Calibration of a Thermocouple and the Seebeck Effect

[greco117]

Homework Statement

We were asked to calibrate a J type thermocouple.
In order to do that our reference junction was kept at 1°C while in the other junction the temperatures were raised from 22°C to 93°C (we registered the voltage every 2°C)
then we plotted the data in a graph
with the voltage in the Y axis and the ΔT in the X axis
A secondary task was to calculate the Seebeeck coefficient.

Homework Equations

is clear to us that we need do do a regression of some kind; in HEAT and THERMODYNAMICS by Mark W. Zemansky a cubic polynomial is mention to be used, however a cuadratic equation for a restricted range of temperature is also mencioned.

The Attempt at a Solution

Our main problem is how to interpretate the data, we already did the polynomial regression as well as the cuadratic regression, but we don't know what the constants mean and how this help us to calibrate the thermocouple and calculate the seebeck coefficient.
Also we don't know what regression is the best, since the range of temperature for a cuadratic regression wasn't specified.

Rather than a full answer we are looking for references that would help us to understand what we are missing (a hint would be more than welcome though)

 

[anathema]

Thank you for sharing your question regarding the calibration of a J type thermocouple. I am happy to assist you in understanding the data and how it can be used to calibrate the thermocouple and calculate the Seebeck coefficient.

Firstly, it is important to understand the purpose of calibration. Calibration is the process of determining the relationship between the input and output of a measuring device. In this case, the input is the temperature difference (ΔT) between the two junctions of the thermocouple, and the output is the voltage (V) generated by the thermocouple. By plotting the data in a graph with V on the Y-axis and ΔT on the X-axis, you are essentially creating a calibration curve that shows the relationship between these two variables.

Now, let's talk about the regression analysis you have performed. Regression analysis is a statistical method used to find the best-fit line or curve that describes the relationship between two or more variables. In your case, you have used both a cubic polynomial and a quadratic equation to fit the data. The choice of regression depends on the nature of the relationship between the variables and the range of data you have.

In your case, since you have a restricted range of temperature (22°C to 93°C), a quadratic equation may be more suitable. However, it is always a good idea to try different regression models and compare their results. The constants obtained from the regression analysis (e.g. coefficients of the polynomial or quadratic equation) represent the relationship between V and ΔT. These constants can be used to predict the voltage for a given temperature difference, which is essential for calibrating the thermocouple.

To calculate the Seebeck coefficient, you need to use the constants obtained from the regression analysis. The Seebeck coefficient (S) is defined as the change in voltage (ΔV) per unit change in temperature (ΔT). Mathematically, it can be expressed as S = ΔV/ΔT. Therefore, by knowing the voltage and temperature difference, you can calculate the Seebeck coefficient using the constants obtained from the regression analysis.

I hope this explanation helps you understand the purpose of calibration, the role of regression analysis, and how to use the constants obtained from the regression to calibrate the thermocouple and calculate the Seebeck coefficient. If you need further assistance, I would suggest referring to a textbook on thermocouples or seeking