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Chapter 12: Problem 50

Imagine that you have a metal bar sitting half in the sun and half in the dark. On a sunny day, the part of the metal that has been sitting in the sun feels hot. If you touch the part of the metal bar that has been sitting in the dark, will it feel hot or cold? Justify your answer in terms of thermal conductivity.

Short Answer

Expert verified
The part of the metal bar in the dark will feel hot due to the high thermal conductivity of metal, which allows heat to transfer easily from the sun-exposed part to the darker part. As heat is conducted from the hotter region to the cooler region, the temperature of the initially cooler part in the dark will increase, attempting to achieve equilibrium. The exact temperature will depend on the time and efficiency of heat transfer, but it will be hotter than the initial state before exposure to sunlight.

Step by step solution

01

Understanding Thermal Conductivity

Thermal conductivity is a property of a material that describes how easily heat can be conducted through it. Materials with high thermal conductivity, such as metals, are good conductors of heat, meaning heat can be easily transmitted from one side of the material to the other.
02

Heat Transfer in the Metal Bar

In the given situation, the part of the metal bar that is exposed to the sun becomes hot due to the absorption of sunlight. Due to the high thermal conductivity of metal, heat starts to transfer from the hotter region (the part exposed to the sun) to the cooler region (the part in the dark). This heat transfer is an attempt to achieve a temperature equilibrium in the entire metal bar.
03

Assessing the Temperature of the Bar in the Dark

As heat is transferred through the metal bar, the initially cooler part in the dark will also start to heat up. The increase in temperature will depend on how long the bar has been exposed to sunlight and how efficient the heat transfer is.
04

Conclusion

Due to the high thermal conductivity of the metal bar and the continuous heat transfer occurring, the part of the metal bar in the dark will also start to feel hot as the heat is being conducted from the sun-exposed part to the darker part. The exact temperature will depend on the time and efficiency of heat transfer, but it will be hotter than the initial state before exposure to sunlight.

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