ENTROPY AND PRINCIPLE OF INCREASE OF ENTROPY

We have already discussed the concept of “Carnot cycle and its efficiency” and we have also seen the concept of “Temperature entropy diagram for water” in our previous posts. In our previous discussion we have also interacted with the concept of “Entropy change in reversible and irreversible process”.

Now it’s time to familiar with the concept of increase of entropy principle. We will also discuss here the concept of entropy generation with the help of this post.

So let us see here first, increase of entropy principle

Let we have a system which is at equilibrium state 1 and system is reaching at another equilibrium state 2 by a process A. Let system is returning to its initial state i.e. state 1 in order to complete the thermodynamic cycle. Let system is returning to state 1 from state 2 via process B.

Let we have assumed that process A is reversible and process B is irreversible, therefore cycle will have one reversible process i.e. process A and one irreversible process i.e. process B.

Now I have one question, above thermodynamic cycle will be reversible cycle or irreversible cycle?

Obviously above cycle will be one irreversible cycle because cycle is associated here with one irreversible process and as we know that if any process of a cycle is irreversible then that cycle will be termed as irreversible cycle.

For more detail about reversible cycle and irreversible cycle, please find the post “thermodynamic reversible cycle, reversible heat engine and reversible heat pump”.

Now let us recall the concept of “Clausius inequality”, we will have following equation as mentioned here

We are having here with one irreversible cycle i.e. 1-A-2-B-1, let us write here the concept of Clausius inequality and we will have following equation as mentioned here

As we know that for a reversible process, we will have

And therefore we will have following equation as mentioned here

Now let us analyze the above equation, we can easily conclude here that entropy change of system will be greater than the entropy transfer and this difference will be produced internally due to irreversibility.

In simple words we can say that there must be internally generated entropy within the system and that’s why the overall change of system entropy is greater than the entropy transfer. The difference between the entropy change of system and entropy transfer will be termed as entropy generation and it will be noted as S_gen.

From above equation, we will have few concepts and let us see here those concepts

S_gen= 0, if there is not any entropy generation then process must be a reversible process. Because for a reversible process, there will not be any entropy generation.

S_gen> 0, if entropy generation is positive, then process must be an irreversible process. Because for an irreversible process, there will be entropy generation and it will be more than zero or we can say that generation of entropy will be positive.

The amount of entropy generation quantifies the intrinsic irreversibility of the process. Let us assume that we have two processes i.e. process A and process B. If entropy generation is higher for path A as compared to the entropy generation for path B then we will say that path A will be more irreversible as compared to path B.

So this was the basic fundamental of increase of entropy principle.

We will see another topic in our next post in the category of thermal engineering

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