67
c n
c n
s~
E 30
>
2 0
0 0 X
/
x
x
/
i
>
X
/
s
y^
X
L^ s
/
f I
20
1
20
40
60
80 100 120 140 160 180 200 220 240
FIGURE 6-2
T (temperature, °C) 25.0
50.0
75.0
100
125
150
175
200
V (voltage, mv)
0.23
1.20
2.24
3.32
4.34
5.35
6.33
7.31
Plot these values of millivolts and temperature. From the resulting graph, determine the mathematical equation that describes V as a function of T.
SOLUTION:
The graph of these values of V and T is shown in Figure 6-2. Note that the best line
passes through only one of the experimental points. In order to include the v
intercept, one must take some negative values along the V axis. The value of the v
intercept then can be taken directly from the graph; it is -0.80. The slope of the
line is calculated by selecting two convenient points on this line, as shown, then
taking the ratio of the two sides of the triangle formed from these points: in the
figure, it is the ratio 2.0/50 = 0.040. Knowing the slope and the v intercept, we can
directly write the mathematical equation for the relationship between V and T as
V = 0.0407 - 0.80
Students often select two of the experimental points in order to calculate the slope
of a straight-line function; doing so usually is bad practice, because there are
experimental errors inherent in the individual data points. The straight line that
best represents all the points minimizes the experimental errors, and the slope
calculated from this best straight line thus will (usually) be more reliable than one
calculated from two randomly selected experimental points.
c n
c n
s~
E 30
>
2 0
0 0 X
/
x
x
/
i
>
X
/
s
y^
X
L^ s
/
f I
20
1
20
40
60
80 100 120 140 160 180 200 220 240
FIGURE 6-2
T (temperature, °C) 25.0
50.0
75.0
100
125
150
175
200
V (voltage, mv)
0.23
1.20
2.24
3.32
4.34
5.35
6.33
7.31
Plot these values of millivolts and temperature. From the resulting graph, determine the mathematical equation that describes V as a function of T.
SOLUTION:
The graph of these values of V and T is shown in Figure 6-2. Note that the best line
passes through only one of the experimental points. In order to include the v
intercept, one must take some negative values along the V axis. The value of the v
intercept then can be taken directly from the graph; it is -0.80. The slope of the
line is calculated by selecting two convenient points on this line, as shown, then
taking the ratio of the two sides of the triangle formed from these points: in the
figure, it is the ratio 2.0/50 = 0.040. Knowing the slope and the v intercept, we can
directly write the mathematical equation for the relationship between V and T as
V = 0.0407 - 0.80
Students often select two of the experimental points in order to calculate the slope
of a straight-line function; doing so usually is bad practice, because there are
experimental errors inherent in the individual data points. The straight line that
best represents all the points minimizes the experimental errors, and the slope
calculated from this best straight line thus will (usually) be more reliable than one
calculated from two randomly selected experimental points.