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

Partial Differential Relations Now let us rewrite Eq. 12–3 as (12–4) where Taking the partial derivative of Mwith respect to yan ...

The first relation is called the reciprocity relation,and it shows that the inverse of a partial derivative is equal to its reci ...

Two of the Gibbs relations were derived in Chap. 7 and expressed as (12–10) (12–11) The other two Gibbs relations are based on t ...

EXAMPLE 12–4 Verification of the Maxwell Relations Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at 250 ...

volume. That is,Psatf(Tsat). Therefore, the partial derivative (P/T)vcan be expressed as a total derivative (dP/dT)sat, which ...

The Clapeyron equation can be simplified for liquid–vapor and solid–vapor phase changes by utilizing some approximations. At low ...

12–4 ■ GENERAL RELATIONS FOR du, dh, ds, cv, AND cp The state postulate established that the state of a simple compressible syst ...

Now we choose the entropy to be a function of Tand v; that is,ss(T,v) and take its total differential, (12–26) Substituting thi ...

Equating the coefficients of dTand dPin Eqs. 12–31 and 12–33, we obtain (12–34) Using the fourth Maxwell relation (Eq. 12–19), w ...

Specific Heats cvand cp Recall that the specific heats of an ideal gas depend on temperature only. For a general pure substance, ...

An alternative form of this relation is obtained by using the cyclic relation: Substituting the result into Eq. 12–45 gives (12– ...

666 | Thermodynamics Analysis The change in internal energy of any simple compressible system in any phase during any process ca ...

Chapter 12 | 667 For an ideal gas PRT/v. Then Thus, which states that cvdoes not change with specific volume. That is, cvis not ...

12–5 ■ THE JOULE-THOMSON COEFFICIENT When a fluid passes through a restriction such as a porous plug, a capillary tube, or an or ...

temperature. This presents a problem for substances whose maximum inver- sion temperature is well below room temperature. For hy ...

In Chap. 3 we accounted for the deviation in properties P,v, and Tby either using more complex equations of state or evaluating ...

vZRT/Pand simplifying Eq. 12–56, we can write the enthalpy departure at any temperature Tand pressure Pas The above equation ca ...

finally along the T 2 constant line to P 2 , as we did for the enthalpy. This approach is not suitable for entropy-change calcu ...

or (12–64) where the values of Zsare determined from the generalized entropy depar- ture chart and the entropy change (s 2 s 1 ...

674 | Thermodynamics and Then the enthalpy and entropy changes of oxygen during this process are determined by substituting the ...