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

452 | Thermodynamics

(b) The reversible work, which represents the minimum work input Wrev,inin

this case, can be determined from the exergy balance by setting the exergy

destruction equal to zero,

Net exergy transfer Exergy Change

by heat, work, and mass destruction in exergy

since KE 
PE 
0 and V 2 
V 1. Noting that T 0 (S 2 S 1 ) 
T 0 Ssystem


19.6 Btu, the reversible work becomes

Therefore, a work input of just 1.0 Btu would be sufficient to accomplish

this process (raise the temperature of air in the tank from 70 to 130°F) if all

the irreversibilities were eliminated.

Discussion The solution is complete at this point. However, to gain some

physical insight, we will set the stage for a discussion. First, let us deter-

mine the actual work (the paddle-wheel work Wpw) done during this process.

Applying the energy balance on the system,

Net energy transfer Change in internal, kinetic,

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

since the system is adiabatic (Q
0) and involves no moving boundaries

(Wb
0).

To put the information into perspective, 20.6 Btu of work is consumed

during the process, 19.6 Btu of exergy is destroyed, and the reversible work

input for the process is 1.0 Btu. What does all this mean? It simply means

that we could have created the same effect on the closed system (raising its

temperature to 130°F at constant volume) by consuming 1.0 Btu of work

only instead of 20.6 Btu, and thus saving 19.6 Btu of work from going to

waste. This would have been accomplished by a reversible heat pump.

To prove what we have just said, consider a Carnot heat pump that absorbs

heat from the surroundings at T 0 
530 R and transfers it to the air in the

rigid tank until the air temperature Trises from 530 to 590 R, as shown in

Fig. 8–39. The system involves no direct work interactions in this case, and

the heat supplied to the system can be expressed in differential form as

The coefficient of performance of a reversible heat pump is given by

COPHP

dQH

dWnet,in

1

1 T 0 >T

dQH
dU
mcv dT

Wpw,in
¢U
20.6 Btu¬¬ 3 from part 1 b 24

EinEout¬
¬ ¢Esystem

1.0 Btu

 1 20.619.6 2 Btu

1 2 lbm 21 0.172 Btu>lbm#°F 21130  702 °F19.6 Btu

Wrev,in
mcv 1 T 2 T 12 T 01 S 2 S 12

 1 U 2 U 12 T 01 S 2 S 12

 1 E 2 E 12 P 01 V 2 V 12 Q

0

T 01 S 2 S 12

Wrev,in
X 2 X 1

XinXout¬  Xdestroyed
¢Xsystem

AIR

70 °F→ 130 °F

Ambient air

70 °F

Wnet,in = 1 Btu

Reversible

heat pump

19.6 Btu

20.6 Btu

FIGURE 8–39

The same effect on the system can be
accomplished by a reversible heat
pump that consumes only 1 Btu of
work.

0 (reversible)

⎭⎪⎬⎪⎫ → ⎭⎪⎬⎪⎫

⎭⎪⎪⎪⎬⎪⎪⎪⎫

⎭⎪⎬⎪⎫ ⎭⎪⎬⎪⎫