Team:Exeter/Team/collab
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).
To measure the temperature three thermocouples were used. The first one was attached to a 0.65m thin plastic coated copper wire (0.05m^2 in area) which ran through the flacon tube providing 5 amps to heat our sample providing the temperature gradient. The second thermocouple was attached to the inside of the falcon tube and the third was in the water to measure the external temperature.
Using this data a straight line of best fit was plotted using the least squares method. This was then used to calculate the average gradient of the graph. By using these value along with $$ \lambda = \frac{Q}{4\pi[T(t_{2})-T(t_{1})]}\ \log{\Big(\frac{t_{2}}{t_{1}}\Big)}$$ 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 (Nagasaka and Nagashima, 1981).
As we used a plastic coated copper wire we had to apply a correction to the values to make them more accurate. This was done by calculating the conductivity of water using the insulated wire and comparing it to the given conductivities from here. We found that the conductivity value was roughly one fourth of the known value at any given temperature and the correction applied to the results of the lb and m9 media.Due to time constraints the lb experiment was repeated 6 times and 5 times for the m9 media with a water calibration being done each time and then the result averaged, 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 similar to that of water.The conductivity of water at room temperature is 598.4 $\frac{mW}{Km}\text{ }$(mili watt per metre kelvin). We found the conductivity to be (605 $\pm$ 20) $\frac{mW}{Km}\text{ }$ and (570 $\pm$ 30) $\frac{mW}{Km}\text{ }$ for LB and m9 respectively.
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 longer than water to cool down which correlated with the fact the conductivity was lower.
References
- Nagasaka Y, Nagashima A. Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot-wire method. Journal of Physics E: Scientific Instruments. 1981 Dec;14(12):1435–40.
