Temperature measurement – which law underpins thermometry? The operational definition and measurement of temperature with thermometers are fundamentally based on which law of thermodynamics?

Introduction / Context:
Thermometers work because systems in thermal contact reach a common property that we call temperature. The conceptual foundation for comparing temperatures and building temperature scales is codified in a specific thermodynamic law. Identifying that law is crucial for understanding why “temperature” is a measurable property.

Given Data / Assumptions:

• Three bodies A, B, and C can be placed in thermal contact or isolated.
• Thermal equilibrium means no net heat exchange when in contact.
• Practical thermometers rely on a property (e.g., expansion of mercury, resistance of a thermistor) that correlates monotonically with temperature in a calibrated range.

Concept / Approach:

The Zeroth law states: If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. This transitive property allows us to assign a numerical scale to temperature and to use a thermometer (system B) to compare the temperatures of other systems (A and C). Without the Zeroth law, “temperature” would lack a consistent operational meaning for measurement and comparison.

Step-by-Step Solution:

Verification / Alternative check:

Calibration procedures (e.g., ice point and steam point) assume transitivity: any thermometer in equilibrium with a standard point has a well-defined reading that transfers to other systems via thermal equilibrium.

Why Other Options Are Wrong:

First law: Energy conservation; does not define temperature scales.Second law: Direction of processes and entropy; informs absolute temperature but not basic comparability for measurement.Third law: Zero entropy at absolute zero; not the basis of routine thermometry.None of these: Incorrect, because the Zeroth law is precisely the foundation.

Common Pitfalls:

Confusing the absolute temperature scale (linked to the Second law) with the general measurability of temperature (Zeroth law).

Final Answer:

Zeroth law of thermodynamics