

Entropy

When we consider only the energy contained within an object, we can say that energy is constantly moved from one location to another in the form of work. This explains why elementary school textbooks often define energy as the ability to do work.

Theoretically, there is a limit to the amount of work that can be obtained in any process. That is, not all the energy in a body is available to do work. This maximum (or minimum) work can only be obtained when the process is done on a reversible path (opens in new tab). To put it simply, a process is said to be reversible if it can be returned to its initial state without a net addition of work or heat. The issue is, almost every real-world process operates on an irreversible path. As a result, we don't attain the theoretical maximum (or minimum) work in real world processes.

So, if a process could give us 10 joules of work in theory, but we only get 6 joules in reality, where does the remaining 4 joules go? Remember that from the first law, energy cannot be created or destroyed, so the remaining 4 joules must be somewhere. Yes, Entropy is the property that is used to quantify this 'lost work'. It represents the portion of a system's energy that is unavailable to do work.

The Second Law of Thermodynamics

The second law of thermodynamics states that in real life processes, the total entropy of the universe always increases. This is because the 'lost work' in every process (entropy) is transferred to the universe.

We can make the following deductions from our discussion so far:

1. In a reversible process, no work is lost, and the total entropy of the universe remains the same.
2. Reversible processes are the most efficient processes possible, because they produce the maximum amount of work or require the minimum amount of work for a given process.
3. The entropy of the universe can never decrease; it can only stay the same or increase. This means that some work is always lost in real-world processes, because real-world processes are never perfectly reversible.

Spontaneous Processes

When a hot substance transfers heat to its relatively colder surroundings, it cools down. This phenomenon is a common occurrence in our daily lives, but what drives it to happen in this specific direction (from hot to cold) and not the other way round?

The interesting thing is, this cooling process occurs naturally, i.e., it happens on its own without any energy input.

In thermodynamics, any process that occurs naturally in this manner is referred to as a spontaneous process. As a general rule of thumb, the change in entropy for any spontaneous process must be greater than zero (i.e positive). Mathematically, Sf - Si > 0, where Sf and Si are final and initial entropy respectively.

In the following section, the connection between entropy and spontaneous processes explains the answer to our initial problem!

Heat Transfer

The natural flow of heat from a hot object to a colder one is a spontaneous process, and it contributes to the overall increase in the universe's entropy. This explains why our hot foods eventually cool down, as this transition from hot to cold leads to a positive change in entropy. If, on the other hand, heat were to flow from cold to hot, it would result in a negative change in entropy, violating the second law of thermodynamics. A detailed mathematical proof is available for further exploration. (opens in new tab).

Regarding the problem introduced at the beginning of this article, we can conclude that, it doesn't contradict the first law of thermodynamics because energy remains conserved. The heat lost by the cold object can be accounted for as the heat gained by the warm object. And this explains why the warm object becomes warmer while the cold object becomes colder. However, we don't observe this phenomenon in our daily experiences because it doesn't occur spontaneously.

Conclusion

The second law of thermodynamics is a fundamental law of physics that has many important implications for the physical world. It explains why heat is always transferred from hot substances to cold substances, and it can be used to predict the spontaneity of processes and to design efficient engines and power plants.

Reference

Dahm, D. K, Visco, D. P, 2015, Fundamentals of Chemical Engineering Thermodynamics, Cengage Learning, Stamford. p-131 Chat