Colaberations
Newcastle were doing an experiment which involved creating biological electronic components and asked our team
if wecould help them by finding the thermal conductivity of growth media. With the help of our resident Biophysist
Ryan Edgeington
we came up with a plan to measure the conductivity
As we were dealing with thermal conductivity of fluids we had to keep the temperatures and sample sizes small
to help reduce
convection currents. We set up a large beaker of water and suspended our sample in a
falcon tube in the middle of the beaker. The falcon tube had a
thermocouple in the centre to measure the sample temperature. We also ran 0.65m of thin plastic coated copper wire
(0.05m^2 in diameter) through the falcon tube
and attatched a thermocouple. This wire was hooked up to a current source which provided around 5 Amps.
This wire was our heat source used to provide a temperature gradient.
The idea was to measure the differnce in temperature between the wire and the sample over time. We recorded
the temperature difference for 10 minutes a test and this produced the graph on the right.
Once this difference was recorded The first 50 seconds of data were extracted and the process reapeated.
We did this at least 5 times per sample to obtain a more relyable result.
From the data we found the difference in temperature
With the data we plotted a straight best fit line using the least squares method. This line was then used to calculate the
average gradient of the graph. Following the guidelines in
this paper we knew that We could use
$$ \lambda = \frac{Q}{4\pi[T(t_{2})-T(t_{1})]}\ \log{\Big(\frac{t_{2}}{t_{1}}\Big)}$$
Where $Q$ is our power per unit length calculated by $Q = \frac{(I \times V)}{Length}$ , $T(t_\alpha)$ is the temperature
at time $\alpha$ and $T(t_{2})-T(t_{1})$ is our gradient.
As we were using plastic coated copper wire we had to ajust the result to find the correct value. To find the
ajustment we set up the experiment to calculate the conductivity of water. Using the standard couductivity from
here We found that the conductivity value was roughly
one fourth of the known value at that temperature so we could this correction to find our result for lb and m9 growth media.
We reapeated the measurement for the lb 6 times, and for the m9 sample 5 times due to time constraints.
Our value was taken from the average conductivity from all 6/5 tests.
Each testing session had its own water calibration taken. Our errors were taken as the standard deviation of the
measurements.
Using the apparatus we had available we found the thermal conductivity of lb and M9 to be roughly
the same as water. The conductivity of water at room temperature is about 598.4 $\frac{mW}{Km}\text{ }$(mili
watt per metre kelvin).
We found the conductivity of LB to be (605 $\pm$ 20) $\frac{mW}{Km}\text{ }$.
We found the conductivity of m9 to be (570 $\pm$ 30) $\frac{mW}{Km}\text{ }$.
These values were fairly reliable to what we experianced during the test. The lb media
took the same time to cool down to equlibrium as the water controll test and thus the conductivitys should be the same.
The m9 sample took a while to cool down so it made sence that the counductivity was lower.
