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Chapter 5: Problem 17

A coin and a piece of glass are both heated to \(60^{\circ} \mathrm{C}\). Which will feel warmer when you touch it?

Short Answer

Expert verified
Answer: The coin will feel warmer when touched compared to the piece of glass. This is because metal, the material used in coins, has a much higher thermal conductivity than glass, allowing heat transfer to the skin at a faster rate.

Step by step solution

01

Find the thermal conductivities

In this step, we need to find the thermal conductivities of a typical coin material (such as metal) and glass. It is important to note that different metals can have different thermal conductivities, but we can use an average value for this comparison. The average thermal conductivity of metals, such as copper or aluminum used in coins, is around \(200 \ \mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\). For glass, the thermal conductivity is around \(1.0 \ \mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\).
02

Compare the thermal conductivities

We have the thermal conductivity values for metals and glass: Metal: \(200 \ \mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\) Glass: \(1.0 \ \mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1}\) Let's compare these values to determine which one would transfer heat quicker to the skin when touched, making it feel warmer. Metal is much more thermally conductive than glass, having a value around 200 times greater than glass.
03

Determine which object feels warmer when touched

Since metal has a much higher thermal conductivity than glass, it transfers heat to the skin at a faster rate when touched compared to glass. Therefore, when both are heated to the same temperature, the coin will feel warmer when touched compared to the piece of glass.

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