Basic Engineering Mathematics, Fifth Edition

142 Basic Engineering Mathematics

horizontallineBDmeets the vertical axis indicates

the equivalent Fahrenheit temperature.

Hence, 55 ◦C is equivalent to 131◦F.

This process of finding an equivalent value in

between the given information in the above table

is calledinterpolation.

(b) To find the Celsius temperature at 167◦F, a

horizontal lineEF is constructed as shown in

Figure 17.17. The pointwhere the vertical lineFG

cuts the horizontal axis indicates the equivalent

Celsius temperature.

Hence, 167◦F is equivalent to 75◦C.

(c) If the graph is assumed to be linear even outside of

the given data, the graph may be extended at both

ends (shown by broken lines in Figure 17.17).

From Figure 17.17, 0 ◦C corresponds to 32◦F.

(d) 230 ◦F is seen to correspond to 110◦C.

The process of finding equivalent values outside

of the given range is calledextrapolation.

Problem 13. In an experiment on Charles’s law,

the value of the volume of gas,Vm^3 , was measured

for various temperaturesT◦C. The results are

shown below.

Vm^3 25.0 25.8 26.6 27.4 28.2 29.0

T◦C 60 65 70 75 80 85

Plot a graph of volume (vertical) against

temperature (horizontal) and from it find (a) the

temperature when the volume is 28.6m^3 and (b) the

volume when the temperature is 67◦C

If a graph is plotted with both the scales starting at zero

then the result is as shown in Figure 17.18. All of the

points lie in the top right-hand corner of the graph,

making interpolation difficult. A more accurate graph

is obtained if the temperature axis starts at 55◦Cand

the volume axis starts at 24.5m^3. The axes correspond-

ing to these values are shown by the broken lines in

Figure 17.18 and are calledfalse axes, since the origin

is not now at zero. A magnified version of this relevant

part of the graph is shown in Figure 17.19. From the

graph,

(a) When the volume is 28.6m^3 , the equivalent tem-

perature is82.5◦C.

(b) When the temperature is 67◦C, the equivalent

volume is26.1m^3.

30

25

20

15

Volume (m

3 )

10

5

(^020406080100)
Temperature ( 8 C)
y
x
Figure 17.18
29
28.6
28
27
Volume (m
3 )
26
25
55 60 65 67 70 75 80 82.5 85
26.1
Temperature (C)
y
x
Figure 17.19
Problem 14. In an experiment demonstrating
Hooke’s law, the strain in an aluminium wire was
measured for various stresses. The results were:
Stress (N/mm^2 ) 4.9 8.7 15.0
Strain 0.00007 0.00013 0.00021
Stress (N/mm^2 )18.4 24.2 27.3
Strain 0.00027 0.00034 0.00039