| MadSci Network: Physics |
Your question is of substantial importance not only in heating water but in cooling electronic devices. Modern integrated circuits use a lot of power and generate a lot of heat that must be removed to keep from cooking the device. The principles for heating water and cooling integrated circuits are the same. Unfortunately, we need to understand some basic principles of heat transfer before we can get to an answer to your question. Just because the question seems simple, doesn’t make the answer short or simple. Heat moves from a higher temperature to a lower temperature by three mechanisms; conduction, convection, and radiation. Conduction is easy to understand; hot atoms vibrate more than cool atoms. So a hot atom is going to vibrate against its neighbors, causing them to vibrate more while it looses some of its energy. This heat transfer by conduction takes place in solids, liquids, and gasses; if you remove all of the atoms (say by operating in a vacuum), there is no conductive heat transfer. A thermos bottle keeps things hot or cool by surrounding the contents with a vacuum. And when you talk about using a sheet of steel or a block of aluminum, you are implying transferring heat by conduction. So heat isn’t really drawn from a higher temperature by something at a lower temperature. Convective heat transfer takes place as a result of fluid movement. In your pot of water, when you stir the pot, hot water near the bottom of the pot is moved around so that it heats the water at the top of the pot. When the water starts to boil, you can easily see that there is a lot of fluid movement. When you drive down the road in your car, air blowing over the “radiator” cools your car engine by convection, just as the antifreeze circulating within the car’s cooling system moves heat from the engine to the “radiator” by convection. Perhaps your "radiator" should more accurately be called a "convector." The last heat transfer mechanism is radiation. Hot objects transfer heat to their surroundings by radiation. The sun’s heat is transferred to your face on a sunny day by radiation. Radiation is a very strong function of temperature. When the coil of your heat plate gets red hot, you can feel the heat transfer by radiation. If you put a pot on top of the red hot coils, the coils often cool down enough to see the decrease in the brightness of the coils; this is because conductive heat transfer away from the coils decreases the amount of power that must be removed by radiation and convection to the air. When you are attempting to heat a pot of water, conduction from the heating coils to the pot containing the water is going to be the most important heat transfer mechanism. And conduction from one metal surface to another is going to provide much better heat transfer than conduction from the heating coils to and insulating layer of air, and then to another metal surface. The thermal conductivity of metals varies from about 10 to 400 Watts per meter per degree C. Steel may have a conductivity of about 30 and aluminum around 200 W/mC. By comparison, the conductivity of air is going to be less than 0.01 W/mK. And now we get to the answer to your question. There are several issues which determine how fast you will heat a pot of water on a hot plate. The first one is the question of how much heat is provided by your hot plate. If it plugs into a wall outlet, the hot plate typically can provide about 1500 watts of heat. Because the metal windings in the hot plate tend to increase in electrical resistance as temperature increases, you might expect the hot plate to put out more heat energy when it is cool and less as it heats up. So, a red hot hotplate may only be putting out 1450 watts of heat, while one that is just plugged in may actually be producing 1550 watts of heat. The amount of heat necessary to heat a pot of water is a function of the amount of water and the starting temperature. So, lets say that you are putting 1 liter (about one quart or 1,000 milliliters) of water in your pot to start with, and lets say that the water is initially 20C. The specific heat of water is about 1 calorie per gram per degree C. So, to bring the 1000 milliliters of water to 100C (to boiling) is going to require (100-20)*1000=80,000 calories. Since you are taking physics, I’ll bet you can find a conversion factor from calories to watt seconds. As I recall, it is about 4.1 watt seconds per calorie. So, if I exercise my calculator a bit, I find it will require about 328000 watt seconds of power to heat the water to boiling. For a 1500 watt hot plate, about 3.64 minutes of heating are required if all of the heat went into the water. So, now we get to the question of heat transfer. Solid surfaces are not flat on a microscopic level (even if they look flat). When I place one solid surface in contact with another (lets call it a heat transfer interface), some of the heat is transferred from metal surface to metal surface, and some of the heat is transferred by conduction through the thin air layer separating the surfaces; some is also transferred by convection through the air and by radiation. So, every time I have a heat transfer interface, my heat transfer is poorer than if there was no interface. Some of the thermal resistance of the interface can be reduced by putting something in-between the solid surfaces that transfers heat better than air. So, when a heat sink is put on top of an integrated circuit, a little bit of heat transfer grease is placed between the heat sink and the circuit. When you start stacking metal layers on top of each other, like a sheet of steel and a sheet of aluminum, you are adding interfaces. And the heat plate is going to have to get hotter to transfer the same amount of heat through these interfaces. Of course, a block of aluminum will transfer heat by conduction through the block pretty well, but there is the heat plate to aluminum block, and the aluminum block to pot interfaces that are the cause of most of the thermal resistance. An experiment that would be interesting to run would be to stack several sheets of aluminum foil; one on top of the other, and then put the water on top of the stack of aluminum foil sheets. I’ll bet that you can see a big difference in how hot the heat plate gets with the aluminum foil, as compared to without. When the heat plate has to get hotter to transfer the same amount of heat, more of the heat is lost to the surroundings by convection and by radiation, plus, as mentioned, a hot heat plate may not produce a full 1500 watts of power. So, although you may still be putting the same 1500 watts of power into the heat plate, you may be losing several hundred watts of heat to the surroundings. That translates into less heat going to heat the water. The final issue is the one of thermal mass. It takes energy to heat the water; it takes energy to heat the pot surrounding the water; it takes energy to heat a block of aluminum or sheet of steel. When you put that block of aluminum on the heat plate, you still only have the 1500 watts of heating power being produced by the hot plate, but now you are heating the water, the pot, and the block of aluminum. It takes more energy to heat the block of aluminum and the pot of water that it would take to heat the pot of water without the block of aluminum. The aluminum will do a good job spreading out the heat, allowing the bottom of the pot to be uniformly heated, but it will hurt your efforts to heat the water fast. Same with the steel. So, the absolute fastest way to heat a pot of water? Immerse the heating coils into the pot; you eliminate convection and radiation to the surroundings, and produce a minimum of thermal interfaces. The coils stay cool, allowing more electrical energy to pass through the coils. Of course, most hot plates are not designed for water immersion but there are some heating coils designed and sold for heating a cup of water by immersing the coil into the water. It is a fundamentally good idea, from a heat transfer standpoint. Of course, if the coil is plugged in when not immersed, it can burn up pretty fast. Hope that helps answer the question of heat transfer and thermal interfaces.
Try the links in the MadSci Library for more information on Physics.