Team:Exeter/project/intensity
Collaboration: Newcastle
The thermal conductivity of growth media.
Part of the Newcastle iGEM team's project this year involved an experiment centred around the creation of biological electronic components. Newcastle asked our team if we could help them out by finding the thermal conductivity of different growth media. With the help of our biophysicist supervisor Ryan Edgington, we came up with a plan to measure the conductivity.
To measure the thermal conductivity of our samples accurately using a temperature gradient, the effect of convection currents must be minimised. To do this we had to reduce the size of our samples (50mL falcon tube) and keep the temperature in a narrow range (roughly between 298K-303K).
We suspended our sample in a falcon tube in the middle of a beaker of water. We had one thermocouple that ran through the falcon tube which was attached to a 0.65m of thin plastic coated copper wire (0.05m^2 in diameter). This wire was hooked up to a current source which provided around 5 Amps and was our heat source used to provide a temperature gradient. A second thermocouple was fitted in the centre of the falcon tube to measure the temperature of the sample.
The aim of the experiment was to measure the difference in temperature between the wire and the sample over time. We recorded the temperature difference over a 10 minute period, producing the graph on the right. The first 50 seconds of data were extracted and the process repeated. We did this 5 times per sample to obtain a more reliable result.
Using the data about the difference in temperature, 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 adjust the result to find the correct value. To find the adjustment we set up the experiment to calculate the conductivity of water. Using the standard conductivity 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 repeated 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 experienced during the test. The lb media took the same time to cool down to equilibrium as the water control test and thus the conductivities should be the same. The m9 sample took a while to cool down so it made sense that the conductivity was lower.
