A tank of water has been outdoors in cold weather, and a slab of ice 5.0 cm thick has formed on

step 1 Good day. In this question we will be solving where the rate of formation of ice is centimeters

A tank of water has been outdoors in cold weather, and a...

A tank of water has been outdoors in cold weather, and a slab of ice $5.0 \mathrm{~cm}$ thick has formed on its surface (Fig. 19-42). The air above the ice is at $-10^{\circ} \mathrm{C}$. Calculate the rate of formation of ice (in centimeters per hour) on the ice slab. Take the thermal conductivity and density of ice to be $0.0040 \mathrm{cal} / \mathrm{s} \cdot \mathrm{cm} \cdot \mathrm{C}^{\circ}$ and $0.92 \mathrm{~g} / \mathrm{cm}^{3}$. Assume that energy is not transferred through the walls or bottom of the tank.

A tank of water has been outdoors in cold weather, and a slab of ice $5.0 \mathrm{~cm}$ thick has formed on its surface (Fig. 19-42). The air above the ice is at $-10^{\circ} \mathrm{C}$. Calculate the rate of formation of ice (in centimeters per hour) on the ice slab. Take the thermal conductivity and density of ice to be $0.0040 \mathrm{cal} / \mathrm{s} \cdot \mathrm{cm} \cdot \mathrm{C}^{\circ}$ and $0.92 \mathrm{~g} / \mathrm{cm}^{3}$. Assume that energy is not
transferred through the walls or bottom of the tank.

Key Concepts

Energy Conservation in Phase Change

This principle involves setting up an energy balance where the rate of heat extraction from a substance equals the energy required to drive the phase change. In the context of freezing water, the heat conducted out of the water must supply the latent heat needed to form new ice, linking thermal conduction with the change in physical state.

Steady-State Heat Transfer Condition

Under steady-state conditions, the temperature distribution in a medium remains constant over time, even though heat is continuously flowing through it. This assumption simplifies the analysis by allowing the application of a constant temperature gradient when determining the rate at which a phase change occurs, such as the growth of an ice layer.

Fourier's Law of Thermal Conduction

This concept explains that the rate of heat transfer through a material is proportional to its thermal conductivity, the temperature gradient across it, and the cross-sectional area, and inversely proportional to the material's thickness. It is a key principle used to calculate how quickly heat moves through substances like ice.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy per unit mass required to change a substance from its liquid phase to its solid phase (or vice versa) without changing its temperature. It plays a crucial role in phase change problems where energy removal leads to the formation of a solid, such as the freezing of water into ice.

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