# 1.6 Mechanisms of heat transfer  (Page 12/27)

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## Key equations

 Linear thermal expansion $\text{Δ}L=\alpha L\text{Δ}T$ Thermal expansion in two dimensions $\text{Δ}A=2\alpha A\text{Δ}T$ Thermal expansion in three dimensions $\text{Δ}V=\beta V\text{Δ}T$ Heat transfer $Q=mc\text{Δ}T$ Transfer of heat in a calorimeter ${Q}_{\text{cold}}+{Q}_{\text{hot}}=0$ Heat due to phase change (melting and freezing) $Q=m{L}_{\text{f}}$ Heat due to phase change (evaporation and condensation) $Q=m{L}_{\text{v}}$ Rate of conductive heat transfer $P=\frac{kA\left({T}_{h}-{T}_{c}\right)}{d}$ Net rate of heat transfer by radiation ${P}_{\text{net}}=\sigma eA\left({T}_{2}{}^{4}-{T}_{1}{}^{4}\right)$

## Conceptual questions

What are the main methods of heat transfer from the hot core of Earth to its surface? From Earth’s surface to outer space?

When our bodies get too warm, they respond by sweating and increasing blood circulation to the surface to transfer thermal energy away from the core. What effect will those processes have on a person in a $40.0\text{-}\text{°}\text{C}$ hot tub?

Increasing circulation to the surface will warm the person, as the temperature of the water is warmer than human body temperature. Sweating will cause no evaporative cooling under water or in the humid air immediately above the tub.

Shown below is a cut-away drawing of a thermos bottle (also known as a Dewar flask), which is a device designed specifically to slow down all forms of heat transfer. Explain the functions of the various parts, such as the vacuum, the silvering of the walls, the thin-walled long glass neck, the rubber support, the air layer, and the stopper.

Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot placed over a heating element will be heated, while the surface only a few centimeters away is safe to touch. Why is ceramic, with a conductivity less than that of a metal but greater than that of a good insulator, an ideal choice for the stove top?

It spread the heat over the area above the heating elements, evening the temperature there, but does not spread the heat much beyond the heating elements.

Loose-fitting white clothing covering most of the body, shown below, is ideal for desert dwellers, both in the hot Sun and during cold evenings. Explain how such clothing is advantageous during both day and night.

One way to make a fireplace more energy-efficient is to have room air circulate around the outside of the fire box and back into the room. Detail the methods of heat transfer involved.

Heat is conducted from the fire through the fire box to the circulating air and then convected by the air into the room (forced convection).

On cold, clear nights horses will sleep under the cover of large trees. How does this help them keep warm?

When watching a circus during the day in a large, dark-colored tent, you sense significant heat transfer from the tent. Explain why this occurs.

The tent is heated by the Sun and transfers heat to you by all three processes, especially radiation.

Satellites designed to observe the radiation from cold (3 K) dark space have sensors that are shaded from the Sun, Earth, and the Moon and are cooled to very low temperatures. Why must the sensors be at low temperature?

Why are thermometers that are used in weather stations shielded from the sunshine? What does a thermometer measure if it is shielded from the sunshine? What does it measure if it is not?

If shielded, it measures the air temperature. If not, it measures the combined effect of air temperature and net radiative heat gain from the Sun.

Maxwell's stress tensor is
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