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

In the absence of compressed liquid data, a general approximation is to treat

compressed liquid as saturated liquid at the given temperature(Fig. 3–42).

This is because the compressed liquid properties depend on temperature

much more strongly than they do on pressure. Thus,

y≅ yf @ T (3–8)

for compressed liquids, where yis v,u, or h. Of these three properties, the

property whose value is most sensitive to variations in the pressure is the

enthalpy h. Although the above approximation results in negligible error in

vand u, the error in hmay reach undesirable levels. However, the error in h

at low to moderate pressures and temperatures can be reduced significantly

by evaluating it from

h≅ hf @ T vf @ T(P Psat @T) (3–9)

instead of taking it to be just hf. Note, however, that the approximation in

Eq. 3–9 does not yield any significant improvement at moderate to high

temperatures and pressures, and it may even backfire and result in greater

error due to overcorrection at very high temperatures and pressures (see

Kostic, Ref. 4).

In general, a compressed liquid is characterized by

Higher pressures (PPsatat a given T)

Lower tempreatures (TTsatat a given P)

Lower specific volumes (vvfat a given P or T)

Lower internal energies (uufat a given P or T)

Lower enthalpies (hhfat a given P or T)

But unlike superheated vapor, the compressed liquid properties are not

much different from the corresponding saturated liquid values.

134 | Thermodynamics

Given: Given: P P and and T

~=v

f^ @T

u=~uf f @T

h=~hf f @T

v

FIGURE 3–42

A compressed liquid may be
approximated as a saturated liquid at
the given temperature.

u

T, °C

5 MPa

T = 80°C

P= 5 MPa

80

u ≅ uf @ 80 °C

FIGURE 3–43

Schematic and T-udiagram for
Example 3–8.

EXAMPLE 3–8 Approximating Compressed Liquid

as Saturated Liquid

Determine the internal energy of compressed liquid water at 80°C and 5

MPa, using (a) data from the compressed liquid table and (b) saturated liq-

uid data. What is the error involved in the second case?

Solution The exact and approximate values of the internal energy of liquid

water are to be determined.

Analysis At 80°C, the saturation pressure of water is 47.416 kPa, and since

5 MPa Psat, we obviously have compressed liquid, as shown in Fig. 3–43.

(a) From the compressed liquid table (Table A–7)

(b) From the saturation table (Table A–4), we read

The error involved is

which is less than 1 percent.

334.97333.82

333.82

 100 
0.34%

u
uf @ 80°C
334.97 kJ>kg

P
5 MPa

T
80°C

f u
333.82 kJ>kg