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

Image courtesy: Google

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