One cross-country skier is wearing a down jacket that is 2.0 cm thick. The thermal conductivity

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One cross-country skier is wearing a down jacket that is 2.0...

One cross-country skier is wearing a down jacket that is $2.0 \mathrm{cm}$ thick. The thermal conductivity of goose down is $0.025 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ Her companion on the ski outing is wearing a wool jacket that is $0.50 \mathrm{cm}$ thick. The thermal conductivity of wool is $0.040 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ (a) If both jackets have the same surface area and the skiers both have the same body temperature, which one will stay warmer longer? (b) How much longer can the person with the warmer jacket stay outside for the same amount of heat loss?

One cross-country skier is wearing a down jacket that is $2.0 \mathrm{cm}$ thick. The thermal conductivity of goose down is $0.025 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ Her companion on the ski outing is wearing a wool jacket that is $0.50 \mathrm{cm}$ thick. The thermal conductivity of wool is $0.040 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ (a) If both jackets have the same surface area and the skiers both have the same body temperature, which one will stay warmer longer?
(b) How much longer can the person with the warmer jacket stay outside for the same amount of heat loss?

Key Concepts

Thermal Resistance

Thermal resistance quantifies how effectively a material resists the flow of heat and is calculated by dividing the material's thickness by its thermal conductivity. Higher thermal resistance indicates improved insulation, as it means that less heat will be lost through the material per unit time for a given temperature difference.

Heat Transfer by Conduction

Heat transfer by conduction is the process through which thermal energy is exchanged within or between objects as a result of a temperature gradient, without the movement of the substance itself. This phenomenon is governed by Fourier's Law, which correlates the rate of heat transfer with the material's thermal conductivity, temperature difference, and the inverse of the material’s thickness.

Thermal Conductivity

Thermal conductivity is a material-specific property that indicates how readily heat is transferred through a material. It is measured in watts per meter-kelvin (W/(m·K)). Lower thermal conductivity values imply that the material is a poorer conductor of heat, making it better suited for insulation purposes.

Thermal Insulation

Thermal insulation refers to the ability of a material or garment to prevent the loss of heat. Its effectiveness depends on both the material's thermal conductivity and its thickness; a material with a low thermal conductivity that is also thicker will typically provide better insulation.

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