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

Chapter 5 | 251

(b) Noting that the microscopic energies of flowing and nonflowing fluids are
represented by enthalpy hand internal energy u, respectively, the mass and
energy balances for this uniform-flow system can be expressed as

Mass balance:

Energy balance:

Net energy transfer Change in internal, kinetic,

by heat, work, and mass potential, etc., energies

Combining the mass and energy balances gives

The amount of heat transfer during this process is found from

Steam leaves the pressure cooker as saturated vapor at 175 kPa at all times
(Fig. 5–51). Thus,

The initial internal energy is found after the quality is determined:

Thus,

and

The mass of the system at the final state is m 2 V/v 2. Substituting this
into the energy equation yields

There are two unknowns in this equation, u 2 and v 2. Thus we need to relate
them to a single unknown before we can determine these unknowns. Assum-
ing there is still some liquid water left in the cooker at the final state (i.e.,
saturation conditions exist), v 2 and u 2 can be expressed as

Recall that during a boiling process at constant pressure, the properties of
each phase remain constant (only the amounts change). When these expres-
sions are substituted into the above energy equation, x 2 becomes the only
unknown, and it is determined to be

x 2 0.009

u 2 ufx 2 ufg486.82x 21 2037.7 2 kJ/kg

v 2 vfx 2 vfg0.001x 21 1.004
0.001 2 m^3 /kg

Qinam 1 

V

v 2

bhea

V

v 2

¬u 2 
m 1 u 1 b

U 1 m 1 u 1 (1 kg)(497 kJ/kg)497 kJ

u 1 ufx 1 ufg486.82 1 0.00499 21 2037.7 2 kJ/kg497 kJ/kg

x 1 

v 1 
vf

vfg



0.006
0.001

1.004
0.001

0.00499

v 1 

V

m 1



0.006 m^3

1 kg

0.006 m^3 /kg

hehg @ 175 kPa2700.2 kJ/kg

QinQ

#

in^ ¢t^1 0.5 kJ/s^2130 60 s^2 900 kJ

Qin(m 1 
m 2 )he(m 2 u 2 
m 1 u 1 )CV

Qin
mehe(m 2 u 2
m 1 u 1 )CV (since W0, kepe0)

Ein
Eout  ¢Esystem

min
mout¢msystem S
me 1 m 2
m 12 CV¬or¬me 1 m 1
m 22 CV

⎭⎪⎬⎪⎫ ⎭⎪⎬⎪⎫

P

he = hg@175 kPa

Sat. vapor

Sat. liquid

Sat. vapor

FIGURE 5–51

In a pressure cooker, the enthalpy of

the exiting steam is hg@ 175 kPa

(enthalpy of the saturated vapor at the

given pressure).