🔥 Temperature Scales: What's Hot and What's Not (Chapter 14.2)

Welcome to the chapter on temperature scales! While you might already be an expert at checking the weather using Celsius, in Physics (9702) we need to understand exactly how temperature is measured and why we use a special scale called the Kelvin scale.

This chapter is fundamental because temperature is a key concept in later topics like Ideal Gases and Thermodynamics. Don't worry if the terminology seems new—we'll break down why scientists need a scale that is truly "universal"!

1. Measuring Temperature: Thermometric Properties

How does a thermometer know how hot it is? It relies on a physical feature of a substance that changes reliably when the temperature changes. This feature is called a thermometric property.

1.1 The Idea of a Thermometric Property

A temperature scale is defined by observing how a measurable property of a substance changes between two fixed points (like freezing and boiling water).

Imagine you want to measure temperature. You need a material whose properties vary consistently with heat.

Examples of Thermometric Properties (Syllabus 14.2.1)

The syllabus requires you to know that the following physical properties can be used for temperature measurement:

  • • Volume of a liquid or gas: As temperature increases, the volume of liquids (like mercury or alcohol in an old-fashioned thermometer) increases.
  • • Resistance of a metal: The electrical resistance of most metals (like platinum, used in resistance thermometers) increases as temperature rises.
  • • e.m.f. of a thermocouple: A thermocouple consists of two different metals joined together. When the two junctions are at different temperatures, a potential difference (or e.m.f.) is generated. This e.m.f. varies with the temperature difference.
  • • Volume of a gas at constant pressure: If you keep the pressure constant, the volume of a fixed mass of gas increases linearly with temperature.

Key Takeaway: All standard thermometers rely on a physical property (the thermometric property) that changes consistently when heat is added or removed.

2. The Celsius Scale (\(\theta /^\circ\text{C}\))

The Celsius scale is the most common scale used globally for everyday measurements. It is defined using the physical properties of water.

2.1 Defining Fixed Points

The Celsius scale uses two easy-to-determine, reproducible points:

1. Ice Point (Lower Fixed Point): The temperature at which pure water freezes at standard atmospheric pressure. This is set at \(0.00 \ ^\circ\text{C}\).

2. Steam Point (Upper Fixed Point): The temperature at which pure water boils at standard atmospheric pressure. This is set at \(100.00 \ ^\circ\text{C}\).

The space between these two points is divided into 100 equal intervals (degrees).

Common Mistake to Avoid: While the Celsius scale is very practical, it relies entirely on the behavior of water (its freezing and boiling points) and the specific thermometric property used (e.g., the expansion of mercury).

3. The Thermodynamic (Kelvin) Scale (T/K)

In serious physics, relying on the properties of a specific substance (like water or mercury) is problematic. If you use a metal resistance thermometer, your scale might be slightly different from one made using a mercury thermometer!

3.1 The Need for Independence (Syllabus 14.2.2)

To overcome the limitations of substance-dependent scales (like Celsius), physicists developed the Thermodynamic Temperature Scale, which uses the unit Kelvin (K).

The key principle here is:

The scale of thermodynamic temperature does not depend on the property of any particular substance.

Analogy: Imagine you are measuring distance. You wouldn't want your ruler to shrink or grow depending on the material it's made of! The Kelvin scale is like the perfect, unchanging SI ruler for temperature. It is based on fundamental principles of energy and motion (specifically, the kinetic energy of particles, which we study in Ideal Gases).

3.2 The Single Fixed Point

Unlike the Celsius scale, which uses two fixed points (\(0^\circ\text{C}\) and \(100^\circ\text{C}\)), the Kelvin scale is defined using just one point: the triple point of water.

The triple point is the unique temperature and pressure at which water, ice, and water vapour can all exist together in thermal equilibrium. This point is set exactly at 273.16 K.

3.3 Absolute Zero (Syllabus 14.2.4)

The lowest possible temperature on the thermodynamic scale is zero kelvin (0 K). This is known as absolute zero.

At absolute zero, particles (atoms and molecules) have the minimum possible internal energy. All random motion of the molecules has stopped (according to classical physics). It is impossible to reach or go below this temperature.

Quick Review Box: Kelvin vs. Celsius

Kelvin (K) is the SI base unit for temperature. It is the scale used for physics calculations because it is absolute (starts at 0 K) and substance-independent.

Celsius (\(^\circ\text{C}\)) is practical for daily life but is defined by the properties of water.

4. Converting Between Scales

Since the size of one degree Celsius is exactly equal to the size of one kelvin (i.e., the interval between freezing and boiling water is 100 K or \(100 \ ^\circ\text{C}\)), the conversion is simply a shift.

4.1 The Conversion Formula (Syllabus 14.2.3)

To convert temperature \(\theta\) in degrees Celsius (\(^\circ\text{C}\)) to temperature \(T\) in Kelvin (K):

$$ T/\text{K} = \theta /^\circ\text{C} + 273.15 $$

Memory Aid: Think of the scale shift: \(0 \ ^\circ\text{C}\) (freezing water) is \(273.15 \ \text{K}\). You just add 273.15 to the Celsius value to get the Kelvin value.

4.2 Examples and Applications

Let's look at key fixed points using this conversion:


1. Absolute Zero: $$ 0 \ \text{K} \approx -273.15 \ ^\circ\text{C} $$
2. Ice Point: $$ 0 \ ^\circ\text{C} = 273.15 \ \text{K} $$
3. Steam Point: $$ 100 \ ^\circ\text{C} = 100 + 273.15 = 373.15 \ \text{K} $$

Crucial Note for Calculations: When dealing with physical laws like the Ideal Gas Equation (\(pV = nRT\)), you must always use the Kelvin (Thermodynamic) temperature scale. If the question gives you temperature in Celsius, convert it immediately!

💡 Did You Know?

A temperature difference or change is the same whether measured in Kelvin or Celsius. For example, if a substance heats up from \(10 \ ^\circ\text{C}\) to \(20 \ ^\circ\text{C}\), the temperature rise is \(10 \ ^\circ\text{C}\). In Kelvin, this is a change from \(283.15 \ \text{K}\) to \(293.15 \ \text{K}\), which is also a rise of \(10 \ \text{K}\).

4.3 Temperature and Internal Energy (Prerequisite for Section 14.1)

Although the definition of thermal equilibrium is covered in the next section (14.1), it's useful to connect temperature scales to energy now:

When two regions of matter are placed in thermal contact, thermal energy (or heat) is spontaneously transferred from the region of higher temperature to the region of lower temperature.

When no net energy transfer occurs, the regions are said to be in thermal equilibrium, meaning they have the same temperature. Temperature is essentially the property that determines the direction of thermal energy flow.

Key Takeaway: Kelvin is the absolute, substance-independent scale used in physics equations. Convert Celsius to Kelvin by adding 273.15.