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

Chapter 5 | 237

AIR

W ̇in =?

T 2 = 400 K

qout = 16 kJ/kg

P 1 = 100 kPa

P 2 = 600 kPa

T 1 = 280 K

m ̇ = 0.02 kg/s

FIGURE 5–27

Schematic for Example 5–6.

Solution Air is compressed steadily by a compressor to a specified temper-
ature and pressure. The power input to the compressor is to be determined.
Assumptions 1 This is a steady-flow process since there is no change with
time at any point and thus mCV0 and ECV0. 2 Air is an ideal gas
since it is at a high temperature and low pressure relative to its critical-point
values. 3 The kinetic and potential energy changes are zero, ke pe 0.
Analysis We take the compressoras the system (Fig. 5–27). This is a control
volume since mass crosses the system boundary during the process. We
observe that there is only one inlet and one exit and thus m. 1 m. 2 m.. Also,
heat is lost from the system and work is supplied to the system.
Under stated assumptions and observations, the energy balance for this
steady-flow system can be expressed in the rate form as

Rate of net energy transfer Rate of change in internal, kinetic,

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

The enthalpy of an ideal gas depends on temperature only, and the
enthalpies of the air at the specified temperatures are determined from the
air table (Table A–17) to be

Substituting, the power input to the compressor is determined to be

Discussion Note that the mechanical energy input to the compressor mani-
fests itself as a rise in enthalpy of air and heat loss from the compressor.

EXAMPLE 5–7 Power Generation by a Steam Turbine

The power output of an adiabatic steam turbine is 5 MW, and the inlet and
the exit conditions of the steam are as indicated in Fig. 5–28.

(a) Compare the magnitudes of h, ke, and pe.
(b) Determine the work done per unit mass of the steam flowing through
the turbine.
(c) Calculate the mass flow rate of the steam.

Solution The inlet and exit conditions of a steam turbine and its power
output are given. The changes in kinetic energy, potential energy, and
enthalpy of steam, as well as the work done per unit mass and the mass flow
rate of steam are to be determined.
Assumptions 1 This is a steady-flow process since there is no change with
time at any point and thus mCV0 and ECV0. 2 The system is adia-
batic and thus there is no heat transfer.

2.74 kW

W

#

in^1 0.02 kg/s^21 16 kJ/kg^2 ^1 0.02 kg/s^21 400.98
280.13^2 kJ/kg

h 2  h@ 400 K400.98 kJ/kg

h 1  h @ 280 K280.13 kJ/kg

W

#

inm

#

qoutm

#

1 h 2 
h 12

W

#

inm

#

h 1 Q

#

outm

#

h 2 ¬¬ 1 since ¢ke¢pe 02

E

#

inE

#

out

E

#

in
E

#

out^ ^ dEsystem>dt^ ^0

0 (steady)

⎭⎪⎪⎬⎪⎪⎫ ⎭⎪⎪⎪⎬⎪¡⎪⎪⎫

STEAM

TURBINE

Wout = 5 MW

P 1 = 2 MPa

T 1 = 400°C

V 1 = 50 m/s

z 1 = 10 m

P 2 = 15 kPa

x 2 = 90%

V 2 = 180 m/s

z 2 = 6 m

FIGURE 5–28

Schematic for Example 5–7.