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

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 this into the Tdsrelation duTdsPdvyields

(12–27)

Equating the coefficients of dTand dvin Eqs. 12–25 and 12–27 gives

(12–28)

Using the third Maxwell relation (Eq. 12–18), we get

Substituting this into Eq. 12–25, we obtain the desired relation for du:

(12–29)

The change in internal energy of a simple compressible system associated

with a change of state from (T 1 ,v 1 ) to (T 2 ,v 2 ) is determined by integration:

(12–30)

Enthalpy Changes

The general relation for dhis determined in exactly the same manner. This

time we choose the enthalpy to be a function of Tand P, that is,hh(T,P),

and take its total differential,

Using the definition of cp, we have

(12–31)

Now we choose the entropy to be a function of Tand P; that is, we take

ss(T,P) and take its total differential,

(12–32)

Substituting this into the T dsrelation dhT dsvdPgives

dhTa (12–33)

0 s

0 T

b

P

dTcvTa

0 s

0 P

b

T

d

dP

dsa

0 s

0 T

b

P

dTa

0 s

0 P

b

T

dP

dhcp dTa

0 h

0 P

b

T

dP

dha

0 h

0 T

b

P

dTa

0 h

0 P

b

T

dP

u 2 u 1 

T 2

T 1

cv¬dT

v 2

v 1

¬cTa

0 P

0 T

b

v

Pd¬dv

ducv¬dTcTa

0 P

0 T

b

v

Pd dv

a

0 u

0 v

b

T

Ta

0 P

0 T

b

v

P

a

0 u

0 v

b

T

Ta

0 s

0 v

b

T

P

a

0 s

0 T

b

v



cv

T

duTa

0 s

0 T

b

v

dTcTa

0 s

0 v

b

T

Pd dv

dsa

0 s

0 T

b

v

dTa

0 s

0 v

b

T

dv

662 | Thermodynamics