Least count of the instruments used.
Leakage of the heat flow through the medium.
There is an error in assuming that no heat lost along the bar, but no correction has been made for this, although this will obviously affect the values of \(T_2\) and \(T_1\).
Errors in m arise from errors in determining the mass of water collected.
Errors in the time t depend on the accuracy of the stop-watch.
Errors in measuring with the Vernier caliper are at least 0.05 mm, but may be bigger.
The fractional error in k is given by:
$$ \frac{\Delta k}{k} = \frac{\Delta m}{m} + \frac{\Delta d}{d} + \frac{\Delta T_3 + \Delta T_4}{T_3 - T_4} + 2\frac{\Delta D}{D} +\frac{\Delta T_1 + \Delta T_2}{T_1 - T_2} +\frac{\Delta t}{t}$$