Questions: Zeroth Law of Thermodynamics

Question 1

A thermometer reads 80°C after being placed in a pot of soup, then reads 80°C after being placed in a cup of tea. The soup and tea have never been in direct contact. What does the zeroth law allow you to conclude?

• A. Nothing — the zeroth law only applies when objects exchange heat directly
• B. The soup and tea are at the same temperature and would be in thermal equilibrium with each other
• C. The thermometer absorbed heat from both, so 80°C is an average of their temperatures
• D. The soup and tea are at different temperatures, because different materials require different amounts of heat to reach 80°C

Answer: (B)

The zeroth law states: if A is in thermal equilibrium with C, and B is in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. Here the thermometer (C) equilibrated with the soup (A) at 80°C, and with the tea (B) at 80°C. By the zeroth law, soup and tea are in thermal equilibrium — at the same temperature — even though they never contacted each other. This is precisely how a thermometer works as a universal temperature comparator.

Question 2

Why does the zeroth law make temperature a 'well-defined' property rather than just a property of a specific pair of interacting objects?

• A. Because it defines a numerical scale (Celsius, Kelvin) for temperature
• B. Because it establishes transitivity of thermal equilibrium, allowing temperature to be consistently compared across different systems via a common reference
• C. Because it states that heat flows from hot to cold, giving temperature a direction
• D. Because it equates temperature with internal energy, making it a fundamental quantity

Answer: (B)

Without the zeroth law, you could only say that two objects 'have the same temperature' if they had directly exchanged heat and reached equilibrium. There would be no transitive chain connecting non-contacting objects. The zeroth law's transitivity means any object at thermal equilibrium with a reference system (a thermometer) is equivalent in temperature to all other objects at equilibrium with that reference — making temperature a consistent, universally comparable property, not a relational one.

Question 3

The zeroth law requires heat to flow directly between the two objects being temperature-compared for the comparison to be valid.

• T. True
• F. False

Answer: False

This is a key misconception. The zeroth law specifically describes a situation where A and B are each in thermal equilibrium with a third system C (the thermometer), but A and B need not interact directly. It is the transitivity of equilibrium — not direct heat exchange — that allows temperature comparison. In fact, the practical value of the zeroth law is precisely that it allows temperature measurement without A and B ever touching.

Question 4

The zeroth law is the logical foundation that justifies using a thermometer to assign a numerical temperature to any object.

• T. True
• F. False

Answer: True

The thermometer works by reaching thermal equilibrium with the object being measured (the thermometer's reading corresponds to its own equilibrium state with C). The zeroth law then guarantees that any two objects both at equilibrium with the thermometer at the same reading are at equilibrium with each other. This gives temperature its meaning as an objective, transitive property — every thermometer-based temperature measurement relies on this reasoning, whether explicitly stated or not.

Question 5

Explain how the zeroth law justifies using a thermometer to compare the temperatures of two objects that never directly contact each other.

Model answer: The zeroth law establishes that thermal equilibrium is transitive. If object A reaches thermal equilibrium with the thermometer (both settle at the same temperature, no net heat flow), and object B separately reaches thermal equilibrium with the thermometer at the same reading, then by the zeroth law, A and B are in thermal equilibrium with each other — meaning they are at the same temperature. The thermometer acts as the 'common third system' that the law describes. A and B never need to touch; their shared equilibrium with the thermometer is sufficient.

Without transitivity, each temperature comparison would require the two objects to exchange heat directly, making universal temperature measurement impossible. The zeroth law is what lets a single thermometer serve as a universal comparator across all materials and systems.