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Hi guys! First time posting here so please be nice. :)
A thermocouple T is connected in the following circuit with two different types of metal wires to measure a temperature ranging from 0°C to 500°C:
[img=http://s12.postimg.org/9y4nuly15/mechatronics_thermocouple.png]
This thermocouple's EMF output E_{AB} is shown in the following graph:
[img=http://s12.postimg.org/hfdv9tnk9/mechatronics_thermocouple_graph.png]
Suppose that the measurement from the digital voltage meter (DVM) is 1.8mV, estimate the measured temperature at thermal junction T (Answer must match to 1 decimal place).
E_{AB} = αT + βT^{2}
What I've done is that I've taken both the points on the graph (T = 100°C and T = 200°C) and solved for values of α and β by using simultaneous equations. From here, I was able to get α = 4.4333 x 10^{5} and β = 1.3333..3x10^{8}
4. Where I'm stuck
My current stab at the solution is basically the substitution of E_{AB} = 1.8mV (the measurement from the DVM) into the equation and substituting the values of α and β into the equation, and then solving for the roots of T. My values as of such have been completely unrealistic (x10^{4}). I can't shake off the feeling that that step is wrong... I've been looking through my lecture notes (which are, by the way, are very much incomplete and only mentions that one equation and doesn't have any examples), and I haven't been able to find anything that could help me. Any help would be very much appreciated.
Homework Statement
A thermocouple T is connected in the following circuit with two different types of metal wires to measure a temperature ranging from 0°C to 500°C:
[img=http://s12.postimg.org/9y4nuly15/mechatronics_thermocouple.png]
This thermocouple's EMF output E_{AB} is shown in the following graph:
[img=http://s12.postimg.org/hfdv9tnk9/mechatronics_thermocouple_graph.png]
Suppose that the measurement from the digital voltage meter (DVM) is 1.8mV, estimate the measured temperature at thermal junction T (Answer must match to 1 decimal place).
Homework Equations
E_{AB} = αT + βT^{2}
The Attempt at a Solution
What I've done is that I've taken both the points on the graph (T = 100°C and T = 200°C) and solved for values of α and β by using simultaneous equations. From here, I was able to get α = 4.4333 x 10^{5} and β = 1.3333..3x10^{8}
4. Where I'm stuck
My current stab at the solution is basically the substitution of E_{AB} = 1.8mV (the measurement from the DVM) into the equation and substituting the values of α and β into the equation, and then solving for the roots of T. My values as of such have been completely unrealistic (x10^{4}). I can't shake off the feeling that that step is wrong... I've been looking through my lecture notes (which are, by the way, are very much incomplete and only mentions that one equation and doesn't have any examples), and I haven't been able to find anything that could help me. Any help would be very much appreciated.
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