1. ME 416 MECHANICAL ENGINERING LABORATORY
DEPARTMENT OF MECHANICAL
ENGINEERING
UNIVERSITY OF GAZIANTEP
TEMPERATURE MEASUREMENT
Submitted to: Res. Assist. İBRAHİM HALİL YILMAZ
Submitted by: (GROUP 7)
HALİL İBRAHİM GÜLMEZ
MESUT GÜNGÖR
FIRAT GÜNYEL
YAŞAR GÜRBÜZ
HACER İLHAN
EMRE KARACA
ERDİ KARAÇAL
DECEMBER 2013

2. INTRODUCTION
Temperature measurement experiment was done for the junior engineers to show that
how is temperature measured in the real life?This experiment zoom us to real life.
Important point is when measuring temperatures, which device is preferable and which
one has better measurements.This is the another point of which must be considered when
doing experiment.
Another important point is in our educational life we have seen lots of parameter on
the Formula sheets and at the books.But when we are doing something at the laboratory This
will be not forgotten during our life.
Our calculations were done by using Excel program and coefficient of determination
square of r was found by used directly from Excel program.We have also know how we can
find the square of r but the using of Excel easier way to find.
There are lots of devices which measures the temperatures.At this experiment we have
measured the temperature by using thermocouple.We have also used the liquid in glass
temperature.There are lots of thermocouple and it has a standarts.We have used T type copper
constantan.
Before the experiment we have predict that there will be lots of error.When we look at
the assembly of experiment it is not hard to predict that…The junctions of the cables are not
suitable.We didnot take care of when we did the experiment.

3. Firstly we draw the voltage/temperature curve on the Excel program to find the thermocouple
constant K.
Figure 1 Thermocouple Constant
K=25,76
If we apply this Formula we can understand our curve is perfectly work.
Formula is -> T=K*V
So the thermocouple constant is 25,76 found at Figure 1.
y = 25,76x
0
10
20
30
40
50
60
70
80
90
0 1 2 3 4
TEMPERATURE
VOLT
Volt / Temperature
Volt / Temperature
Doğrusal (Volt /
Temperature)

4. Secondly We seek to fit a straight line of the for Y=Ax+B through the datas.
We would like to obtain values of the constans ‘’a’’ and ‘’b’’.If we have only two
pairs of data,the solution is simple since the points completely determine straight line.Linear
approximation of the datas.So we should use ‘’the least-square linear fit’’ method for best
fit.Calculations are at table 1.
xi xi*xi yi xi*yi yi*yi
0 0 0 0 0
0,9 0,81 25 22,5 625
1,2 1,44 33 39,6 1089
1,5 2,25 42 63 1764
1,8 3,24 47 84,6 2209
2,1 4,41 55 115,5 3025
2,4 5,76 62 148,8 3844
2,7 7,29 70 189 4900
3 9 76 228 5776
3,3 10,89 82 270,6 6724
total xi total xi*xi total yi total xi*yi
total
yi*yi
18,9 45,09 492 1161,6 29956
Table : 1
= 24,733 + 2,455
24,733
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5. We have found that = 24,733 + 2,455 and If we put our datas in the Formula,There
will be some mistakes.As we learned that from our course, There is a value that shows how our
equation fit the datas.Correlation coefficient is the exactly name of this value.We can find this value
from the formulation which is given in the course book but it is simple way that Excel program can
give this value easily.
Figure 2 :Graph of Least square method
At figure 2 there is a value of = 0,996 .This value should be as closest to unity ‘’1’’
This shows that our experimental datas and theoretical datas did not match.There is some mistake on
the formulation of least square method.We can find unceartainy for the y=ax+b equation.At course
book from equation (6.71a)
∗
= (ax + )+ , ∗ / , セ√( + 1)/ + ( ∗
−
_
) / − ∗
But we dont have to find this uncertainty because there is another error which comes from the given
experimental data sheet.Thermocouple calibration datas are not match with the experimental datas.
This situation makes another errors.The measured values are not correct with respect to calibration
datas.
y = 24,73x + 2,455
R² = 0,996
0
10
20
30
40
50
60
70
80
90
0 1 2 3 4
TEMPERATURE
VOLT
Volt / Temperature
Volt / Temperature
Doğrusal (Volt /
Temperature)

6. As we said that there are some errors due to making a least square methods.After this point we
will calculate the errors which come from least square methods.
The Formula was found as
= 24,733 + 2,455
at this Formula x refers to Volt
y refers to temperature.
The temperature values have been written to this Formula and we find the voltage value from the
Formula.This is our x values.
Experimental Values From Formulation
ERROR
%
Volt Temperature Volt
0,9 25 0,912 1,28
1,2 33 1,235 2,84
1,5 42 1,599 6,20
1,8 47 1,801 0,07
2,1 55 2,125 1,16
2,4 62 2,408 0,32
2,7 70 2,731 1,15
3 76 2,974 -0,88
3,3 82 3,217 -2,59
Table 2: Error from formulation
As it seen at table 2 we have datas from experiment and we have some error from the
formulation of this datas.

7. Finally we compare the experimental datas and calibration table.As it seen that in the table 3
errors are seen in each measured values.We can say that our thermocouple primarly measure the
values incorrectly.We dont have the actual values of each measurement.We mean that we dont have
the correct value and after this point we have done some mistake.
Measured Values
From Table for T type
Thermocouple
ERROR
%
Temperature Volt Temperature Volt
25 0,9 25 0,992 9,27
33 1,2 33 1,320 9,09
42 1,5 42 1,696 11,56
47 1,8 47 1,908 5,66
55 2,1 55 2,251 6,71
62 2,4 62 2,556 6,10
70 2,7 70 2,909 7,18
76 3 76 3,177 5,57
82 3,3 82 3,448 4,29
Table 3:Comparing the datas

8. CONCLUSION
As we said that at the introduction part of this experiment.We predicted that there will be lots
of error through out the experiment.Junctions of the cables were not suitable to measure the correct
voltage.
And another important point is when we were doing the experiment we have seen that liquid
in glass temperature of mercury temperature has good accuracy and it protects its calibration thought
years.
Also thermocouple has some errors We think it has lost its calibration.
We took 10 measurements by increments of 0,3 volt.We found the thermocouple constant and
after that point we calculate the linear equations coefficients ‘’a’’ and ‘’b’’.The formulation was
written and some errors were predicted when doing the linear equations.This errors were compared
with the experimental values.
Also there were another errors which were seen.For this point we compared our experimental
values with the calibration curves of thermocouples.
Finally we can say that when doing some experiment There will be lots of parameter which
the experimenter take care.’’Errors begets error.’’ ın turkish mean ‘’hata hatayı doğurur.’’ 