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

172 | Thermodynamics

the gas, and (c) the fraction of this work done against the spring to

compress it.

Solution A gas in a piston–cylinder device equipped with a linear spring

expands as a result of heating. The final gas pressure, the total work done, and

the fraction of the work done to compress the spring are to be determined.

Assumptions 1 The expansion process is quasi-equilibrium. 2 The spring is

linear in the range of interest.

Analysis A sketch of the system and the P-Vdiagram of the process are

shown in Fig. 4–10.

(a) The enclosed volume at the final state is

Then the displacement of the piston (and of the spring) becomes

The force applied by the linear spring at the final state is

The additional pressure applied by the spring on the gas at this state is

Without the spring, the pressure of the gas would remain constant at

200 kPa while the piston is rising. But under the effect of the spring, the

pressure rises linearly from 200 kPa to

at the final state.

(b) An easy way of finding the work done is to plot the process on a

P-Vdiagram and find the area under the process curve. From Fig. 4–10 the

area under the process curve (a trapezoid) is determined to be

Warea

1200  3202 kPa

2

¬ 31 0.1
0.05 2 m^3 4a

1 kJ

1 kPa#m^3

b13 kJ

200  120 320 kPa

P

F

A



30 kN

0.25 m^2

120 kPa

Fkx 1 150 kN>m 21 0.2 m 2 30 kN

x

¢V

A



1 0.1
0.05 2 m^3

0.25 m^2

0.2 m

V 2  2 V 1  1221 0.05 m^32 0.1 m^3

P, kPa

V, m^3

P 1 = 200 kPa

II

0.05 0.1

V 1 = 0.05 m^3

I

320

200

Heat

A = 0.25 m^2

k = 150 kN/m

FIGURE 4 –10

Schematic and P-Vdiagram for
Example 4 –4.