Temperature, Thermodynamic Equilibrium, and the Zeroth Law

Temperature is not just an indicator of cold or heat; it is a fundamental magnitude to understand how physical systems reach equilibrium. In this context, the Zeroth Law of Thermodynamics and its relationship with temperature measurement play a crucial role in explaining why thermometers work and how reliable scales can be established. This principle, which connects seemingly isolated bodies, is the foundation for understanding thermal phenomena that influence both science and our daily lives. Join us as we explore how this concept gives meaning to the behavior of heat and energy.

Learning Objectives:
By the end of this class, the student will be able to

1. Understand the concept of temperature as a magnitude related to thermodynamic equilibrium.
2. Explain the process of thermalization and its irreversible nature in physical systems.
3. Define thermodynamic equilibrium and its relationship to the temperature of bodies.
4. Analyze the Zeroth Law of Thermodynamics as the basis for temperature measurement.
5. Describe the functioning of thermometers and their dependence on thermometric properties.
6. Identify the physical properties used in different types of thermometers, such as electrical resistance and thermal expansion.

CONTENTS INDEX:
Thermodynamic Equilibrium
Thermometers and Temperature Measurement

In previous classes, when reviewing the concept of heat, it was necessary to talk in terms of temperature, even though little or nothing had been explained to establish this concept. Now we will begin to fill that gap by addressing temperature and thermodynamic equilibrium between physical systems.

Thermodynamic Equilibrium

When two bodies come into contact, we say that energy exchange occurs. As we saw earlier, heat is “certain thermal energy in transit.” Furthermore, experiments suggest that, in the absence of external agents, heat always flows from the hotter body to the colder one. Due to this, the energy contained in the bodies and their temperature are expected to change over time.

After some time in contact, the heat exchange stops. When this happens, the bodies are said to be in thermodynamic equilibrium and, consequently, have the same temperature.

The first thing we notice about this phenomenon is that it is an irreversible process. Two bodies at different temperatures, when put into contact, will always tend toward thermal equilibrium. However, the reverse process will not occur unless an external action is applied. This process of approaching thermal equilibrium is known as thermalization.

Zeroth Law of Thermodynamics

These ideas can be generalized to many bodies; that is, when several bodies are in thermal equilibrium, their temperatures are expected to be the same. This idea is crystallized by the zeroth law of thermodynamics.

If two systems are each separately in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

The zeroth law is the foundational basis for temperature measurement: we place a body whose temperature we want to measure in contact with a second body that exhibits some behavior whose dependence on temperature is well known and wait for them to reach thermal equilibrium. The second body is called a “thermometer.” The zeroth law guarantees that if we have calibrated this second body relative to some other standard thermometer, we will always obtain consistent results. On reflection, this infers a more intuitive way to establish the zeroth law, which is the following: “Thermometers work.”

Thermometers and Temperature Measurement

In terms of what we have reviewed so far, we can establish the following considerations for thermometers:

• For a thermometer to work correctly, its heat capacity must be much smaller than that of the object whose temperature is to be measured. If this does not happen, the act of measuring could affect the object’s temperature.
• Thermometers rely on some thermometric property to make their measurements. Galileo used a water thermometer based on thermal expansion, Fahrenheit did the same with alcohol- and mercury-based thermometers. Other methods include observing how the electrical resistance of a conductor changes due to temperature, using the thermal expansion of gases (from the ideal gas equation), etc.

Thermometric Properties

All these methods use a property that is measurable, such as electrical resistance, pressure, or size, which generally depends on a complex function of temperature. Although none of these properties is completely linear over their entire range of possibilities, we do not need to consider the full range; if the range is narrow enough, we have an almost linear relationship that we can exploit.

The Problem of Absolute Temperature

The problem with these considerations is that temperature measurements are obtained relative to some thermometric property. They are measured relatively. This raises the question: Is there an absolute measure of temperature? During the 19th century, this problem was solved through an argument based on the “Carnot engine.” Later, it was found that temperature could be defined statistically, and this is what we currently use. However, to properly review these ideas, we must first go through the notions of micro and macro states.