Introduction

When a hot object touches a cold object, energy is transferred from the hotter object to the cooler one. This transfer continues until both objects reach the same temperature. At that point, thermal equilibrium has been reached, and there is no further net transfer of heat between them.

The concept of thermal equilibrium is so fundamental that it forms the basis of the Zeroth Law of Thermodynamics. Although it was named after the First and Second Laws, scientists realised later that this principle was even more basic. The Zeroth Law explains what temperature really means and why thermometers can accurately measure it.

---

What Is Thermal Equilibrium?

Thermal equilibrium is the state in which two objects in thermal contact have the same temperature.

When thermal equilibrium is reached:

• No net heat flows between the objects.
• Both objects remain at the same temperature.
• Their temperatures stay constant unless conditions change.

Heat transfer stops because there is no longer a temperature difference.

---

Figure 1. Heat flows from the hotter object to the cooler object until thermal equilibrium is reached.

---

Heat Flow and Thermal Equilibrium

Heat always flows:

• From a hotter object.
• To a cooler object.

As heat is transferred:

• The hotter object cools.
• The cooler object warms.

Eventually:

• Both objects reach the same temperature.
• Net heat transfer stops.

This state is called thermal equilibrium.

---

The Zeroth Law of Thermodynamics

The Zeroth Law of Thermodynamics states:

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

In simple terms:

If two objects have the same temperature as a third object, they must also have the same temperature as each other.

This law allows us to compare temperatures using a thermometer.

---

Figure 2. The Zeroth Law allows temperature to be compared using a third object, such as a thermometer.

---

Why Is the Zeroth Law Important?

The Zeroth Law provides the scientific basis for measuring temperature.

It allows us to:

• Compare temperatures.
• Use thermometers.
• Define temperature scales.
• Determine when systems are in thermal equilibrium.

Without the Zeroth Law, temperature measurement would not be reliable.

---

What Is Temperature?

Temperature is a measure of the average kinetic energy of the particles in a substance.

Higher temperature means:

• Particles move faster.
• Particles have greater average kinetic energy.

Lower temperature means:

• Particles move more slowly.
• Particles have lower average kinetic energy.

Temperature tells us how hot or cold an object is.

---

Temperature and Heat

Although closely related, temperature and heat are different.

A hot cup of coffee and a hot swimming pool may have the same temperature, but the swimming pool contains much more thermal energy because it has far more particles.

---

Figure 3. Temperature measures particle motion, while heat is energy transferred between objects.

---

How Thermometers Work

A thermometer measures temperature by reaching thermal equilibrium with the object being measured.

The process is:

1. The thermometer is placed in contact with the object.
2. Heat flows between the object and the thermometer.
3. They reach thermal equilibrium.
4. The thermometer displays the common temperature.

Because of the Zeroth Law, the thermometer now has the same temperature as the object.

---

Types of Thermometers

Several types of thermometers are used in science and everyday life.

Liquid-in-Glass Thermometers

• Use expanding liquids such as coloured alcohol.
• The liquid rises as temperature increases.

---

Digital Thermometers

• Use electronic sensors.
• Provide fast, accurate readings.

---

Infrared Thermometers

• Detect infrared radiation emitted by objects.
• Measure temperature without direct contact.

Each type relies on reaching or relating to thermal equilibrium.

---

Figure 4. Different types of thermometers measure temperature using different physical principles.

---

Applying the Zeroth Law

The Zeroth Law is used in many everyday situations.

Measuring Body Temperature

A thermometer reaches thermal equilibrium with the body.

---

Cooking

An oven thermometer measures the oven temperature after reaching thermal equilibrium with the air inside.

---

Weather Stations

Thermometers measure air temperature by reaching equilibrium with the surrounding air.

---

Scientific Experiments

Researchers ensure systems reach thermal equilibrium before taking accurate measurements.

---

Thermal Equilibrium in Everyday Life

Examples include:

• A hot drink cooling to room temperature.
• Ice melting in warm water.
• Metal left outdoors reaching the air temperature.
• Food cooling before being refrigerated.

In each case:

• Heat flows.
• Temperatures become equal.
• Thermal equilibrium is reached.

---

Figure 5. Thermal equilibrium occurs in many everyday situations involving heat transfer.

---

Worked Example

Question

A metal spoon is placed in a cup of hot tea.

Describe what happens.

Solution

Initially:

• The tea is hotter than the spoon.

Therefore:

• Heat flows from the tea to the spoon.
• The spoon's temperature increases.
• The tea cools slightly.

Eventually:

• The spoon and tea reach the same temperature.
• No net heat transfer occurs.

They are now in thermal equilibrium.

---

Real-World Connection

Doctors use digital thermometers to measure body temperature because they quickly reach thermal equilibrium with the tissues they are measuring. Once the thermometer and the body are at the same temperature, the device displays an accurate reading. This simple procedure depends directly on the Zeroth Law of Thermodynamics, which makes reliable temperature measurement possible.

---

Did You Know?

The Zeroth Law of Thermodynamics was named after the First and Second Laws had already been established. Scientists later realised that this principle was even more fundamental because the other laws rely on the concept of temperature. Rather than renumber the existing laws, they called it the Zeroth Law.

---

Key Terms

Heat – Energy transferred between objects because of a temperature difference.

Temperature – A measure of the average kinetic energy of the particles in a substance.

Thermal contact – A situation in which two objects can exchange heat.

Thermal equilibrium – A state in which two objects have the same temperature and no net heat transfer occurs between them.

Thermometer – An instrument used to measure temperature.

Zeroth Law of Thermodynamics – The law stating that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

---

Key Takeaways

• Thermal equilibrium occurs when two objects have the same temperature and no net heat flows between them.
• The Zeroth Law of Thermodynamics provides the basis for defining temperature and comparing temperatures.
• Temperature measures the average kinetic energy of particles, while heat is energy transferred because of a temperature difference.
• Thermometers work by reaching thermal equilibrium with the object being measured.
• The Zeroth Law makes accurate temperature measurement possible in medicine, science, engineering, and everyday life.
• Understanding thermal equilibrium is fundamental to the study of thermodynamics and heat transfer.