LECTURE 13
13.1 Entropy-Introduction



First Law of Thermodynamics
Energy
Second Law of Thermodynamics
Entropy

Unlike energy, entropy is a nonconserved property.

 
13.2 Clausius Inequality


Clausius Inequality
The cyclic integral of is always less than or equal to zero.
This inequality is valid for all cycles, reversible or irreversible.
The symbol is used to indicate that the integration is to be performed over the entire cycle.
Any heat flow to or from a system can be considered to consist of differential amounts of heat. The cyclic integral of can be viewed as the sum of all these differential amounts of heat divided by the temperature at the boundary.

 

Reversible Heat Engine

For a reversible heat engine operating between a high-temperature reservoir at and a low-temperature reservoir at ,

 

Irreversible Heat Engine

For an irreversible heat engine operating between the same reservoirs:

From the Carnot first principle, we have. Therefore,

and where .

 

 
13.3 Definition of Entropy


If a quantity whose cyclic integral is zero depends on the state only and not the process path, then it is a property.

A, B are any two internally reversible process paths between states 1 and 2.

(S: Entropy)

S is an extensive property of a system. Entropy per unit mass, designated s, is an intensive property.

To perform the integration, one needs to know the relation between Q and T during a process.

The integral of will give us the value of entropy change only if the integration is carried out along an internally reversible path between two states.

The integral of along an irreversible path is not a property, and in general, different values will be obtained when the integration is carried out along different irreversible paths.

is the value of entropy specified at the reference state.

 
(: entropy production)
Reversible Cycles
= 0
Irreversible Cycles
> 0
Impossible Cycles
< 0

 
13.4 Isothermal Heat Transfer Processes


The entropy change of a system during an internally reversible process can be positive or negative depending on the direction of heat transfer. Heat transfer to a system (Q > 0) will increase the entropy of that system whereas heat transfer from a system (Q < 0) will decrease it. In fact, losing heat is the only way the entropy of a system can be decreased.

 
13.5 The Increase-In-Entropy Principle


The entropy change of a closed system during an irreversible process is greater than the integral of evaluated for that process.

For an adiabatic process, Q = 0

The entropy of an adiabatic closed system always increases or, in the limiting case, remains constant during a process.

In the absence of any heat transfer, entropy change is due to irreversibilities only, and their effect is always to increase the entropy.

A General Case

A system plus its surroundings constitutes an adiabatic system, assuming both can be enclosed by a sufficient large arbitrary boundary across which there is no heat or mass transfer.

which is applicable to both closed or open (control volume) systems.

The total entropy change associated with a process must be positive or zero. The equality holds for reversible processes and the inequality for irreversible processes.

The above equation does not imply that the entropy of a system or the surroundings cannot decrease. It only implies that their sum cannot decrease.

 
 
Reversible Processes
= 0
 
Irreversible Processes
> 0
 
Impossible Processes
< 0


The more irreversible a process is, the larger the entropy is generated during the process

 
13.6 Cause of Entropy Change


 
Causes of Entropy Change
Heat Transfer
Irreversibilities

 

 
Isentropic Process
If a process involves no heat transfer (adiabatic) and no irreversibilities within the system (internally reversible), the entropy of a system must remain constant during that process. Such a process is called an isentropic process.

 

Remarks about Entropy
1. Process can occur in a certain direction only, not in any direction. A process must proceed in the direction that complies with the increase-in-entropy principle, that is, .
2. Entropy is a nonconserved property, and there is no such thing as the conservation of entropy principle. Entropy is conserved during the idealized reversible processes only and increases during all actual processes.
3. The performance of engineering system is degraded by the presence of irreversibilities, and the entropy generation is a measure of the magnitude of the irreversibilities present during that process.

 
13.7 What is Entropy?


Entropy can be viewed as a measure of molecular disorder, or molecular randomness.

Heat is, in essence, a form of disorganized energy, and some disorganization (entropy) will flow with heat.

Work instead is an organized form of energy, and is free of disorder or randomness and thus free of entropy. There is no entropy transfer associated with energy transfer as work.

The quantity of energy is always preserved during an actual process (the first law), but the quality is bound to decrease (the second law). This decrease in quality is always accompanied by an increase in entropy.

From a statistical point of view, entropy is a measure of molecular randomness, i.e., the uncertainty about the position of molecules at any instant. Even in the solid phase, the molecules of a substance continually oscillate, creating an uncertainty about their position.

Third Law of Thermodynamics
The entropy of a pure crystalline substance at absolute zero temperature is zero since there is no uncertainty about the state of the molecules at that instant.

The third law of thermodynamics provides an absolute reference point for the determination of entropy.