Problem Set #8 - Solutions
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.
In a move combining business and pleasure, you have opened a pizza parlor, with delivery service, in your off-grounds apartment. Being a responsible citizen, you have naturally obtained all the appropriate licenses. And you've developed a Frisbee-shaped plastic carton so that you can deliver the pizzas by flinging them across town with a high-tech catapult. Your slogan is “When you're a-drag-en, get a lift from our pizza,” and your poster features that mythical creature flying around and cooking pizza with its fiery breathe (get it? “a-drag-en” = “a dragon” and lift and drag are both aerodynamic terms? I know, things are pretty bad when I have to explain my own jokes.) However, our focus today is not on making pizzas fly; it's on cooking them.
1. You cook your pizzas in a wood-burning brick oven. While it seems that the oven would be most energy efficient if it were perfectly sealed and didn't exchange any air with the rest of the apartment, the fire would go out if you sealed it. Why?

Answer: The trapped air would run out of oxygen and the reaction (that is, the fire) would stop.

Why: As you learned in grade school, a fire needs both fuel and oxygen to proceed. Without a fresh supply of oxygen, the fire will go out.
2. To make sure the fire doesn't go out, the oven has an arched opening on one side and a chimney coming out of its top and passing up through the roof. When the fire is burning, the oven develops a natural draft: air enters the side opening and exits through the chimney. What force or imbalance in forces propels this draft?

Answer: The heated air above the fire experiences two forces: its weight downward and a buoyant force upward. The buoyant force is the stronger of the two forces, so the air experiences a net upward force.

Why: The draft is propelled by the imbalance between the heated air's weight downward and the buoyant force it experiences upward. Because heated air is less dense than cold air, the heated air weighs less than the cool air it displaces and it rises. In effect, this heated air is a hot air balloon without the actual balloon. It rises anyway.
3. Brick is a wise choice for the oven walls because the outside of the oven remains cool to the touch even when the inside surface of the oven is quite hot. If you had used metal oven walls, you'd burn your fingers on the outside of the oven. Explain briefly what physical difference between brick and metal makes brick the better choice for the oven.

Answer: Bricks have no mobile electrons and therefore do not conduct heat well. Metal has mobile electrons and is a better conductor of heat.

Why: Brick walls trap the thermal energy inside the oven, whereas metal walls would convey heat quickly to their outside surfaces. A metal-walled oven would leak heat like crazy and be a burn hazard.
4. The brick walls are dark in color, particularly in the infrared. What heat transfer mechanisms convey heat from the burning wood to the oven walls?

Answer: Convection and radiation.

Why: The brick walls are above the fire, so rising hot air conveys heat to them via convection. And because the bricks are dark in color (meaning that they interact well with light), thermal radiation from the hot coals conveys heat to the bricks via radiation.
5. Both the burning wood and the pizzas rest on opposite sides of the oven's flat bottom surface. Why don't convection or conduction directly heat the pizzas?

Answer: Hot air from the fire rises up the chimney and never visits the low-lying pizza. And the bricks are such terrible conductors of heat that very little heat flows through them from the fire to the pizza.

Why: This cooking arrangement: pizza and fire at the same height and widely separated by bricks, frustrates both conduction and convection. The hot air rising from the fire just can't get to the pizza and there are no good conductors of heat connecting the fire and the pizza.
6. This cooking system rarely burns the bottom of the pizza crust. Why?

Answer: Very little heat flows into the pizza from below, so the crust is the last thing to cook, not the first.

Why: With conduction and convection out of the picture, the only thing heating the pizza significantly is radiation. Since that comes from above, it cooks the pizza from above. The bottom of the pizza is cooked mostly by heat flowing downward from the top of the pizza, so the crust doesn't burn on the bottom easily.
7. Since the wood and pizzas are side-by-side on the oven bottom, they don't “see” one another very well. In particular, the pizza has almost no view of the glowing wood coals. What steps are involved in the flow of heat from the wood to pizzas? How are the oven walls involved?

Answer: Heat flows from fire to pizza mostly indirectly: heat flows from the fire to the oven walls via convection and radiation and then heat flows from the oven walls to the pizza via radiation.

Why: The brick oven cooks via radiant heat. The walls of the oven become very hot and it is their thermal radiation that cooks the pizzas lying on the hearth.
8. If you were to install a big fan inside the oven to circulate the air artificially, the cooking process would change significantly. Why?

Answer: By forcing convection, you would bring hot air in contact with the pizza and the pizza would cook via both radiation (as before) and convection (something new).

Why: Convectional doesn't heat the pizza when the oven has no fan. But with the fan circulating the air vigorously, convection becomes a significant conveyer of heat to the pizza. How this affects the taste of the finished pizza, I don't know. But the absence of fans in most brick ovens implies that it isn't desirable.