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12/02/09 - Temperature and Heat
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 | What we call heat is really kinetic energy on a molecular or atomic level, the motion of submicroscopic particles. When we slide a book across a table, the molecules in the book interact (push and pull) the molecules in the tabletop. In accordance with Newton's third law, the molecules in the table top similarly push and pull on the molecules in the book, slowing it down as momentum and kinetic energy are transfered from the book to the molecules in the tabletop. We call these interactions "friction". The book eventually stops, but it's kinetic energy has been transferred to the molecules in the tabletop and its own surface, which are now vibrating a little faster than they were previously. We measure this increased vibration as a rise in temperature and say the surfaces have been heated by the friction. The study of heat flow and temperature changes is called thermodynamics.
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| Heat can be measured in Joules (J). Historically, the amount of heat required to raise the temperature of 1 g of water by 1°C is called a calorie. One calorie = 4.186 J, so one kilocalorie (kcal) = 4.186 kJ. One kcal of heat will raise one kilogram of water by 1°C.
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| The total of all the energy of all the molecules in an object is called its internal energy.
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| Heat flows naturally from higher temperatures to lower temperatures, just as a ball naturally rolls down a hill from higher elevation to lower elevation. This idea of linking temperature and atomic and molecular motion is referred to as "kinetic theory."
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 | Pressure of a volume of gas varies directly with temperature at low pressures, and surprisingly, this behavior doesn't depend on the particular gas you use (as long as you're above the point where it condenses to a liquid).
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| Temperature scales: Celsius (used to be called Centigrade), Fahrenheit and Kelvin
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| What happens when you heat a solid?
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| Specific heat and heat capacity
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 | When heat flows into a material (with no phase change from solid to liquid or liquid to gas, etc.), its temperature rises. The amount of temperature rise depends on the mass of the material and the nature of the material. This is summarized by the equation: Q = mc∆T, where Q is the amount of heat, m is the mass of the material in kg, c is the specific heat of the material in kcal/(kg•°C), and ∆T is the temperature change in °C.
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| How much heat is required to heat a cup of water (about 8 ounces or 240 g) from room temperature (20°C) to boiling (100°C) in a copper pot whose mass is 500 g?
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| mass of water = mwater = 0.240 kg
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| specific heat of water = cwater = 1 kcal/(kg•°C)
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| Qwater = mwater cwater ∆T = (0.240 kg)(1 kcal/(kg•°C))(80°C) = 19.2 kcal
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| mass of copper = mcopper = 0.500 kg
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| specific heat of copper = ccopper = 0.093 kcal/(kg•°C)
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| Qcopper = mcopper ccopper ∆T = (0.500 kg)(0.093 kcal/(kg•°C))(80°C) = 3.7 kcal
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| Total amount of heat = Qwater + Qcopper = 19.2 + 3.7 = 22.9 kcal
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| Latent Heat in Phase Changes
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| If we start with one kg of ice at -40°C and heat it until it turns to water and then to steam at 140°C and measure its temperature, we get results something like the following:
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| This graph was drawn assuming heat was added to the ice-water-steam at a rate of 5 kcal/min. Initially, the heat goes into raising the temperature of the ice. Since the specific heat of ice is 0.5 kcal/(kg•°C) it takes (1kg)(0.5kcal/(kg•°C)(40°C) = 20 kcal to raise the temperature from -40°C to 0°C. At 5 kcal/min this takes about 4 minutes. Once the ice starts to melt at 0°C, the temperature stops rising because the heat is going into separating the water molecules from their rigid ice crystalline structure to freely-moving molecules that can slip and slide over each other. The heat that causes an object to go from solid to liquid is called the latent heat of fusion. It's exactly the amount of heat that is released when the water freezes (hence the name). The heat of fusion for water is 79.7 kcal/kg, so for 1 kg of water with heat being added at a rate of 5 kcal/min, it takes about 16 minutes to melt the ice. Once the ice is melted, the heat goes into raising the temperature of the liquid water. Since the specific heat of water is 1 kcal/(kg•°C) and heat is being added at a rate of 5 kcal/min, the water temperature will rise 5°C/min and it will take about 20 minutes to heat the water from 0°C to 100°C. At that point the water changes phase from liquid to gas (steam) and the temperature quits rising once more. This time, the energy goes into separating water molecules from a small volume where they are essentially in contact to a volume a thousand or more times larger in the gaseous state. This takes even more energy than melting the solid. This heat is called the latent heat of vaporization, and for water its value is 539 kcal/kg, almost 7 times more heat than it took to melt the same mass of ice. Once the water is vaporized into steam, the heat again goes into raising the temperature of the gas. The specific heat of steam is 0.482 kcal/(kg•°C), and at 5 kcal/min it takes about 4 minutes to heat the steam from 100°C to 140°C.
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| If we start with the steam at 140°C and let it cool, we get a similar graph, only backwards. As the steam cools, it releases the heat we added previously.
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| Heat Transfer by Contact -- Conduction
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| If you've ever bitten into a pizza that was too hot, you've burned your mouth by conduction. When heat is transferred from a hotter object to a colder object by contact, we call it conduction.
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| Some materials, such as metals, are good conductors of heat. Other materials, like wood or glass are poor conductors of heat. Poor conductors of heat are called insulators.
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| The rate of heat transfer (in units of energy per unit time) is described by the following equation:
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| Example - Heat loss through a window
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| Suppose you're inside a house at 20°C (68°F) on a winter day when the outside temperature is 0°C (32°F). You have a glass window with an area of 1 m2 and a thickness of about 1/8-inch (about 3 mm or 0.003 m). At what rate are you losing heat through the window?
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| The R-value of a material is a measure of how good an insulator it is. Materials with high R-values are good insulators. Materials will low R-values are poor insulators but good conductors of heat. R-value is defined as R = L/k, thickness divided by conductivity. You can increase the R-value by making the material thicker or by reducing its conductivity.
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| The R-value of the single-pane window we used above is Rglass = 0.003 m/(2x10-4 kcal/(kg•°C)) = 15 kg•m•°C/kcal.
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| The R-value of 3 mm of air is Rair = 0.003 m/(0.055 kcal/(kg•°C)) = 545 kg•m•°C/kcal.
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| R-values in series add together.
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| Suppose you replace your single-pane window with a double-pane window with an air space between the two glass panes. For simplicity, assume each of the panes and the air space are 3 mm thick. The R-value for this combination is the sum of the individual R-values: Rcombo = Rglass + Rair + Rglass = 15 + 545 + 15 = 575. The ratio of Rcombo to Rglass is 575/15 = 38.3. So the double-pane glass should lose about 38 times less heat than the single-pane window or about 145 W.
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| Heat Transfer by Fluid Flow -- Convection
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| Have you ever heard the expression "heat rises"? That's what convections means. When you heat air, for example, it expands, becomes less dense, and then rises in the more dense, cooler air around it. So, heater vents should be near the floor so the hot air will rise and warm you on its way up. When heater vents are near the ceiling, the ceiling is warmed and the air must cool before it descends and reaches you, so you've wasted a lot of energy. These same principles apply in liquids, when liquids are heated, they expand, become less dense and rise in the more dense, cooler liquid around them.
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| Heat Transfer by Radiation
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| The third form of heat transfer is by radiation of electromagnetic rays. This is how we get heat from the sun. We don't have direct material contact with the sun, so conduction is out. There is no fluid (gas or liquid) between us and the sun, so convection can't work. But the sun radiates lots of electromagnetic radiation (such as sunlight) which travels through the vacuum of outer space and is absorbed by our atmosphere, water, plants, skin, roofs, sidewalks, sandy beaches, etc.
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| The rate at which heat is radiated from an object at temperature T1 to an object at temperature T2 is described by the Stefan-Boltzmann equation:
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| Suppose you are standing outside on a sunny day. At what rate are you losing heat to the sun (about 6000°K)?
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| Assume your skin or clothing has an emissivity e = 0.10, your area is 1 m2 and your temperature is about 34°C (310K).
This result is really only valid if there were no atmosphere on the earth. Because of reflection of light and absorption and scattering of light by the air and moisture in the atmosphere, a more realistic result would be about ten thousand times smaller. The usual intensity of sunlight at the earth's surface is about 1 kW/m2.
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| Read pp. 433-462 of the text.
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