Problem Set #8

Goal of Problem Set #8: This assignment is meant to help you understand:
  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.

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

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?

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?

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.

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?

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?

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?