An ice cube at 0^∘ C measures 10.0 cm on a side. It sits on top of a copper block with a square

step 1 So here, the heat required to melt the ice, m, it would be the mass of the ice, times the latent

An ice cube at 0^∘ C measures 10.0 cm on a side. It sits on...

An ice cube at $0^{\circ} \mathrm{C}$ measures $10.0 \mathrm{~cm}$ on a side. It sits on top of a copper block with a square cross section $10.0 \mathrm{~cm}$ on a side and a length of $20.0 \mathrm{~cm} .$ The block is partially immersed in a large pool of water at $90.0^{\circ} \mathrm{C} .$ How long does it take the ice cube to melt? Assume that only the part in contact with the copper liquefies; that is, the cube gets shorter as it melts. The density of ice is $0.917 \mathrm{~g} / \mathrm{cm}^{3}$.

Key Concepts

Thermal Conduction

Thermal conduction is the process by which heat energy is transferred through a material from a region of higher temperature to a region of lower temperature. This occurs at the microscopic level as particles collide and interact, and is governed by the material's properties, such as its thermal conductivity, and the temperature gradient within the material.

Fourier's Law

Fourier's Law provides a quantitative description of thermal conduction, stating that the heat flux through a material is proportional to the negative of the temperature gradient. This law is essential for calculating the rate of heat transfer through a material with a known thermal conductivity and helps relate the temperature difference across a barrier to the rate at which energy is transmitted.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy required to change a substance from a solid phase to a liquid phase at its melting point without a change in temperature. This concept is critical in phase change processes, as it quantifies the energy needed to overcome the molecular forces maintaining the solid structure, and thereby allows one to calculate the time necessary for complete melting given a specific energy flux.

Energy Conservation in Heat Transfer

Energy conservation in heat transfer problems involves balancing the heat supplied to a system with the energy required for any temperature changes or phase transitions. By applying energy conservation principles, one can determine the time frame over which a process, such as melting or heating, occurs by comparing the input energy from conduction with the energy necessary for the phase change or temperature increase.

Material Density

Material density is the mass per unit volume of a substance and is an important physical property in heat transfer calculations. It allows for the conversion between the volume of a material and its mass, which is necessary when calculating the total energy required for a phase change, as this energy is typically defined on a per-mass basis.

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