Thermometry and equilibrium: Measurement and definition of temperature are fundamentally enabled by which law of thermodynamics?

Introduction:
Before we can write energy or entropy balances, we must be able to define and measure temperature. The foundational principle behind thermometry is the recognition of thermal equilibrium as an equivalence relation, which is formalized by the zeroth law of thermodynamics.

Given Data / Assumptions:

• Thermometers reach thermal equilibrium with the system they measure.
• No heat sources or sinks disturb the equilibrium during measurement.
• Thermal contact does not significantly alter the system state.

Concept / Approach:
The zeroth law states: If body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C, then A and C are in thermal equilibrium with each other. This transitive property justifies the use of a thermometer (body B) to compare and assign consistent temperature values to other systems (A and C). Without the zeroth law, temperature would lack a consistent operational definition.

Step-by-Step Solution:
Identify the measurement problem: assigning a scalar quantity (temperature) consistently.Invoke the zeroth law: defines equivalence classes of thermal states.Conclude that thermometers can be calibrated and used to measure temperature reliably.

Verification / Alternative check:
Temperature scales (Kelvin, Celsius, Fahrenheit) are built upon fixed points (e.g., triple point of water) and rely on equilibrium comparisons, directly referencing the zeroth law.

Why Other Options Are Wrong:

• First law: energy conservation; does not define temperature.
• Second law: directionality of processes; defines absolute temperature scale indirectly but not measurement per se.
• Third law: behavior near absolute zero.

Common Pitfalls:
Assuming the first law alone explains temperature; it does not establish equilibrium comparability.

Final Answer:
zeroth