1.6 Mechanisms of heat transfer  (Page 2/27)

Conduction

As you walk barefoot across the living room carpet in a cold house and then step onto the kitchen tile floor, your feet feel colder on the tile. This result is intriguing, since the carpet and tile floor are both at the same temperature. The different sensation is explained by the different rates of heat transfer: The heat loss is faster for skin in contact with the tiles than with the carpet, so the sensation of cold is more intense.

Some materials conduct thermal energy faster than others. [link] shows a material that conducts heat slowly—it is a good thermal insulator, or poor heat conductor—used to reduce heat flow into and out of a house.

A molecular picture of heat conduction will help justify the equation that describes it. [link] shows molecules in two bodies at different temperatures, $T_{\text{h}}$ and $T_{\text{c}},$ for “hot” and “cold.” The average kinetic energy of a molecule in the hot body is higher than in the colder body. If two molecules collide, energy transfers from the high-energy to the low-energy molecule. In a metal, the picture would also include free valence electrons colliding with each other and with atoms, likewise transferring energy. The cumulative effect of all collisions is a net flux of heat from the hotter body to the colder body. Thus, the rate of heat transfer increases with increasing temperature difference $\text{Δ}T=T_{\text{h}}-T_{\text{c}}.$ If the temperatures are the same, the net heat transfer rate is zero. Because the number of collisions increases with increasing area, heat conduction is proportional to the cross-sectional area—a second factor in the equation.

A third quantity that affects the conduction rate is the thickness of the material through which heat transfers. [link] shows a slab of material with a higher temperature on the left than on the right. Heat transfers from the left to the right by a series of molecular collisions. The greater the distance between hot and cold, the more time the material takes to transfer the same amount of heat.

All four of these quantities appear in a simple equation deduced from and confirmed by experiments. The rate of conductive heat transfer    through a slab of material, such as the one in [link] , is given by