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

is highly irreversible since this generates entropy, and it can cause consider-

able damage. A person who gets up in anger is bound to sit down at a loss.

Hopefully, someday we will be able to come up with some procedures to

quantify entropy generated during nontechnical activities, and maybe even

pinpoint its primary sources and magnitude.

7–7 ■ THE T ds RELATIONS

Recall that the quantity (dQ/T)int revcorresponds to a differential change in

the property entropy. The entropy change for a process, then, can be evalu-

ated by integrating dQ/Talong some imaginary internally reversible path

between the actual end states. For isothermal internally reversible processes,

this integration is straightforward. But when the temperature varies during

the process, we have to have a relation between dQand Tto perform this

integration. Finding such relations is what we intend to do in this section.

The differential form of the conservation of energy equation for a closed

stationary system (a fixed mass) containing a simple compressible substance

can be expressed for an internally reversible process as

(7–21)

But

Thus,

(7–22)

or

(7–23)

This equation is known as the first T ds, or Gibbs,equation. Notice that the

only type of work interaction a simple compressible system may involve as

it undergoes an internally reversible process is the boundary work.

The second T dsequation is obtained by eliminating dufrom Eq. 7–23 by

using the definition of enthalpy (hu
Pv):

(7–24)

Equations 7–23 and 7–24 are extremely valuable since they relate entropy

changes of a system to the changes in other properties. Unlike Eq. 7–4, they

are property relations and therefore are independent of the type of the

processes.

These T dsrelations are developed with an internally reversible process in

mind since the entropy change between two states must be evaluated along

a reversible path. However, the results obtained are valid for both reversible

and irreversible processes since entropy is a property and the change in a

property between two states is independent of the type of process the sys-

tem undergoes. Equations 7–23 and 7–24 are relations between the proper-

ties of a unit mass of a simple compressible system as it undergoes a change

of state, and they are applicable whether the change occurs in a closed or an

open system (Fig. 7–28).

hu
Pv

1 Eq. 7–23 2

¡

¡

dhdu
P¬dv
v¬dP

T¬dsdu
P¬dv

f T¬dsdhv¬dP

T¬dsdu
P¬dv¬¬ 1 kJ>kg 2

T¬dSdU
P¬dV¬¬ 1 kJ 2

dWint rev,outP¬dV

dQint revT¬dS

dQint revdWint rev,outdU

350 | Thermodynamics

Closed CV

system

T ds = du + P dv

T ds = dh – v dP

FIGURE 7–28

The T dsrelations are valid for both
reversible and irreversible processes
and for both closed and open systems.

SEE TUTORIAL CH. 7, SEC. 7 ON THE DVD.

INTERACTIVE

TUTORIAL