A group of students is tasked with experimentally determining the thermal conductivity \(k\) of a newly developed solid cylindrical metal alloy rod. The students are provided with a room-temperature laboratory (approximately \(20^\circ\text{C}\)) and the following equipment:

- The solid cylindrical alloy rod
- A boiling water bath maintained at \(100^\circ\text{C}\)
- A large block of ice at \(0^\circ\text{C}\) resting on a stand with a funnel beneath it
- An electronic balance
- Empty beakers
- A stopwatch
- Calipers and a metric ruler
- A foam insulation sleeve that perfectly fits around the rod

The students set up the equipment so that one end of the rod is submerged in the boiling water and the other end is pressed firmly into the ice block. Water from the melting ice drips through the funnel into a beaker resting on the electronic balance. The foam insulation sleeve covers the entire exposed length of the rod between the water bath and the ice.