You are here

Example 7.2

20 January, 2016 - 09:21

The following is a collection of data for an iron-constantan thermocouple (data available for download 1). 2

Table 7.2 Temperature [C] vs Voltage [mV]

Temperature [C]

Voltage [mV]

50

2.6

100

6.7

150

8.8

200

11.2

300

17.0

400

22.5

500

26

600

32.5

700

37.7

800

41

900

48

1000

55.2

 
  1. Plot a graph with Temperature as the independent variable.
  2. Determine the equation of the relationship using the Basic Fitting tools.
  3. Estimate the Voltage that corresponds to a Temperature of 650 C and 1150 C.

We will input the variables first:

Temp=[50;100;150;200;/00;400;500;600;700;800;900;1000] Voltage=[2.6;6.7;8.8;11.2;17;22.5;/6;/2.5;/7.7;41;48;55.2] 

To plot the graph, type in:

plot(Temp,Voltage) 

We can now use the Plot Tools and Basic Fitting settings and determine the equation:

media/image6.png
Figure 7.5 Basic Fitting window is used to select the desired regression analysis parameters. 
 

By clicking the right arrow twice at the bottom right corner on the Basic Fitting window, we can evaluate the function at a desired value. See the figure below which illustrates this process for the temperature value 1150 C.

media/image7.png
Figure 7.6 Estimating the Voltage that corresponds to a Temperature of 1150 C. 
 

Now let us check our answer with a technique we learned earlier. As displayed on the plot, we have obtained the following equation: y = 0.053x+ 1.4 This equation can be entered as polynomial and evaluated at 650 and 1150 as follows:

    » p=[0.053,1.4]
p =
    0.0530 1.4000
» polyval(p,650)
ans =
    35.8500
» polyval(p,1150)
ans =
    62.3500