Compare rates of thermal energy transfer, distinguish conductors from insulators, explain absorption and emission of thermal radiation, and describe thermal equilibrium

Learning goal: Explain that thermal energy is the energy of the random motion of particles and that temperature measures their average kinetic energy; describe conduction, convection and radiation as processes of transfer; define thermal conductivity and distinguish thermal conductors from thermal insulators with examples; explain how temperature, color, texture and surface area affect the rate at which a system absorbs or emits thermal radiation; and predict whether a system's temperature rises, falls or stays constant from the balance of absorption and emission, including thermal equilibrium.

Thermal energy, temperature and transfer. Middle school introduced thermal energy as the energy of the movement of the particles that make up matter, and transfer by conduction (particles passing energy to neighbors by contact), convection (a warmer fluid rising and carrying its energy with it) and radiation (energy traveling as electromagnetic waves, needing no matter in between). Temperature measures the average kinetic energy of the particles; thermal energy is the total, so a bathtub of warm water holds far more thermal energy than a cup of boiling water even though the cup is hotter. Thermal energy is transferred spontaneously from a higher-temperature object to a lower-temperature one, never the reverse on its own. The word heat in science names that transfer, not a substance an object contains. This course adds two ideas: the rate at which transfer happens, and what happens when transfers balance.

Thermal conductivity. Materials differ in how fast thermal energy moves through them. Thermal conductivity describes the rate at which thermal energy is transferred from one end of a material to the other. A thermal conductor has a high rate: metals such as copper, aluminum and steel conduct quickly, which is why a metal spoon in hot soup is soon hot at the handle and why a metal railing feels colder than a wooden one at the same temperature; it draws thermal energy out of your hand faster. A thermal insulator has a slow rate: wood, plastics, glass, wool, foam and still air conduct slowly. Air trapped in small pockets is one of the best practical insulators, which is why foam cups, double-pane windows, fibrous attic insulation and a bird's fluffed feathers all work by holding air still. Conductivity is a property of the material; the rate of transfer through an actual object also depends on its thickness, its area and the temperature difference across it, so a thin sheet of insulator can still leak energy faster than a thick one. The condition on "feels cold": touch tells you how fast energy leaves your skin, not the temperature of the object.

Absorption and emission of thermal radiation. Every object is continuously absorbing thermal radiation from its surroundings and emitting its own. The rate at which a system absorbs or emits depends on its temperature, color, texture and exposed surface area. Hotter objects emit faster. All else being equal, in a given time a matte black surface absorbs more radiant energy than a shiny metal one, and it is also the better emitter; a shiny metal surface reflects most of what reaches it and emits poorly. (A good absorber is a good emitter at the same wavelengths: white paint reflects visible light but still emits infrared well, so color in visible light is only a rough guide.) That is why a dark car interior gets hotter in the sun than a light one, why solar water heaters have matte black collectors, and why emergency blankets and vacuum-bottle linings are shiny. A larger exposed surface exchanges more radiation, which is why a radiator has fins and why a curled-up animal loses less energy on a cold night.

Rising, falling or steady: the balance. Whether a system's temperature changes depends on the net transfer, counting every route by which energy arrives or leaves: radiation, conduction and convection. If a system absorbs more thermal energy than it emits, and no phase change is under way, its temperature rises. If it emits more than it absorbs, its temperature falls. If the energy coming in equals the energy going out, the temperature stays constant even though energy is still flowing: a steady state. When a system has reached the same temperature as its surroundings, so that there is no net transfer between them, it is in thermal equilibrium. A covered cup of tea left in a room cools because it emits and conducts away more than it absorbs from the cooler room; the rate of cooling is fastest at the start, when the temperature difference is largest, and slows as the tea approaches room temperature, until at equilibrium the two rates are equal and the temperature holds. (The cup is covered so that evaporation, which carries energy away, stays out of the account.) A sunlit pavement warms in the morning while it gains energy faster than it loses it (by radiation, conduction to the ground and air, and convection), holds a steady temperature when gains and losses match, and cools after sunset; that steady temperature is above the air's, so it is a steady state, not thermal equilibrium with the air. The phase-change condition matters: melting ice in a warm room absorbs more than it emits but stays at 0 °C until it has melted, because the energy is going into potential energy of the particles, as the heating-curve lesson showed.

A fully worked model: three cups of hot water. Three identical volumes of water at 80 °C are placed in a room at 20 °C in a foam cup, a paper cup and a thin metal cup, each with a lid, and their temperatures are read every 5 minutes. Suppose the readings at 10 minutes are 72 °C, 64 °C and 52 °C. The average rate of temperature drop over the first 10 minutes is (80 − 72) ÷ 10 = 0.8 °C per minute for foam, (80 − 64) ÷ 10 = 1.6 °C per minute for paper and (80 − 52) ÷ 10 = 2.8 °C per minute for metal. The metal cup is the best thermal conductor and loses energy fastest; the foam cup, full of trapped air, is the best insulator. Reading the graph further, each curve flattens as it nears 20 °C, and all three would eventually sit at 20 °C in thermal equilibrium with the room. The graph ranks materials by rate; it does not give a value of conductivity, and the numbers here are illustrative, not measured.

Investigation: rank materials for a "cooler" cooler. Materials: four identical small jars with lids, hot tap water at about 50 °C, four thermometers or probes, wrapping materials to test (bubble wrap, aluminum foil, wool cloth, newspaper, foam sheet), rubber bands, a timer, goggles. Steps: wrap three jars each in one material of the same thickness and leave the fourth bare as the control; fill all four with the same volume of hot water at the same starting temperature, fit lids and thermometers, and record the temperature every 2 minutes for 20 minutes; plot all four curves on one graph. Record: a table of time and temperature for each jar, the temperature drop in the first 10 minutes for each, and the rate in °C per minute. A result that supports the claim: the bare jar cools fastest; the wrapped jars cool more slowly, and the one with the smallest rate is the best insulator among those tested; a shiny foil layer may reduce radiation losses even though foil itself is a conductor, which is worth a sentence in the conclusion. Then design an improved wrapping that combines the best insulator with a shiny outer layer and test it. Safety: goggles; keep the water at about 50 °C, since hotter tap water can scald within seconds, and still handle the jars with care; wipe spills. What the model cannot show: a temperature drop compares rates but does not measure thermal conductivity itself, cannot separate conduction, convection and radiation losses, and says nothing about how much thermal energy left, which is quantified in a later course.

Worked example 1 — conductor or insulator, and why touch misleads. A steel bench and a wooden bench sit outside overnight and both reach 5 °C. The steel feels much colder. Both are at the same temperature; steel is a thermal conductor and transfers energy out of your hand at a high rate, while wood is an insulator and transfers slowly. The sensation reports the rate of transfer from your skin, not the object's temperature. A thermometer touched to each would read 5 °C on both.

Worked example 2 — rates from data. Three cups of water start at 80 °C in a 20 °C room; after 10 minutes they read 72, 64 and 52 °C. Rates over the first 10 minutes: 0.8, 1.6 and 2.8 °C per minute. The fastest cooling cup lost energy at the highest rate and is made of the best conductor. Over the next 10 minutes each rate is smaller than before, because the temperature difference driving the transfer has shrunk; none of the cups would ever fall below 20 °C, the room's temperature, where absorption and emission balance.

Worked example 3 — absorption and emission. Two identical cans of water at 20 °C are placed in sunlight, one painted matte black and one polished silver. The black can's surface absorbs a larger share of the radiation reaching it, so, with everything else about the two cans the same, its net gain of energy is larger and its temperature rises faster; the silver can reflects most of the radiation and warms slowly. Moved into a dark cold room, the black can also cools faster, because a good absorber is also a good emitter. Color and texture affect both directions of radiative transfer.

Worked example 4 — predict the direction of temperature change. A cool metal plate is put out in the sun. To predict what its temperature does, compare everything it gains with everything it loses. At first the radiation it absorbs is more than its total losses (its own emission plus conduction and convection to the air), so its temperature rises. As it gets hotter, it emits at a greater rate and passes more energy to the air, until its losses equal what it absorbs: the temperature stops rising and holds, a steady state with energy still flowing through the plate, not thermal equilibrium, because the plate stays hotter than the air around it. A cloud covers the sun; what the plate absorbs falls below its total losses and the plate cools. (Comparing absorbed with emitted radiation alone is not enough: on a cold, windy day a plate can absorb more radiation than it emits and still cool, because the moving air carries energy away.) If a block of ice were on the plate instead, the ice's gains would exceed its losses but its temperature would stay at 0 °C until it had melted, because a phase change was under way; that is the one exception to the rule.

Representation task: a cooling-curve graph and a transfer diagram. Plot the three cups' data (start 80 °C; at 10 minutes 72, 64 and 52 °C; at 20 minutes 65, 53 and 38 °C; room 20 °C) on one set of axes, label each curve with its material, and draw a dashed line at 20 °C labeled "thermal equilibrium with the room". Beside the graph draw one cup with arrows for conduction through the wall, convection in the air above and radiation from the surface, and write which of the three the lid mainly reduces.

Independent performance: design and test a better cooler. Starting from your ranked materials, build a container for one cold drink can from a shoebox or similar that must slow warming as much as possible for 30 minutes at room temperature. Success criteria: the design names at least two features and states for each which transfer process it targets (conduction, convection or radiation) and why the material was chosen; a control (the bare can) and the cooler are tested at the same time with temperatures every 5 minutes; the two warming rates in °C per minute over the first 15 minutes are calculated and compared on one graph; one improvement is made and retested with its effect reported; and a paragraph explains, using the words absorb, emit and thermal equilibrium, why the drink would eventually reach room temperature in any cooler.