Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

conditions, the slope of the linear model is given by (T 2 T 1 )/L 60 F/ft, as shown in

Figure 18.2. Note that for the given conditions, the line that describes the relationship between

the temperature and position intercepts the temperature axis at the value of 68 (i.e., atx0,

T 68 F).

We can describe many other engineering situations for which linear relationships exist

between dependent and independent variables. For example, as we explained in Chapter 12,

resistivityis a measure of the resistance of a piece of material to electric current. The resistivity

values usually are measured using samples made of a centimeter cube or a cylinder having a

diameter of 1 mil and length of 1 ft. The resistance of the sample is then given by

where ris the resistivity, /is the length of the sample, andais the cross-sectional area of the

sample. As you can see, for constant values of randa, there exists a linear relationship between

Rand the length /.

The relationship among various systems of units is also linear. Let us demonstrate this fact

using an example dealing with temperature scales. In Chapter 11, we discussed the relationship

between the two temperature scales Fahrenheit and Celsius, which is given by

(18.3)

We have plotted the relationship between the Fahrenheit and Celsius scales for the temperature

range shown in Figure 18.3. Note the slope of the line describing the relationship is 9/5 1.8,

and the line intercepts the Fahrenheit axis at 32 (i.e.,T( C) 0,T( F) 32).

T 1 °F 2 

9

5

T 1 °C 2  32

R

r/

a

18.2 Linear Models 589

T

(°F)

80

70

60

50

40

30

20

10

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

x (ft)

T   60 x  68

■Figure 18.2 Temperature distribution along a wall.

x(ft) T(x)

068

0.1 62

0.2 56

0.3 50

0.4 44

0.5 38

T 1  68 F

T 2  38 F

L0.5 ft

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