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title: "A cylindrical rod of length \\(L\\), cross-sectional area \\(A\\), and thermal conductivity \\(k\\) connects a heat reservoir at constant temperature \\(T_H\\) to a large block of ice at \\(0\\text{ }^\\circ\\text{C}\\). The latent heat of fusion of ice is \\(L_f\\). Assuming no heat is lost through the sides of the rod, which of the following gives the correct expression for the rate \\(\\dfrac{\\Delta m}{\\Delta t}\\) at which the ice melts, and provides the correct physical justification for why the temperature of the ice remains at \\(0\\text{ }^\\circ\\text{C}\\) during the melting process?"
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url: "https://nerd-notes.com/ubq/116252/"
date_modified: "2026-08-03T11:46:28+00:00"
---

# A cylindrical rod of length \(L\), cross-sectional area \(A\), and thermal conductivity \(k\) connects a heat reservoir at constant temperature \(T_H\) to a large block of ice at \(0\text{ }^\circ\text{C}\). The latent heat of fusion of ice is \(L_f\). Assuming no heat is lost through the sides of the rod, which of the following gives the correct expression for the rate \(\dfrac{\Delta m}{\Delta t}\) at which the ice melts, and provides the correct physical justification for why the temperature of the ice remains at \(0\text{ }^\circ\text{C}\) during the melting process?

A cylindrical rod of length \(L\), cross-sectional area \(A\), and thermal conductivity \(k\) connects a heat reservoir at constant temperature \(T_H\) to a large block of ice at \(0\text{ }^\circ\text{C}\). The latent heat of fusion of ice is \(L_f\). Assuming no heat is lost through the sides of the rod, which of the following gives the correct expression for the rate \(\dfrac{\Delta m}{\Delta t}\) at which the ice melts, and provides the correct physical justification for why the temperature of the ice remains at \(0\text{ }^\circ\text{C}\) during the melting process?

![A horizontal diagram showing two rectangular blocks connected by a horizontal cylindrical rod. On the left is a large shaded rectangle labeled 'Hot Reservoir' at temperature \(T_H\). On the right is a large shaded rectangle labeled 'Ice Block' at temperature \(0\text{ }^\circ\text{C}\). Between them is a horizontal cylinder of length \(L\) and cross-sectional area \(A\), labeled 'Rod (\(k\))'. A horizontal arrow inside the rod points from left to right, labeled '\(Q/\Delta t\)'. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757588-YZWZDN.jpg)

- **A.** \(\dfrac{\Delta m}{\Delta t} = \dfrac{k A T_H L_f}{L}\), because the absorbed heat increases the average kinetic energy of the molecules without altering their potential energy.
- **B.** \(\dfrac{\Delta m}{\Delta t} = \dfrac{k A T_H L_f}{L}\), because the absorbed heat increases the potential energy associated with intermolecular bonds rather than the average kinetic energy of the molecules.
- **C.** \(\dfrac{\Delta m}{\Delta t} = \dfrac{k A T_H}{L L_f}\), because the absorbed heat increases the potential energy associated with intermolecular bonds rather than the average kinetic energy of the molecules.
- **D.** \(\dfrac{\Delta m}{\Delta t} = \dfrac{k A T_H}{L L_f}\), because the absorbed heat is entirely converted into mechanical work done on the surrounding environment as the ice expands.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116252/*