When we were discussing fundamentals of thermal engineering, we have discussed various basic concepts of thermodynamics such as “Enthalpy”, “Specific heat of a substance” and also we have proved that “Internal energy is a property of the system”.

Today we will prove here that entropy is also a property of the system, in the subject of thermal engineering, with the help of this post.

### Entropy as property of the system

Let us consider we have a system which is at equilibrium state 1 and system is reaching at equilibrium state 2 by following the reversible process A. Now system is at equilibrium state 2. Now let we have assumed that system is returning back to its initial state i.e. state 1 from state 2 by following the process B.
Let us assume that there is one more path i.e. process C and system is returning back to initial state i.e. state 1 from by following the reversible process C.

Therefore we have following processes and thermodynamic cycle.
Process 1-A-2, Reversible process
Process 2-B-1, Reversible process
Process 2-C-1, Reversible process
Thermodynamic reversible cycle, 1-A-2-B-1
Thermodynamic reversible cycle, 1-A-2-C-1

Let us recall the “Clausius theorem”. According to Clausius theorem, we will have following equations
Let us apply the concept of Clausius theorem in both the reversible cycle’s i.e. reversible cycle 1-A-2-B-1 and reversible cycle 1-A-2-C-1 and we will have following equations as mentioned here.
From above both equations, it could be easily determined that we will have following equation after subtracting
As we are looking here that Process B and process C are two different processes. What is more important point to be noted here?

dQ/T is basically a function of initial and final states and it will not be dependent over the path selected by the system for completing the cycle. Processes must be reversible processes.

Now it is cleared that there must be one property of the system as above function i.e. dQ/T is not depending over the path but also it will be dependent over the initial state and final state of the system. So we can say that entropy is a point function or state function.

Therefore, this property will be termed as entropy in thermal engineering and it will be measured in J/K. Entropy is an extensive property.

We will discuss another topic i.e. "Triple point phase diagram of water" in our next post in the category of thermal engineering.
Do you have suggestions? Please write in comment box

#### Reference:

Engineering thermodynamics by P.K. Nag
Engineering thermodynamics by Prof R. K. Rajput
1. 2. 