Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Entropy is an extensive property of a system and sometimes is referred to as

total entropy. Entropy per unit mass, designated s, is an intensive property

and has the unit kJ/kg · K. The term entropyis generally used to refer to

both total entropy and entropy per unit mass since the context usually clari-

fies which one is meant.

The entropy change of a system during a process can be determined by

integrating Eq. 7–4 between the initial and the final states:

(7–5)

Notice that we have actually defined the changein entropy instead of

entropy itself, just as we defined the change in energy instead of the energy

itself when we developed the first-law relation. Absolute values of entropy

are determined on the basis of the third law of thermodynamics, which is

discussed later in this chapter. Engineers are usually concerned with the

changesin entropy. Therefore, the entropy of a substance can be assigned a

zero value at some arbitrarily selected reference state, and the entropy val-

ues at other states can be determined from Eq. 7–5 by choosing state 1 to be

the reference state (S0) and state 2 to be the state at which entropy is to

be determined.

To perform the integration in Eq. 7–5, one needs to know the relation

between Qand Tduring a process. This relation is often not available, and

the integral in Eq. 7–5 can be performed for a few cases only. For the

majority of cases we have to rely on tabulated data for entropy.

Note that entropy is a property, and like all other properties, it has fixed

values at fixed states. Therefore, the entropy change Sbetween two speci-

fied states is the same no matter what path, reversible or irreversible, is fol-

lowed during a process (Fig. 7–3).

Also note that the integral of dQ/Tgives us the value of entropy change

only if the integration is carried out along an internally reversiblepath

between the two states. The integral of dQ/Talong 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. Therefore, even

for irreversible processes, the entropy change should be determined by carry-

ing out this integration along some convenient imaginary internally

reversible path between the specified states.

A Special Case: Internally Reversible

Isothermal Heat Transfer Processes

Recall that isothermal heat transfer processes are internally reversible.

Therefore, the entropy change of a system during an internally reversible

isothermal heat transfer process can be determined by performing the inte-

gration in Eq. 7–5:

which reduces to

¢S (7–6)

Q

T 0

¬¬ 1 kJ>K 2

¢S

2

1

a

dQ

T

b

int rev



2

1

a

dQ

T 0

b

int rev



1

T 0

(^) 
2
1
1 dQ (^2) int rev
¢SS 2 S 1 
2
1
a
dQ
T
b
int rev
¬¬ 1 kJ>K 2
334 | Thermodynamics
Irreversible
process
Reversible
process
1
2
0.3 0.7 S, kJ/K
∆S = S 2 – S 1 = 0.4 kJ/K
T
FIGURE 7–3
The entropy change between two
specified states is the same whether
the process is reversible or
irreversible.