1. the relationships between thermal energy, heat, and temperature,
2. the physics of combustion,
3. the mechanisms of heat transfer: conduction, convection, and radiation,
4. the black body spectrum,
5. how the rates of heat transfer depend on temperatures.

You are taking a semester off from UVa to get some practical experience in your chosen field of study: literary criticism of 11th Century Italian palimpsests. Somehow, you have had trouble finding a good internship in that area and have had to settle for a slightly less related job: Artic Mountain Rescue. Well, at least you get to eat lots of Italian food. Actually, it's just Pizza, but it's a start.

The present story begins on a bitter cold afternoon when a small commercial airliner develops engine trouble and has to ditch in a remote wilderness area near your base camp. You and your crew set out across the frozen landscape and reach the crumpled plane shortly before sunset. The ambient temperature at the rescue site is -30 °C. None of the passengers is seriously injured, but all are extremely cold and, with no hope of evacuating them until morning, your priority for the night is to keep everyone warm. No, there is no Saint Bernard dog there with a keg of whisky hanging from its neck so you'll have to do this work yourself. Besides, this is a thermal physics problem set, not one of applied chemistry.

1. You find two logs on the ground, one about twice as heavy as the other. Compare (A) the thermal energy contents and (B) the temperatures of these two logs.

Answer: (A) The heavier log contains about twice as much thermal energy as the lighter log. (B) The two logs have the same temperature.

Why: For similar objects, such as two logs, at a given temperature, their thermal energy content is roughly proportional to their weights. Since one log weighs twice as much as the other, the heavier log is equivalent to two of the smaller logs and contains twice as much thermal energy. But temperature doesn't scale with weight. Instead, it is related to thermal energy per unit of material. The heavier log may have more thermal energy, but it also has more material. Thus the two logs have the same temperature: the ambient -30 °C.

2. If you touch these two logs together, which way will heat flow between them? Explain.

Answer: No heat will flow between the logs.

Why: Both logs are at the same temperature (-30 °C), so they are in thermal equilibrium. Heat does not flow between two objects that are in thermal equilibrium.

3. While you were gathering logs for a fire, your colleagues were trying to keep the airplane passengers from losing heat to their surroundings. Why was it important to (A) keep the passengers from touching their surroundings, (B) block airflow around the passengers, and (C) minimize the area of passenger-skin that faced the surroundings, even at a distance?

Answer: (A) Touching cold objects encourages conductive heat transfer to the colder object, (B) permitting airflow allows convective heat transfer to the colder surroundings, and (C) exposing skin to the colder surroundings allows radiative heat transfer to those surroundings.

Why: Because the passengers are the hottest things in their current environment, they must minimize natural heat transfers whenever possible if they want to stay warm. Touching cold objects permits conductive heat transfer, allowing air movement permits convective heat transfer, and exposing skin to the surroundings permits radiative heat transfer.

4. You strike a match and hold its flame to a pile of log shavings. They soon begin to burn and ignite the nearby logs. The surface temperature of each log surges upward from -30 °C to roughly 1500 °C. Each log's thermal energy has increased. (A) Where did this thermal energy come from? (B) What physics purpose did the burning match serve?

Answer: (A) Each log's increased thermal energy has come from its previous store of chemical potential energy. (B) The match provided the activation energy required to initiate the chemical reactions of combustion and thereby begin the transformation of chemical potential energy into thermal energy.

Why: As they burn, the logs are still conserving energy. The thermal energy doesn't appear out of thin air. Instead, they are transforming their chemical potential energy into thermal energy via the process of combustion. That combustion, initiated by in influx of activation energy from the burning match, rearranges the chemical constituents of the logs and the atmosphere and converts this chemical potential energy into thermal energy.

5. With the fire blazing in front of them, the passengers begin to feel warm. Of course, no one wants to actually touch the hot coals or hover directly over the fire in the smoke, so they settle for sitting around the fire at a reasonable distance. What is conveying heat from the fire to the passengers? Explain.

Answer: Thermal radiation has been conveying heat from the hot contents of the fire to the cooler skin and clothing of the passengers. The fire emits large amounts of infrared and visible light, some of which is absorbed by the passengers. This emission of thermal radiation by the fire and absorption by the passengers is a transfer of heat.

Why: The glow of the fire is actually the fire's thermal radiation and the principal mechanism whereby heat flows from the fire to the passengers. Because the fire is so much hotter than the passengers, the direction of radiative heat transfer is from fire to passengers.

6. As they face the fire, the passengers' backs remain cold. Because you and your crew had to travel light, you have only thin, shiny aluminized plastic sheets to give to the passengers to keep them warm. Each passenger drapes one of these shiny sheets over his or her back. Amazingly enough, this thin covering helps them feel significantly warmer. Why is this thin shiny layer so effective at keeping a passenger warm?

Answer: In addition to slowing convective heat transfer, the shiny sheet blocks most radiative heat transfer between a passenger's back and the cold surroundings. Thermal radiation emitted by the passenger's back reflects from the sheet and is reabsorbed by the passenger. Without the sheet, this thermal radiation would be lost to the surroundings. Because those surroundings are much colder, they radiate relatively little thermal radiation in return.

Why: Radiative heat transfer moves thermal energy from hotter to colder. In this case, the passenger is hotter than the surroundings, so thermal radiation would cause the passenger to transfer heat to the surroundings. The aluminized sheet reflects most of the passenger's thermal radiation, so that the heat transfer is slowed significantly.

7. While you stir the fire, a glowing coal falls into the dirt and soon stops burning. You pick it up and notice that it is jet black. How could a jet black object have appeared bright yellow while it was burning?

Answer: The black coal always emits a black body spectrum characteristic of its temperature. When it is cold, that spectrum includes no visible light, so it appears black. When hot, that spectrum includes the red, yellow, and green portions of the visible spectrum, so it appears bright yellow.

Why: A black object is one that is extremely efficient at both absorbing and emitting electromagnetic radiation. Any light that hits it is absorbed, so exposing it to external light has no effect on its appearance. But it nonetheless emits a spectrum of thermal radiation that is characteristic of its own temperature. If you heat it hot enough, it will begin to glow visibly. Its black body spectrum has nothing to do with the light that strikes it from outside. The cold coal emits no visible light in its thermal spectrum and looks black. The hot coal glows with visible thermal radiation.

8. You step away from the campfire and into the woods. Despite the darkness, you can tell whether you are standing under a tree or under the open sky. You don't even have to look for stars. You just feel colder whenever you have no tree above you. Why?

Answer: Despite having a temperature of only -30 °C, the trees are still radiating thermal radiation. You feel warmer because of this thermal radiation when you stand under one. In contrast, the sky radiates almost no thermal radiation and you feel colder because of the absence of that thermal radiation.

Why: The night sky has a temperature of less than 3 K (3 Kelvin), which is roughly -270 °C. It radiates very little thermal radiation at you. While you stand under the night sky, you radiate away thermal radiation to the sky and it returns virtually nothing to you. You feel cold.