Entropy & Second Law of Thermodynamics

When the word entropy is whispered around you, the words “irreversibility” and “disorder”, must involuntarily spring to your mind. But what is the meaning of Entropy?

Entropy is a slightly perplexing topic and many struggle with it. If this topic is not studied right, it wouldn’t be a surprise if later on, you too can’t place your finger on what exactly entropy or entropy change is. Let’s begin with the basics.

Irreversibility and disorder are central concepts that will drive your comprehension of entropy. One way to define entropy is the number of ways a system can be arranged. Another way to define it is higher the entropy, the more the system is disordered or with a positive change in entropy, the system moves towards disorder.

Entropy can be defined in a thousand different ways. It can be defined at the thermodynamic stage, at the cosmology stage, on a macroscopic level or so on. So you see this concept is prevalent everywhere. It talks about the tendency of the universe towards disorder. It also brings up the concept of true randomness.

For example take a bottle of perfume and spray it in the corner of a room, would it just stick to that corner? Definitely not, the perfume molecules will eventually fill up the room. Did you notice that transition from order towards disorder? And it obeys the laws set down by randomness too. The molecules wouldn’t spread in a proper fashion, it would be truly random. This is one way to explain entropy. The concept of irreversibility is already quite familiar to us. The arrow of time is straight ahead, it doesn’t bend and neither will it reverse. Hence if you drop a glass and watch it shatter, you know there is no way of going back in time and holding the unbroken glass. This is irreversibility.

By now we can see that first law of thermodynamics is only concerned with the energy of the processes. But in real world even if the energy relation holds good some processes do not take place. Such as heat flowing from colder to hotter body even though conservation of energy will still be valid.

To explain this, we need second law of thermodynamics. But before that we need to introduce ‘entropy’. In simple terms entropy means randomness of the system. So those processes in which randomness increases and it takes place readily are known as spontaneous processes. Just like internal energy, entropy is also a state function. It has been found that entropy depends on heat transferred and the temperature of the system.

We know that there are two types of processes

(i) Reversible

(ii) Irreversible

For example a free expansion of gas is irreversible process because it cannot be made to take place in backward direction by a small change. If the same expansion is done as shown in the following figure:

We remove iron balls one by one so the system is in equilibrium state throughout the process and can be reversed in the backward direction by a small change. So in an irreversible process the change in temperature is abrupt so we will not be able to find the change in entropy. So what shall we do? We know Change in entropy is a state function and hence we can go from the initial state to final state by a reversible process. The change will be same as in case of irreversible process.

According to the law, the entropy of a system increases during a process. Mathematically it can be stated as

∆S ≥ 0