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Chapter 18: Problem 13

Why does tile feel so much colder to your feet after a bath than a bath rug? Why is this effect more striking when your feet are cold?

Short Answer

Expert verified
Answer: Tile feels colder than a rug because it has higher thermal conductivity, which means it can transfer heat more quickly. When we step on the tile with warm, wet feet, it absorbs the heat faster, making our feet lose heat more quickly and feel colder. In contrast, stepping on a rug causes slower heat transfer, keeping our feet warmer. This effect is more noticeable when our feet are already cold because the greater temperature difference between the cold feet and the tile results in even faster heat transfer, making the tile feel even colder. The slower heat transfer on a rug remains consistent, so the sensation of coldness is not as striking.

Step by step solution

01

Understand the thermal properties of materials

Different materials have different thermal properties, which includes their thermal conductivity, specific heat capacity, and thermal expansion. Thermal conductivity is a measure of how easily a material conducts heat. In this exercise, we will be primarily focusing on thermal conductivity.
02

Comparison of thermal conductivity of tile and rug

Tile is a material with higher thermal conductivity compared to a rug, which is made of fabric. In simpler terms, tile can transfer heat more quickly than a rug. When you step out of a bath with wet, warm feet, the heat from your feet transfers to the tile or rug you step onto.
03

Effect of thermal conductivity on the sensation of warmth

Since the tile has a higher thermal conductivity than a rug, it absorbs the heat from your feet faster, making your feet lose heat quickly and thus feel colder. On the other hand, when stepping on a rug, the heat transfer is slower, so your feet do not lose heat as quickly, and they feel warmer.
04

Effect of cold feet on the sensation of warmth

When your feet are cold, the temperature difference between your feet and the tile is greater than when your feet are warm. This increased temperature difference causes even faster heat transfer from your feet to the tile, making the sensation of coldness on the tile more pronounced. When stepping on a rug with cold feet, the slower heat transfer still remains, so the sensation of coldness is not as striking.

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Most popular questions from this chapter

A gas has an initial volume of \(2.00 \mathrm{~m}^{3}\). It is expanded to three times its original volume through a process for which \(P=\alpha V^{3},\) with \(\alpha=4.00 \mathrm{~N} / \mathrm{m}^{11} .\) How much work is done by the expanding gas?

A cryogenic storage container holds liquid helium, which boils at \(4.2 \mathrm{~K}\). Suppose a student painted the outer shell of the container black, turning it into a pseudoblackbody, and that the shell has an effective area of \(0.50 \mathrm{~m}^{2}\) and is at \(3.0 \cdot 10^{2} \mathrm{~K}\). a) Determine the rate of heat loss due to radiation. b) What is the rate at which the volume of the liquid helium in the container decreases as a result of boiling off? The latent heat of vaporization of liquid helium is \(20.9 \mathrm{~kJ} / \mathrm{kg} .\) The density of liquid helium is \(0.125 \mathrm{~kg} / \mathrm{L}\).

Water is an excellent coolant as a result of its very high heat capacity. Calculate the amount of heat that is required to change the temperature of \(10.0 \mathrm{~kg}\) of water by \(10.0 \mathrm{~K}\). Now calculate the kinetic energy of a car with \(m=1.00 \cdot 10^{3} \mathrm{~kg}\) moving at a speed of \(27.0 \mathrm{~m} / \mathrm{s}(60.0 \mathrm{mph}) .\) Compare the two quantities.

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