# Finding such relations is what we intend to do in

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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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