Unformatted text preview: 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
dQint rev dWint rev, out dU (7–21) But
dQint rev
dWint rev, out T dS
P dV Thus,
T dS dU P dV (kJ) (7–22) P dυ (kJ/kg) (7–23) or
T ds du 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 ds equation is obtained by eliminating du from Eq. 7–23 by
using the definition of enthalpy (h u Pυ):
h u Pυ
(Eq. 6–23) Closed
system CV T ds = du + P dυ
T ds = dh – υ dP FIGURE 7–28
The T ds relations are valid for both
reversible and irreversible processes
and for both closed and open systems. →
→ dh
T ds du
du P dυ
P dυ υ dP T ds dh υ dP (7–24) Equations 7–23 and 7–24 are extremely valuable since they relate entropy
changes of a system to the ch...
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 Spring '09

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