A Tungsten-Rhenium thermocouple system was evaluated for use in temperature meas
ID: 2082962 • Letter: A
Question
A Tungsten-Rhenium thermocouple system was evaluated for use in temperature measurements between 1600 degree C and 3000 degree C. A temperature-millivolts relation were extended from 2300 degree C to 3000 degree C for the sample of bare wire W3Re/W25Re. Three experimental runs were conducted and the results are tabulated below. a) Based on the experimental data provided, sketch and estimate the sensitivities of the device assuming a linear range between 1800 degree C and 2000 degree C. b) Using the result obtained in part (a), determine the respective error of measurements at 3000 degree C. c) Assuming a linear range between 1800 degree C and 2500 degree C, determine the respective error of measurements at 3000 degree C. d) Discuss the benefits and disadvantages of the two methods above.Explanation / Answer
a) Now sensitivity S1 for V1 set of data between 1800 to 2000 deg.C
S1 = V1(at 2000 deg.c) - V1(at 1800 deg.c) / 2000 - 1800
= 35.5 - 32.1 / 200
S1 = 0.017 mV / deg.C
Simillarly
S2 = V2(at 2000 deg.c) - V2(at 1800 deg.c) / 2000 - 1800
= 35.3 - 31.9 / 200
S2 = 0.017 mV / deg.C
Simillarly
S3 = V3(at 2000 deg.c) - V3(at 1800 deg.c) / 2000 - 1800
= 35.4 - 32.0 / 200
S3 = 0.017 mV / deg.C
From S1,S2&S3 it is clear that sensitivity of thes device beween 1800 to 2000 deg.C 0.017 mV / deg.C
b) Now let's calculate voltage output considering sensitivity of 0.017 mV / deg.C
S = V1(at 3000 deg.c) - V(at 1800 deg.c) / 3000 - 1800
V1(at 3000 deg.C) = S*1200 + V1(at 1800 deg.c)
=0.017*1200 mV + 32.1
= 20.4 + 32.1
V1(at 3000 deg.C) = 52.5 mV
Measured value V1(at 3000 deg.C) = 44.5 mV
Error of measurement = E1 = (52.5 - 44.5)*100 / 52.5 %
Error of measurement = E1 = 15.23 %
Simillarly
V2(at 3000 deg.C) = S*1200 + V2(at 1800 deg.c)
= 0.017*1200 + 31.9 mV
= 20.4 + 31.9
V2(at 3000 deg.C) = 52.3 mV
Error of measurement = E2 = (52.3 - 44.2)*100 / 52.3 %
Error of measurement = E2 = 15.48 %
Simillarly
V3(at 3000 deg.C) = S*1200 + V3(at 1800 deg.c)
= 0.017*1200 + 32.0 mV
= 20.4 + 32
V3(at 3000 deg.C) = 52.4 mV
Error of measurement = E3 = (52.4 - 44.2)*100 / 52.4 %
Error of measurement = E3 = 15.64 %
These are the respective errore E1,E2& E3 at 3000 deg.C
c) Now we will need to calculate sensitivity assuming linear range between 1800 and 2500 deg.C
Now sensitivity S1 for V1 set of data between 1800 to 2500 deg.C
S1 = V1(at 2500 deg.c) - V1(at 1800 deg.c) / 2500 - 1800
= 42.3 - 32.1 / 700
S1 = 0.014 mV / deg.C
Simillarly
S2 = V2(at 2500 deg.c) - V2(at 1800 deg.c) / 2500 - 1800
= 42.1 - 31.9 / 700
S2 = 0.014 mV / deg.C
Simillarly
S3 = V3(at 2500 deg.c) - V3(at 1800 deg.c) / 2500 - 1800
= 42.2 - 32.0 / 700
S3 = 0.014 mV / deg.C
From S1,S2&S3 it is clear that sensitivity of thes device beween 1800 to 2500 deg.C 0.014 mV / deg.C
V1(at 3000 deg.C) = S*1200 + V1(at 2500 deg.c)
=0.014*1200 mV + 42.3
= 16.8 + 42.3
V1(at 3000 deg.C) = 59.1 mV
Measured value V1(at 3000 deg.C) = 44.5 mV
Error of measurement = E1 = (59.1 - 44.5)*100 / 59.1 %
Error of measurement = E1 = 24.7 %
Similliarly
V2(at 3000 deg.C) = S*1200 + V2(at 2500 deg.c)
=0.014*1200 mV + 42.3
= 16.8 + 42.1
V2(at 3000 deg.C) = 58.9 mV
Measured value V2(at 3000 deg.C) = 44.2 mV
Error of measurement = E2 = (58.9 - 44.2)*100 / 58.9 %
Error of measurement = E2 = 24.95 %
Similliarly
V3(at 3000 deg.C) = S*1200 + V3(at 2500 deg.c)
=0.014*1200 mV + 42.2
= 16.8 + 42.2
V3(at 3000 deg.C) = 59.0 mV
Measured value V3(at 3000 deg.C) = 44.4 mV
Error of measurement = E3 = (59.0 - 44.4)*100 / 59.0 %
Error of measurement = E3 = 24.74%
These are the respective errors E1,E2& E3 at 3000 deg.C
d) Benifit of these method is that by assuming linear realationship we can calculate output at unknown temperature easily.
Disavantage of this method is clear from b & c result that assuming linear relation between different ranges we get different readings and error is also significant.This is the price we pay for assuming linear relation for non linear system.
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