understand that regions of equal temperature are in thermal equilibrium

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Thermal Equilibrium – Cambridge A-Level Physics 9702

Thermal Equilibrium

Learning Objective

Understand that regions of equal temperature are in thermal equilibrium.

Key Concepts

  • Temperature as a measure of the average kinetic energy of particles.
  • Thermal contact and heat flow.
  • Definition of thermal equilibrium.
  • Zero‑law of thermodynamics.

Definition

Two or more regions are said to be in thermal equilibrium when no net heat flows between them, which occurs when they are at the same temperature.

Zero‑Law of Thermodynamics

If region A is in thermal equilibrium with region B, and region B is in thermal equilibrium with region C, then region A is in thermal equilibrium with region C.

Mathematical Expression

The condition for thermal equilibrium between two regions $1$ and $2$ can be written as

$$ T_1 = T_2 $$

where $T$ denotes temperature.

Illustrative Example

  1. Place a metal block at temperature $T_{\text{block}} = 300\ \text{K}$ on a wooden board at $T_{\text{board}} = 300\ \text{K}$.
  2. After a short time the temperatures equalise; no further heat flows.
  3. Both the block and the board are now in thermal equilibrium.
Suggested diagram: Metal block on wooden board with temperature arrows indicating equal temperature.

Common Misconceptions

  • “Equal temperature means no energy is present.” – Incorrect. Energy is still present; it is just evenly distributed.
  • “Heat flow stops only when temperatures become zero.” – Incorrect. Heat flow stops when temperatures become equal, regardless of the absolute value.

Check Your Understanding

  1. Two cups of water, one at $20^\circ\text{C}$ and the other at $80^\circ\text{C}$, are placed in contact. Describe the temperature evolution until thermal equilibrium is reached.
  2. Explain why the zero‑law allows us to define temperature as a property of a system.
  3. Given three objects A, B, C with temperatures $T_A = 250\ \text{K}$, $T_B = 250\ \text{K}$, $T_C = 250\ \text{K}$, state whether they are in thermal equilibrium and justify using the zero‑law.

Summary Table

Concept Condition Result
Thermal equilibrium $T_1 = T_2$ No net heat flow between regions 1 and 2
Zero‑law If $T_A = T_B$ and $T_B = T_C$ Then $T_A = T_C$ (all three in equilibrium)
Temperature gradient $abla T eq 0$ Heat flows from higher to lower temperature

Further Reading

  • Cambridge International AS & A Level Physics (9702) – Chapter on Thermal Physics.
  • Thermodynamics textbooks covering the zero‑law and temperature measurement.