Lesson 9.4 · Unit 9 · CED topic 9.3
Thermal energy transfer and equilibrium
Pick up a spoon that has been sitting in a hot cup of tea and your fingers get warm, while the tea cools slightly. Nobody pushed anything with a force that did work; energy simply moved from the hot object to the colder one because of their difference in temperature. This is the most familiar thermal process, and it is the starting point for the first and second laws of thermodynamics. In this lesson we name the ways energy is transferred, explain why it flows from hot to cold in terms of atomic collisions, and define thermal equilibrium.
Describe the transfer of energy between two systems in thermal contact due to temperature differences of those two systems.
- Two systems are in thermal contact if the systems may transfer energy by thermal processes. Heating is the transfer of energy into a system by thermal processes; cooling is the transfer of energy out of a system by thermal processes.
- The thermal processes by which energy may be transferred between systems at different temperatures are conduction, convection, and radiation.
- Energy is transferred through thermal processes spontaneously from a higher-temperature system to a lower-temperature system. In collisions between atoms from different systems, energy is most likely to be transferred from higher-energy atoms to lower-energy atoms. After many collisions, the most probable state is one in which both systems have the same temperature.
- Thermal equilibrium results when no net energy is transferred by thermal processes between two systems in thermal contact with each other.
Heating, cooling and the word “heat”
We use heating for the transfer of energy into a system by thermal processes, and cooling for the transfer out of a system. The amount of energy transferred this way is written \(Q\) and measured in joules. In everyday speech people say an object “has heat,” and that causes confusion. An object has internal energy and a temperature; it does not contain a quantity called heat. Heating is a process, a way energy gets into or out of the system, just as doing work is a process. Two systems are in thermal contact if they can exchange energy this way, even if they never touch (the Sun and the Earth are in thermal contact by radiation).
Three thermal processes
| Process | How energy moves | Needs a medium? | Example |
|---|---|---|---|
| Conduction | Collisions between neighboring atoms and free electrons pass kinetic energy along, with no bulk motion of the material. | Yes, matter in contact | A metal spoon in hot soup |
| Convection | Moving fluid carries energy from one place to another. Warm fluid is less dense and rises; cooler fluid sinks. | Yes, a fluid | Warm air rising from a radiator; ocean currents |
| Radiation | Electromagnetic waves carry energy. Every object with a temperature emits it. | No; it crosses a vacuum | Sunlight; the glow of a heating coil |
Several of these usually act together. Standing in front of a fire you feel radiation directly, the air near the fire warms by conduction and convection, and a metal poker handle warms by conduction. Part of the skill on the exam is to identify which process is the main one in a given situation. Metals conduct well because their free electrons carry energy quickly; air and foam conduct poorly (they are good insulators), which is why a fluffy jacket or double-pane window slows the loss of energy.
Why energy flows from hot to cold
The atoms of a hot object have, on average, more kinetic energy than the atoms of a cold object. Place them in contact and atoms collide across the boundary. In a collision between a high-energy atom and a low-energy atom the energy is shared, and on average the low-energy atom gains and the high-energy atom loses. It is possible for a single collision to go the other way, but with trillions of collisions the net result is overwhelmingly one-sided: the cold object’s atoms speed up and the hot object’s slow down. The direction is not forced by a law of motion for each collision; it is the most probable outcome for the whole crowd. Lesson 9.8 returns to this idea under the name entropy.
The transfer continues until the two sides have the same average kinetic energy per atom, the same temperature. Then collisions still occur, but on average as much energy passes one way as the other, so there is no net transfer. That state is thermal equilibrium. Two systems in equilibrium with a third are in equilibrium with each other, which is why a thermometer works: it reaches equilibrium with the object, and its own temperature is then the object’s.
The graph of temperature against time for two objects in contact shows the pattern. The hot object cools, the cold object warms, both curves flatten as they approach a common final temperature, and the rate of transfer is greatest at the start, when the temperature difference is largest. The final temperature lies between the two starting values; it is closer to the one belonging to the system that can store more energy per degree (larger mass or larger specific heat, a topic for lesson 9.7).
Name the main thermal process in each case: (a) sunlight warming a parked car; (b) a pot of water on a stove, once the bottom has heated; (c) the handle of a pot on a stove; (d) the Earth’s interior heat reaching the surface through rock.
(a) Radiation: the Sun’s energy crosses a vacuum and passes through the glass. (b) Convection: the heated water at the bottom becomes less dense and rises while cooler water sinks. (c) Conduction: energy passes along the metal. (d) Conduction through the solid rock (with some convection deep in the mantle).
Two identical, rigid, insulated-from-the-outside containers each hold 1.0 mol of the same ideal monatomic gas, one at 300 K and the other at 500 K. They are placed in thermal contact. Find the final temperature and the average kinetic energy of an atom afterward.
Reasoning. The samples are identical, so they hold equal amounts of energy per kelvin. The energy given up by the hot gas equals the energy gained by the cold gas, so the final temperature is the average: \(T_f = (300+500)/2 = 400\) K.
Energy per atom. \(K_{avg} = \tfrac{3}{2}k_BT_f = \tfrac{3}{2}(1.38\times10^{-23})(400) = 8.28\times10^{-21}\) J, the same for atoms of both samples.
A student places a metal block at 80\(^\circ\)C against a wooden block at 20\(^\circ\)C. After a long time a thermometer reads the same temperature for both. Explain, in terms of atoms, why the energy transfer stopped.
Argument. At first, atoms in the metal block had higher average kinetic energy than atoms in the wood. In collisions across the contact surface, energy was transferred on average from the faster metal atoms to the slower wood atoms, lowering the metal’s temperature and raising the wood’s. This continued until the average kinetic energies of atoms in the two blocks were equal. Then collisions in either direction transfer equal amounts of energy on average, so there is no net transfer: the blocks are in thermal equilibrium.
- Vocabulary. Heating and cooling are processes; use \(Q\) for the energy transferred, never “an amount of heat.”
- Three processes. Conduction (contact, atoms colliding), convection (moving fluid), radiation (electromagnetic waves, no medium).
- Direction. Spontaneously from higher to lower temperature, because high-energy atoms most probably give energy to low-energy atoms.
- Equilibrium. No net transfer; both systems have the same temperature. Collisions continue.
- Writing. Argue from average kinetic energy of atoms in collisions, not from the idea that “cold flows in.”
- Which thermal process allows the Sun’s energy to reach the Earth?
Show answer
Radiation, since there is no medium in space.
- Why does a metal tray feel colder than a wooden tray in the same room, even though both are at the room temperature?
Show answer
Metal conducts energy away from your hand much faster than wood does, so your skin loses energy at a greater rate and feels colder, although the two trays are at the same temperature.
- Two objects are in thermal equilibrium. What can you say about their temperatures, and about the energy transferred between them?
Show answer
Their temperatures are equal, and the net energy transferred between them is zero (equal amounts pass in each direction).
- An ideal gas sample at 200 K is placed in contact with an identical sample at 400 K. What is the final temperature if no energy is lost to the surroundings?
Show answer
The two samples are identical, so the final temperature is the average, 300 K.
- A student says, “When ice touches your hand, cold flows from the ice into your hand.” Rewrite the statement correctly.
Show answer
Energy flows from the hand (higher temperature) into the ice (lower temperature), by conduction. The hand is being cooled and the ice is being heated.
- Why is a thermal-energy transfer from cold to hot not impossible in a single collision, yet it never occurs for macroscopic objects?
Show answer
A single collision may transfer energy either way, but for enormous numbers of atoms the most probable outcome by far is that energy moves from the higher-energy atoms to the lower-energy atoms on average; the probability of a net reverse transfer for a macroscopic system is vanishingly small.