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

374 | Thermodynamics

EXAMPLE 7–15 Effect of Efficiency on Compressor Power Input

Air is compressed by an adiabatic compressor from 100 kPa and 12°C to a

pressure of 800 kPa at a steady rate of 0.2 kg/s. If the isentropic efficiency

of the compressor is 80 percent, determine (a) the exit temperature of air and

(b) the required power input to the compressor.

Solution Air is compressed to a specified pressure at a specified rate. For a

given isentropic efficiency, the exit temperature and the power input are to be

determined.

Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 The

changes in kinetic and potential energies are negligible.

Analysis A sketch of the system and the T- sdiagram of the process are given

in Fig. 7–53.

(a) We know only one property (pressure) at the exit state, and we need to

know one more to fix the state and thus determine the exit temperature. The

property that can be determined with minimal effort in this case is h 2 asince

the isentropic efficiency of the compressor is given. At the compressor inlet,

The enthalpy of the air at the end of the isentropic compression process is

determined by using one of the isentropic relations of ideal gases,

and

Substituting the known quantities into the isentropic efficiency relation, we have

Thus,

h 2 a575.03 kJ>kg¬S¬T 2 a569.5 K

hC

h 2 sh 1

h 2 ah 1

¬S¬0.80

1 517.05285.14 2 kJ>kg

1 h 2 a285.14 2 kJ>kg

Pr 2 9.2672¬S¬h 2 s517.05 kJ>kg

Pr 2 Pr 1 a

P 2

P 1

b1.1584a

800 kPa

100 kPa

b9.2672

1 Pr 1 1.1584 2

T 1 285 K¬S¬h 1 285.14 kJ>kg¬¬ 1 Table A–17 2

AIR

COMPRESSOR

m = 0.2 kg/s

T, K

s

1

2 s

s 2 s = s 1

Isentropic process

285

Actual process

P 2 = 800 kPa

P 1 = 100 kPa

T 1 = 285 K

T 2 a

T 2 s

2 a

800 kPa

100 kPa

·

FIGURE 7–53

Schematic and T-sdiagram for
Example 7–15.