Converting Resistance (ohms) to Temperature (K) : Results
The equations to convert resistance to temperature for three different resistors – Resistor 2 (the still), Resistor 14 (the cold plate), and Resistor 15 (the mixing chamber with one damaged wire) – were found using data tables supplied by Rich Schmitt. Microsoft Excel was used to extract the equations. Data of resistance and temperature were entered in, graphs were made from the data, and trendlines and equations were found for the graphs. The data for temperatures of 4.2 K and below came from the Oxford Generic Data. On Resistors 2 and 14, for temperatures of 4.2 K and above, data from the Oxford Test Results was used. On Resistor 15, for temperatures of 4.2 K and above, 200 ohms were added to the resistance in the data for Resistor 14.
It was too difficult to get one equation per resistor; as a result, the data was broken into two (Resistor 2) or three (Resistors 14 and 15) sections to graph. For the data of temperatures of 4.2 K and above, there were only three points, which were not enough to get an accurate trendline and equation. To remedy this, those three points were graphed by hand, connected using a French Curve, and then other points were found on the curve to add to the original data. These points helped to find a betterfitted trendline and a more accurate equation. For Resistor 2, a power equation was used. For Resistors 14 and 15, exponential equations were used. Even with the extra data, accuracy is not very good for temperatures of 4.2 K. The error for each resistor is in the plots below.
For Resistor 2, the coldest data was not essential, so it was cut to make it easier to find a wellfit trendline. Then a graph was made of the natural log of the resistance and the natural log of the temperature for temperatures of 4.2 K and below. Using the natural log made it easier to find a trendline that fit. A third degree polynomial equation was used. The accuracy for this equation is significantly better than the data for temperatures of 4.2 K and above. Again, the error is given on the plots below.
For Resistors 14 and 15, the cold data (4.2 K and below) was broken into two pieces. For Resistor 14, second degree polynomials were used for both the midrange temperatures data and the coldest temperatures data. For Resistor 15, a third degree polynomial was used for the midrange temperatures data, and a second degree polynomial was used for the coldest temperatures data. All these equations have good accuracy – the error can be seen below.
On all of the polynomial equations (all of the data at 4.2 K and below), if the degree was increased, Excel showed a trendline that supposedly fit closer to the data. However, when the equations of the fourth, fifth, or sixth degree were tested by putting the natural log of resistance into them and seeing how close they came out to the natural log of the temperature, they were found to actually be less accurate. When the equations of the second or third degree were tested, things came out much closer to their actual values.
Resistor Two  The Still:
The equation used for warmer temperatures (4.2  300 K) was: The equation used for colder temperatures (4.2 K and below)
was:
Intercept is at 2760 Ohms Error: At 300 K, it is off 181.1991 K


Resistor Fourteen  The Cold Plate:
The equation used for warmer temperatures (4.2  300 K) was: The equation used for the middle range of temperatures (4.2 K
 0.3 K)
was: The equation used for the coldest temperartues (.25 K and
below) was
Intercept 1: 2718 Ohms Error: At 300 K it is off by 186.69099 K


Resistor Fifteen  The Mixing Chamber With One Damaged Wire:
The equation used for the warmest temperatures (4.2  300 K)
was:
The equation used for the middle range of temperatures (0.3 
4.2 K) was:
The equation used for the coldest temperatures (.25 K and
below) was:
Intercept 1 : 2920 Ohms Error: At 300 K it is off by 147.192954 K

