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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

[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

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

My current stab at the solution is basically the substitution of E

## 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.