Thermal Energy Transfer and Equilibrium
Distinguish thermal-transfer mechanisms and explain statistical approach to equilibrium.
AP Physics 2 Topic 9.3 · College Board CED printed p. 30 / PDF p. 37 · See this topic in the course outline
Heat is energy in transit because of a temperature difference. Choose a system boundary before calling an energy transfer heating or cooling: the same transfer heats one system and cools the other.
Before you start
- Microscopic kinetic energy and temperature.
- Conservation of energy and system boundaries.
Thermal contact and the sign of heat
Systems are in thermal contact when energy can pass between them by thermal processes. They need not touch directly: a warm object and a cooler object can exchange radiation across a vacuum. Draw the boundary of the chosen system. Heating transfers energy into it, so Q is positive; cooling transfers energy out, so Q is negative. The receiving system’s gain equals the supplying system’s loss when the two-system combination is isolated.
Heat is the name for the transfer, not a substance stored in an object. Internal energy describes what the object has in its present state. A hot small object can have less total internal energy than a cool large one, yet net thermal energy still flows from the hotter object to the cooler object.
Three ways a temperature difference transfers energy
Conduction: neighboring particles interact, transferring microscopic energy without an overall flow of the material. A metal spoon in hot water warms along its length; mobile electrons can also carry energy through metal. Convection: moving fluid carries energy as matter circulates, as in warm water rising and cooler water sinking. Forced circulation from a fan or pump can also carry energy. Radiation: electromagnetic waves transfer energy; this mechanism works through empty space. All objects emit and absorb radiation, and net radiative transfer is from hotter to cooler objects.
Several mechanisms can act together. A warm mug conducts energy to a hand, drives convection in nearby air, and emits radiation to its surroundings. Identify the path and the temperature difference instead of assigning an entire situation one permanent label.
Why repeated random transfers lead toward equal temperature
Atoms in a hotter system have greater average kinetic energy. When atoms from the two systems interact, an individual collision may transfer energy in either direction, but statistically the more energetic atoms are more likely to give energy to less energetic atoms. After many collisions, the net transfer is from the hotter system to the cooler one. This is a statement about an ensemble, not a rule that every hot atom must lose energy in every collision.
As the hot system loses energy and the cool system gains it, the temperature difference shrinks. For two finite systems in an insulated enclosure, the most probable final state has the same temperature in both. At thermal equilibrium there is no net transfer by thermal processes. Microscopic exchanges continue, but their opposing contributions balance. If instead one system is held at a fixed temperature by a large reservoir, the finite system approaches the reservoir temperature.
The same transfer heats one system and cools another
A 70 °C metal block is placed in 20 °C water inside an insulated cup. During an interval 250 J passes from the block into the water. Neglect the cup’s energy change. Describe Q and the eventual temperatures.
Choose the block alone: Q_block = −250 J; choose the water alone: Q_water = +250 J.
Why this step? The signs refer to transfer across each chosen boundary, not to whether a Celsius temperature is positive.
Choose block plus water: Q_total = 0 to the surroundings. The transfers within the boundary cancel.
Why this step? An insulated combined system does not receive or lose thermal energy externally.
The block cools and the water warms until their temperatures match.
Why this step? Many interactions carry net energy from the higher-temperature block to the lower-temperature water until no net transfer remains.
Answer and check
Block Q = −250 J, water Q = +250 J, and the combined system has no external thermal transfer. The eventual common temperature lies between 20 °C and 70 °C; its exact value needs masses and specific heats.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
A warm plate faces a cool plate across a vacuum. Are they in thermal contact? What mechanism can exchange energy?
Worked answer and reason
Yes. They can exchange radiation, with net energy flowing from warm to cool. Conduction through matter and convection across the vacuum cannot occur.
Thermal contact concerns possible thermal exchange, not a requirement of physical touching.
Question 2
Two bodies are at the same temperature. One student says no energy ever passes between them. Correct the statement.
Worked answer and reason
At thermal equilibrium there is no net energy transfer. Microscopic exchanges can still take place in both directions and balance.
Equilibrium is a macroscopic average; atom-level motion and interactions do not stop.
Question 3
Could one collision transfer energy from a low-energy atom to a high-energy atom even when the first system is cooler?
Worked answer and reason
Yes. The spontaneous net direction after many collisions is from the hotter system to the cooler one; a single collision need not follow that net trend.
Temperature characterizes a distribution and the thermal direction is statistical.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- An object contains heat.
- An object has internal energy. Heat describes transfer across a boundary because of a temperature difference.
- Equal temperatures mean no atom-level energy exchanges occur.
- Collisions and radiation can still exchange energy in both directions; equilibrium means no net thermal transfer.
- The larger or more energetic object always heats the smaller one.
- The spontaneous net direction depends on temperature, not total energy or mass.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 5 · created mechanism table; signed thermal transfers
- Problem 6 · microscopic explanation; equilibrium comparison
- Problem 14 · procedure; calorimetry balance; uncertainty interval; entropy
Scientific calculator workspace
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Scientific calculator
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+ − * / ^ ! · pi · e · sqrt · sin, cos, tan · asin, acos, atan · atan2(y,x) · ln, log · abs · exp · hypot(x,y). Use * between factors. Keep units in your written working.
For the teacher
- Use arrows crossing a drawn boundary. Ask whose Q is positive and whose is negative for the same interaction.
- Ask students to classify mechanism and direction separately: radiation can carry energy across empty space; direction follows temperature.
- At equilibrium press for the words no net transfer, rather than no transfer.
Source objectives and scope
- 9.3.A — Describe the transfer of energy between two systems in thermal contact due to temperature differences of those two systems.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- College Board AP Physics 2 Course and Exam Description, Unit 9 (PDF pages 34–42; printed pages 27–35) — All Unit 9 learning objectives, essential knowledge clauses, and AP scope boundaries; source equations checked in the supplied pinned PDF.
- OpenStax University Physics Volume 2, Molecular Model of an Ideal Gas — Supporting open-textbook reading for ideal-gas assumptions, absolute pressure, and state-variable graphs; real-gas extensions in the source are beyond this unit’s AP requirements.
- OpenStax University Physics Volume 2, First Law of Thermodynamics — Supporting open-textbook reading for energy accounting; authoring translates any work-by convention into the AP work-on convention.
- OpenStax University Physics Volume 2, Entropy — Optional conceptual supporting reading for qualitative entropy and reversibility; quantitative entropy calculations in the source are outside this AP treatment.
Related source reading
These alternative explanations and examples retain their source context. Draft placement does not add accepted exam coverage.
- Phase-change heating · source context; placement review pending
Glossary and deeper reading · 10 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Heat
Heat is energy transferred between systems because of a temperature difference. It describes a transfer rather than a substance or energy store contained in an object. For example, when a warmer mug transfers energy to a cooler hand, the mug loses internal energy and the hand gains it.
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Temperature
Temperature is a state quantity that determines the direction of net energy transfer through thermal contact. For a classical ideal gas it is proportional to the average translational kinetic energy per particle, rather than to the total energy of the sample. For example, a small hot metal sample can have a higher temperature but less total internal energy than a large cooler sample.
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Kinetic energy
Kinetic energy is energy associated with motion relative to a chosen reference frame. For a nonrelativistic translating object it is one half of its mass times speed squared. For example, doubling a cart’s speed quadruples its translational kinetic energy when its mass stays fixed.
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Conservation of energy
Conservation of energy means total energy is unchanged when the full isolated system is considered. Energy can transfer between objects or change form, so one selected energy store need not remain constant. For example, friction can reduce a sliding block’s kinetic energy while increasing the thermal energy of the block and floor.
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Physical system
A physical system is the object or collection of objects chosen for an analysis. Its boundary determines which forces and energy transfers count as internal or external. For example, friction between a block and a floor is an external interaction for the block alone but internal when both are included.
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Thermal radiation
Thermal radiation is electromagnetic energy emitted by matter because of its temperature. It can transfer energy through a vacuum, and net radiative transfer between ordinary bodies is from hotter to cooler. For example, sunlight warming a surface does not need air to carry the energy across space.
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Internal energy
Internal energy is energy associated with the microscopic motion and configuration of a system’s constituents. It excludes the kinetic energy of the whole system’s bulk motion and depends on the thermodynamic state. For example, a stationary solid can gain internal energy as its atomic vibrations become more energetic.
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Thermal conduction
Thermal conduction transfers energy through microscopic interactions without bulk flow of the material. Particles and, in metals, mobile electrons can carry energy from hotter regions toward cooler regions. For example, the handle of a metal spoon warms when its other end is placed in hot water.
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Convection
Convection transfers energy as a fluid moves from place to place. The circulation can arise from density differences or be driven by a pump or fan. For example, warmer water can rise while cooler water sinks, carrying thermal energy through a container.
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Thermal equilibrium
Thermal equilibrium between systems means their temperatures are equal and there is no net energy transfer between them through thermal processes. Microscopic energy exchanges can continue while their opposing contributions balance. For example, water and a metal sample left together in an insulated cup approach a common equilibrium temperature.