Entropy

Chapter 8

1

2

• The important point is that since entropy is a property, the change in the entropy of a substance in going from one state to another is the same for all processes, both reversible and irreversible, between these two states.

• From the third law of thermodynamicsthe third law of thermodynamics, which is based on observations of low-temperature chemical reactions, it is concluded that the entropy of all pure substances (in the appropriate structural form) can be assigned the absolute value of zero at the absolute zero of temperature. It also follows from the subject of statistical thermodynamics that all pure substances in the (hypothetical) ideal-gas state at absolute zero temperature have zero entropy.

• However, when there is no change of composition, as would occur in a chemical reaction, for example, it is quite adequate to give values of entropy relative to some arbitrarily selected reference state, such as was done earlier when tabulating values of internal energy and enthalpy. In each case, whatever reference value is chosen, it will cancel out when the change of property is calculated between any two states.

• In the steam tables the entropy of saturated liquid at 0.01C is given the value of zero.

• For many refrigerants, the entropy of saturated liquid at 400C is assigned the value of zero.

• 1/T serves as the integrating factor in converting the inexact differential δQ to the exact differential δQ/T for a reversible process.

8.3 The Entropy of Pure Substance8.3 The Entropy of Pure Substance

8.4 ENTROPY CHANGE IN REVERSIBLE PROCESSES

1

2

3

4

Net work

Eq.6.13

1

2

( Gibbs equations )

1

2

2 1-

0 + -

1

2

8.7 ENTROPY GENERATION

2

1

Some Important ConclusionsSome Important Conclusions

• There are two ways in which There are two ways in which the entropy of a system cathe entropy of a system can be increasedn be increased—by transferring heat to it and by having —by transferring heat to it and by having an irreversible process. an irreversible process.

• Since the entropy generation cannot be less than zero, tSince the entropy generation cannot be less than zero, there is only one way in which here is only one way in which the entropy of a system cathe entropy of a system can be decreasedn be decreased, and that is to transfer heat from the sys, and that is to transfer heat from the system.tem.

• For an adiabatic process, For an adiabatic process, δδQ Q = = 0, and therefore the incr0, and therefore the increase in entropy is always associated with the ease in entropy is always associated with the irreversibiirreversibilitieslities..

• Finally, the presence of irreversibilities will cause the wFinally, the presence of irreversibilities will cause the work to be smaller than the reversible work. ork to be smaller than the reversible work. This means lThis means less work out in an expansion process and more work intess work out in an expansion process and more work into the control mass o the control mass (δ(δW W <<0) in a compression process0) in a compression process..

• In fact, in many situations we are not certain of the exact state through which a system passes when it undergoes an irreversible process.• The work for an irreversible process (fig. 8.11a) is not equal to P dV, and the heat transfer is not equal to T dS. • Therefore, the area underneath the path does not represent work and heat on the P–V and T –S diagrams, respectively.

8.8

1

2

For the control mass

c.m.2

• Thus we conclude that the net entropy change is the sum of a number of terms, each of which is positive, due to a specific cause of irreversible entropy generation, such that the net entropy change could also be termed the total entropy generation:

dSnet =dScm +dSsurr = Σδ Sgen ≥ 0 --------- (8.16)

where the equality holds for reversible processes and the inequality for irreversible processes.

8.9 ENTROPY CHANGE OF A SOLID OR LIQUID

8.10 ENTROPY CHANGE OF AN IDEAL GAS

1

23