Physics (9702) | Temperature

AS & A Level Physics (9702) Study Notes: Chapter 14 – Temperature

Welcome to the chapter on Temperature! This topic is crucial because it bridges the world of mechanics (forces and motion) with the world of thermal physics (energy and heat). Understanding temperature isn't just about reading a thermometer; it’s about grasping how energy flows and how different substances respond to that energy.

Don't worry if concepts like "latent heat" sound abstract. We’ll break them down using everyday examples, like boiling water and melting ice cream. Let’s dive into what makes things hot or cold!

14.1 Thermal Equilibrium

Thermal physics is fundamentally about the transfer of energy.

Energy Transfer and Temperature

Syllabus Requirement: Understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature.

Imagine you put a hot slice of pizza onto a cold plate. What happens? Energy flows from the hot pizza to the cold plate.

• The type of energy being transferred is often referred to as thermal energy (or heat).
• This transfer always occurs spontaneously from the object at the higher temperature to the object at the lower temperature.
• This is a fundamental direction rule in thermodynamics—you never see a cold object spontaneously get colder and a hot object spontaneously get hotter when they are placed together.

What is Thermal Equilibrium?

Syllabus Requirement: Understand that regions of equal temperature are in thermal equilibrium.

When the hot pizza and the cold plate have been in contact for a long time, the temperature difference gradually disappears. When both objects reach the same temperature, energy transfer stops (or, more accurately, the rate of energy transfer in both directions is equal).

Definition: Thermal Equilibrium

Thermal Equilibrium is the state reached when two or more objects in thermal contact achieve the same temperature, meaning there is no net flow of thermal energy between them.

Analogy: Think of two water tanks connected by a pipe. Water (representing thermal energy) flows from the higher tank (higher temperature) to the lower tank (lower temperature) until the water levels are equal (thermal equilibrium is reached).

14.2 Temperature Scales

To measure temperature, we need a reliable scale. A thermometer works by using a physical property that changes linearly and predictably with temperature.

Thermometric Properties

Syllabus Requirement: Understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties.

A thermometric property is a measurable physical characteristic that changes as temperature changes. We use this change to calibrate a temperature scale.

Examples of Thermometric Properties:

• Volume/Density of a liquid: e.g., The expansion of mercury or alcohol in a traditional glass thermometer.
• Volume of a gas at constant pressure: As temperature increases, the gas expands.
• Resistance of a metal: The electrical resistance of most metals increases with temperature (used in resistance thermometers).
• Electromotive Force (e.m.f.) of a thermocouple: When two different metal wires are joined at two junctions, a temperature difference between the junctions creates a small voltage (e.m.f.).

The Thermodynamic (Kelvin) Scale

Syllabus Requirement: Understand that the scale of thermodynamic temperature does not depend on the property of any particular substance.

While Celsius thermometers rely on the properties of water (freezing point, boiling point), the Thermodynamic Temperature Scale (Kelvin scale) is truly fundamental.

The Kelvin scale is defined using the absolute properties of an ideal gas (which we will explore in the next chapter). Crucially, the size of the Kelvin unit (the Kelvin, K) does not depend on the specific material used to measure it. This makes it the standard SI unit for temperature.

Absolute Zero

Syllabus Requirement: Understand that the lowest possible temperature is zero kelvin on the thermodynamic temperature scale and that this is known as absolute zero.

Absolute Zero is the theoretical lowest temperature where the particles of a substance have minimum (zero translational) kinetic energy. It is defined as 0 K.

Did you know? Scientists have managed to get substances incredibly close to absolute zero (fractions of a billionth of a degree), but reaching exactly 0 K is physically impossible.

Converting Between Scales

Syllabus Requirement: Convert temperatures between kelvin and degrees Celsius and recall that \(T/K = \theta/^\circ C + 273.15\).

The Celsius scale (\(\theta\)) is defined relative to the freezing and boiling points of water. The Kelvin scale (\(T\)) starts at absolute zero.

The conversion formula is:

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

• To convert from Celsius to Kelvin, you add 273.15.
• To convert from Kelvin to Celsius, you subtract 273.15.

Memory Trick: When going from Celsius ($\theta$) to Kelvin ($T$), think of Kelvin as being the "bigger" scale in terms of physical significance, so you add the 273.15 to make the number bigger!

Example: The boiling point of water is $100^\circ$C. In Kelvin, this is \(100 + 273.15 = 373.15\) K.

14.3 Specific Heat Capacity and Specific Latent Heat

When we add thermal energy to a substance, one of two things usually happens: either its temperature increases, or its state changes (e.g., melting or boiling).

1. Specific Heat Capacity (SHC)

Syllabus Requirement: Define and use specific heat capacity.

Different materials require different amounts of energy to change their temperature. Think about metal vs. water. Metal heats up quickly; water takes ages.

Definition: Specific Heat Capacity ($c$)

The Specific Heat Capacity (c) of a substance is the amount of energy required to raise the temperature of unit mass (1 kg) of the substance by 1 Kelvin (or $1^\circ$C).

• Unit: Joules per kilogram per Kelvin (\(J\,kg^{-1}\,K^{-1}\)) or (\(J\,kg^{-1}\,^\circ C^{-1}\)).

If you want to calculate the total thermal energy ($Q$) required to change the temperature ($\Delta \theta$ or $\Delta T$) of a mass ($m$), use the formula:

$$\text{Energy transferred } Q = mc\Delta \theta$$

Example: Water has a very high SHC ($c \approx 4200 \, J\,kg^{-1}\,K^{-1}$). This means it takes a lot of energy to heat up water, which is why water-filled hot bottles stay warm for a long time.

2. Specific Latent Heat (SLH)

Syllabus Requirement: Define and use specific latent heat and distinguish between specific latent heat of fusion and specific latent heat of vaporisation.

When a substance changes state (e.g., from solid to liquid), you must add or remove energy, but the temperature remains constant during the process. This "hidden" energy is called Latent Heat.

Definition: Specific Latent Heat ($L$)

The Specific Latent Heat (L) of a substance is the amount of energy required to change the state of unit mass (1 kg) of the substance without any change in temperature.

• Unit: Joules per kilogram (\(J\,kg^{-1}\)). (Note: No Kelvin unit here because temperature is constant!)

The total thermal energy ($Q$) required for a state change is:

$$Q = mL$$

Distinguishing the Two Types of SLH

Latent heat comes in two forms, depending on the phase transition:

a) Specific Latent Heat of Fusion ($L_f$)

This is the energy needed to change 1 kg of a substance from solid to liquid (melting) or from liquid to solid (freezing) at its melting point.

Example: To melt 1 kg of ice at $0^\circ$C into 1 kg of water at $0^\circ$C, you use $Q = m L_f$.

b) Specific Latent Heat of Vaporisation ($L_v$)

This is the energy needed to change 1 kg of a substance from liquid to gas (boiling/vaporising) or from gas to liquid (condensing) at its boiling point.

Example: To boil 1 kg of water at $100^\circ$C into 1 kg of steam at $100^\circ$C, you use $Q = m L_v$.

Why is $L_v$ usually much larger than $L_f$?
When vaporising (boiling), particles must gain enough potential energy to completely break free from the attractive forces holding them in the liquid, resulting in a much larger volume change and requiring significantly more energy than just melting (fusion).

Analogy: Heating water from ice to steam is like climbing a mountain. You need energy to climb the slopes (raising temperature, using SHC), and then you need energy to cross a flat plateau (changing state, using SLH, where your height/temperature doesn't change).

Step-by-Step Thermal Calculations

In A-Level problems, you often need to calculate the energy needed for both temperature changes and state changes in one sequence. You must split the calculation into stages:

1. Heating Stage (SHC): Calculate $Q_1$ to raise the temperature to the phase change point (e.g., $0^\circ$C or $100^\circ$C). Use \(Q_1 = mc\Delta \theta\).
2. Phase Change Stage (SLH): Calculate $Q_2$ to change the state (e.g., melt the ice). Use \(Q_2 = m L\). (Temperature is constant here.)
3. Heating Stage (SHC): Calculate $Q_3$ to raise the temperature of the new phase (e.g., water) to the final temperature. Use \(Q_3 = mc\Delta \theta\).

The Total Energy required is $Q_{total} = Q_1 + Q_2 + Q_3 + ...$