Students on a spring break picnic bring a cooler that contains 5.1 kg of ice at 0.0^∘ C . The co

step 1 Rate of flow of heat by conduction is given by DQ by D .T is equal to KA. DT by DT by DT tags. S

Students on a spring break picnic bring a cooler that...

Students on a spring break picnic bring a cooler that contains $5.1 \mathrm{kg}$ of ice at $0.0^{\circ} \mathrm{C} .$ The cooler has walls that are $3.8 \mathrm{cm}$ thick and are made of Styrofoam, which has a thermal conductivity of $0.030 \mathrm{W} / \mathrm{m} \cdot \mathrm{C}^{\circ}$ ). The surface area of the cooler is $15 \mathrm{m}^{2}$, and it rests in the shade where the air temperature is $21^{\circ} \mathrm{C}$. (a) Find the rate at which heat flows into the cooler. (b) How long does it take for the ice in the cooler to melt?

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a unit mass of a substance from a solid to a liquid state at its melting point without a change in temperature. This concept is vital in calculating the total energy needed to melt a substance, linking thermal energy input directly to a phase change process.

Heat Transfer Rate

The heat transfer rate quantifies the amount of thermal energy transferred per unit time, often measured in watts (W). In conduction problems, it is determined using material properties and geometry, and is crucial for predicting how quickly a system’s thermal state will change over time.

Fourier's Law

Fourier's Law provides the quantitative framework for understanding conduction heat transfer. It states that the rate at which heat is conducted through a material is proportional to the product of the material’s thermal conductivity, the cross-sectional area through which heat is flowing, and the temperature difference across the material, and inversely proportional to the thickness of the material.

Thermal Conduction

Thermal conduction is the process by which heat energy is transmitted through collisions between neighboring molecules or electrons in a material. It is especially important in determining how heat moves through insulators and conductors, where the rate of energy transfer depends on the material’s properties and the temperature difference across it.

Thermal Conductivity

Thermal conductivity is an intrinsic property of a material that measures its ability to conduct heat. Materials with higher thermal conductivity transfer heat more efficiently, while those with lower conductivity, such as Styrofoam, act as insulators. This concept is key to calculating the heat flow between two regions at different temperatures.

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