Physics (9702) | Thermal equilibrium

🌡 Thermal Equilibrium: Understanding Heat Flow (9702 Syllabus 14.1)

Welcome to the start of the Thermodynamics section! This chapter might seem abstract, but it explains things you experience every single day—like why your hot chocolate eventually gets cold, or why ice cream melts in your hand.

The concept of thermal equilibrium is the fundamental rule governing temperature and energy transfer. If you grasp this simple idea, the rest of the temperature topics will be much easier!

1. The Difference Between Temperature and Thermal Energy

Before we discuss equilibrium, we need to make sure we know the difference between temperature and energy. Many students confuse these, so pay close attention!

Key Definitions

• Temperature (\(T\)): This is a measure of the average random kinetic energy of the particles (atoms or molecules) within a substance.
• Thermal Energy (or Internal Energy, \(U\)): This is the total energy contained within a system due to the random motion and positions of its molecules. It is the sum of their kinetic energy and potential energy.

Analogy: Imagine two classrooms. Classroom A has 10 students running around slowly. Classroom B has 5 students running around very quickly.

• Temperature is like the average speed of the students. Classroom B has a higher temperature (faster average speed).
• Thermal Energy is like the total kinetic energy of all students combined. Classroom A might have more thermal energy if it has many more students, even if their average speed is lower.

In short: Temperature dictates the direction of energy flow. Thermal energy is the total amount of energy present.

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2. The Principle of Thermal Energy Transfer

Thermal energy transfer (or heating, symbol \(Q\)) only happens when there is a difference in temperature between two objects or regions.

Syllabus Point 1: Direction of Flow

Thermal energy is always transferred spontaneously (on its own) from a region of higher temperature to a region of lower temperature.

Real-World Example:

1. You put a cube of ice (low temperature, e.g., 0 °C) into a warm drink (high temperature, e.g., 20 °C).
2. Thermal energy flows out of the warm drink (higher T) and into the ice (lower T).
3. The drink cools down, and the ice melts and warms up.

The energy transfer continues until both objects reach the same temperature.

💯 Common Mistake Alert

We often say that "cold moves" into a room or an object. This is misleading! Cold is simply the absence of thermal energy. Energy always flows from hot to cold, never the other way around (unless external work is done, like in a refrigerator).

Key Takeaway for Syllabus 14.1 (1): Thermal energy flows downhill, from high temperature to low temperature, just like water.

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3. Defining Thermal Equilibrium

When two objects or regions have been in contact long enough for the energy transfer to stop, they have reached thermal equilibrium.

Syllabus Point 2: Condition for Equilibrium

Regions or objects are in thermal equilibrium when they are at the same temperature.

When the temperatures are equal (\(T_A = T_B\)), there is no net transfer of thermal energy between the objects.

Wait, does this mean no energy moves at all?

No, at the molecular level, energy is always being exchanged (due to random collisions). However, if the objects are in thermal equilibrium, the rate at which Object A transfers energy to Object B is exactly equal to the rate at which Object B transfers energy back to Object A. Therefore, the net transfer is zero.

Did you know?
If you leave a cup of tea on a table long enough, it reaches thermal equilibrium with the room. This equilibrium is always dynamic—energy is still moving, but the overall temperatures remain constant.

Key Takeaway for Syllabus 14.1 (2): Thermal equilibrium means temperature equality, resulting in zero net heat flow.

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4. The Zeroth Law of Thermodynamics

The concept of thermal equilibrium is so fundamental that physicists named a law after it, preceding the other two laws (First and Second Laws of Thermodynamics)! This is called the Zeroth Law of Thermodynamics.

Understanding the Zeroth Law

The Zeroth Law states:

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

Let's use A, B, and C as our three systems:

1. System A is in equilibrium with System C (so \(T_A = T_C\)).
2. System B is in equilibrium with System C (so \(T_B = T_C\)).
3. Therefore, System A must be in equilibrium with System B (so \(T_A = T_B\)).

The Importance of the Zeroth Law

Why is this law so important? Because it justifies the use of a thermometer!

• The thermometer is System C.
• When you measure the temperature of Object A, you are allowing the thermometer (C) to reach equilibrium with A.
• You then assume that if Object B gives the same thermometer reading, A and B would be in equilibrium if they touched.

The Zeroth Law ensures that temperature is a consistent property that can be measured universally.