---
title: "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."
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url: "https://nerd-notes.com/ubq/117725/"
date_modified: "2026-08-04T07:54:06+00:00"
---

# 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.

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.

![A horizontal cylindrical rod connects a heated water bath on the left to an ice block on the right. On the left, a beaker labeled 'Boiling Water (100°C)' sits on a hot plate, with the left end of the rod submerged in the water. On the right, the right end of the rod touches a block of ice labeled 'Ice (0°C)'. The ice block sits on a grated stand with a funnel underneath. Below the funnel, a small beaker rests on a rectangular box labeled 'Electronic Balance'. The middle section of the rod is covered by a thick outer cylinder labeled 'Foam Insulation'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830046-lxO2ci.jpg)

**Part a)** **Describe** an experimental procedure the students could use to collect the necessary data to determine the thermal conductivity \(k\) of the alloy rod. Assume the setup in Figure 1 has already been assembled and has reached a steady state where heat flows at a constant rate. Include what quantities are to be measured, the equipment used to measure them, and steps to reduce experimental uncertainty.

**Part b)** The students follow their procedure and collect the data shown in the table below. | Time \(t\) (s) | Mass of Melted Ice \(m\) (kg) | |---|---| | \(0\) | \(0.000\) | | \(120\) | \(0.0012\) | | \(240\) | \(0.0025\) | | \(360\) | \(0.0036\) | | \(480\) | \(0.0049\) | | \(600\) | \(0.0061\) |

**Part c)** A second group of students performs the identical experiment, but they forget to place the foam insulation sleeve over the exposed length of the rod. As a result, the exposed rod is in direct contact with the \(20^\circ\text{C}\) air in the laboratory. **Predict** whether the calculated thermal conductivity for this group will be greater than, less than, or equal to the actual thermal conductivity of the alloy. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your reasoning.

**Part d)** The students are given a second rod made of the exact same alloy. This second rod has twice the diameter and half the length of the original rod. Assuming the temperature difference remains the same, **determine** the ratio of the rate of energy transfer through the second rod to the rate of energy transfer through the original rod.


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117725/*