Heat flows until temperatures agree
You will be able to: Distinguish temperature, heat transfer and thermal equilibrium.
Why does a warm mug cool beside a cooler room?
A warm metal block touches a cooler block. Energy passes between them, and the warm block cools while the cool block warms. When their temperatures match, microscopic exchanges still happen but there is no net thermal transfer.
A useful starting point: Use gas graphs to test a relationship →
Words and symbols before equations
- Thermal contact
- A connection that allows energy transfer through thermal processes.
- Heat Q
- Energy transferred because of a temperature difference, measured in J; not a stored substance.
- Thermal equilibrium
- No net energy transfer by thermal processes between systems in thermal contact.
- Heat capacity C
- Energy per degree of temperature change, in J/K; introduced here for a simple equal-block model.
What this picture assumes
Two identical blocks, each C=100 J/K, initially 80 °C and 20 °C; insulated combined system, negligible work, constant C and no phase change. Slider is fraction of final energy transferred, not time.
Connect the picture to the physics
Particles continue to move and interact at equilibrium. Over many interactions, energy tends to pass from the hotter system to the colder one. A single microscopic exchange need not follow that direction; the macroscopic net transfer does.
Equal temperatures do not imply equal total internal energies. A larger sample can contain more internal energy than a smaller sample at the same T. A thermometer reaches thermal equilibrium with what it measures; it must not disturb the object too much.
For two identical blocks with constant equal heat capacities, insulated together with negligible work, the final temperature is the average of their initial temperatures. Unequal heat capacities require a weighted energy balance, developed in the calorimetry lesson.
A worked example, step by step
Two identical insulated blocks begin at 80 °C and 20 °C. Each has C=100 J/K. Find their final temperature and energy transferred.
- Energy lost by one block equals energy gained by the other.
- 100(80−T_f)=100(T_f−20), so T_f=50 °C.
- The hot block loses 100(30)=3000 J; the cold one gains 3000 J.
- Their temperatures become equal; their particles do not stop moving.
Thermal equilibrium means equal temperature and zero net thermal transfer, not zero microscopic motion.
At equilibrium, do particles stop colliding?
Compare with an explanation
No. Exchanges continue, but neither system has a net thermal energy gain.
Predict. Change one thing. Explain.
Move the energy-transfer fraction from initial separation to equilibrium. This slider represents progress through a balance calculation, not elapsed time or a rate law. Compare the two temperatures and the equal energy gained/lost.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Hot block 80 °C; cold block 20 °C. Energy transferred=0 J; hot change −0 J and cold change +0 J. Net transfer proceeds from the hotter block toward the cooler one.
Two identical blocks, each C=100 J/K, initially 80 °C and 20 °C; insulated combined system, negligible work, constant C and no phase change. Slider is fraction of final energy transferred, not time.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant particle, temperature or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTwo identical blocks with C=200 J/K start at 70 °C and 30 °C in an insulated enclosure. (a) Predict net energy-transfer direction. (b) Find T_f. (c) Find energy transferred. (d) Describe microscopic motion after equilibrium.
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Compare with the answer and four-point rubric
- 1 point: From the 70 °C block toward the 30 °C block.
- 1 point: T_f=50 °C.
- 1 point: Energy transferred=200(20)=4000 J.
- 1 point: Particles keep moving and interacting; net thermal transfer is zero.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is heat?
Energy transferred by a thermal process due to a temperature difference.
RECALL 2Equilibrium criterion?
Equal temperatures and no net thermal transfer in thermal contact.
RECALL 3Must final temperature be the arithmetic average?
Only for equal constant heat capacities in the stated isolated two-body model.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Heat flows until temperatures agree
- Heat flows spontaneously from hotter to colder on the macroscopic scale.
- For identical isolated blocks: T_f=(T_hot+T_cold)/2.
- Heat is energy in transfer; internal energy belongs to a system.
Remember: Thermal equilibrium means equal temperature and zero net thermal transfer, not zero microscopic motion.
Conditions: Two identical blocks, each C=100 J/K, initially 80 °C and 20 °C; insulated combined system, negligible work, constant C and no phase change. Slider is fraction of final energy transferred, not time.
Refresh Kid · AP Physics 2 Unit 1 (official Unit 9) · Objectives 9.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 9.3, objectives 9.3.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the first AP Physics 2 unit; College Board numbers it Unit 9, continuing after AP Physics 1. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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