# Thermodynamics (Edexcel IAL Physics Unit 5)

> Physics · Edexcel IAL (2018 Spec)
> Source: https://www.owlsprep.com/study/edexcel-ial-physics-u5-thermodynamics/

This guide covers all Edexcel IAL Physics Unit 5 thermodynamics content for the WPH15 exam, including energy transfer equations, ideal gas laws, kinetic theory, and all three required core practicals, with worked examples and exam tips.

**Prerequisites:** [Edexcel IAL Physics Unit 2: Thermal Energy Transfer Basics](https://www.owlsprep.com/study/edexcel-ial-physics-u2-thermal-energy/); [Algebraic rearrangement skills for physics formulae](https://www.owlsprep.com/study/edexcel-ial-physics-maths-skills/)

## Learning objectives

- Apply specific heat capacity and latent heat equations to solve energy transfer problems
- Explain internal energy as the sum of molecular kinetic and potential energy
- Relate absolute temperature to average molecular kinetic energy and define absolute zero
- Use the ideal gas equation $pV=NkT$ for quantitative calculations
- Derive and apply the kinetic theory equation $\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT$
- Analyse data and evaluate procedures for the 3 required core practicals

## Thermal Energy Transfer: Specific Heat & Latent Heat

When energy is transferred to a substance by heating, it either increases the temperature of the substance (measured using specific heat capacity) or changes its state (measured using specific latent heat). No temperature change occurs during a state change, as all energy goes into breaking or forming intermolecular bonds.

**Specific Heat Capacity** — Energy required to raise 1 kg of a substance by 1 K with no state change

*Notation:* $c$

*Example:* Specific heat capacity of water = 4200 $J kg^{-1} K^{-1}$

**Specific Latent Heat** — Energy required to change the state of 1 kg of a substance at constant temperature

*Notation:* $L$

*Example:* Specific latent heat of fusion of water = $3.34 \times 10^5 J kg^{-1}$

**Worked example:** A 0.2 kg block of aluminium is heated from 20 °C to its melting point of 660 °C, then 0.05 kg of the aluminium is melted. Calculate the total energy transferred. Specific heat capacity of aluminium = 900 $J kg^{-1} K^{-1}$, specific latent heat of fusion of aluminium = $3.97 \times 10^5 J kg^{-1}$.

1. 1. Calculate energy to heat the block to melting point:

   $$\Delta E_1 = mc\Delta\theta = 0.2 \times 900 \times (660 - 20) = 115200 J = 1.15 \times 10^5 J$$
2. 2. Calculate energy to melt 0.05 kg of aluminium:

   $$\Delta E_2 = L\Delta m = 3.97 \times 10^5 \times 0.05 = 19850 J = 2.0 \times 10^4 J$$
3. 3. Sum the two values for total energy:

   $$\Delta E_{total} = 1.15 \times 10^5 + 2.0 \times 10^4 = 1.4 \times 10^5 J (2 s.f.)$$

> **Exam tip:** Always calculate temperature change and state change energy separately, then sum the values to get total energy transferred.

## Internal Energy & Absolute Temperature

Internal energy of a system is the total sum of the random kinetic energy (from translational, rotational, and vibrational motion of molecules) and potential energy (from intermolecular forces between molecules) of all molecules in the system. It does not include the macroscopic kinetic energy of the system as a whole.

**Absolute Zero** — The lowest theoretically possible temperature, 0 K = -273.15 °C, where average molecular kinetic energy is at its minimum value.

The average kinetic energy of gas molecules is directly proportional to the absolute temperature in Kelvin. At absolute zero, quantum effects prevent complete cessation of molecular motion, so kinetic energy is not zero, just at its minimum possible value.

**Worked example:** Explain why the internal energy of a fixed mass of ice increases as it melts into water at a constant temperature of 0 °C.

1. 1. At constant temperature, the average kinetic energy of the water molecules does not change.
2. 2. Energy is transferred to the ice to break the rigid intermolecular bonds holding the ice crystal structure together.
3. 3. This increases the potential energy of the molecules, so total internal energy (sum of KE and PE) increases.

> **Exam tip:** When explaining internal energy changes for constant-temperature state changes, explicitly state kinetic energy is constant and the change comes from potential energy to gain full marks.

## Ideal Gas Law: $pV=NkT$

The ideal gas law relates the macroscopic properties of an ideal gas (theoretical gas with no intermolecular forces and negligible molecular volume) to the number of molecules present. Edexcel IAL only uses the molecular form of this law, with Boltzmann constant $k$ (given on the data sheet).

$$pV = NkT$$

**Worked example:** A helium balloon has a volume of 0.01 $m^3$ at a pressure of $1.01 \times 10^5$ Pa and temperature of 20 °C. Calculate the number of helium molecules in the balloon. $k = 1.38 \times 10^{-23} J K^{-1}$.

1. 1. Convert temperature to Kelvin:

   $$T = 20 + 273 = 293 K$$
2. 2. Rearrange the ideal gas law for $N$:

   $$N = \frac{pV}{kT}$$
3. 3. Substitute values and calculate:

   $$N = \frac{1.01 \times 10^5 \times 0.01}{1.38 \times 10^{-23} \times 293} \approx 2.5 \times 10^{23} (2 s.f.)$$

> **Exam tip:** You will lose all marks for gas law questions if you use Celsius temperature: always convert to Kelvin first before substituting values.

*Calculator:* allowed

## Kinetic Theory of Gases: Derivation & Application

The kinetic theory equation links the microscopic properties of gas molecules (mass, speed) to the macroscopic temperature of the gas. You will be required to derive this equation algebraically in exams, as well as use it for calculations.

**Derivation:** Derive $\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT$

*Starting from:* Ideal gas law $pV=NkT$ and kinetic theory pressure equation $p = \frac{1}{3}\frac{Nm\langle c^2 \rangle}{V}$

1. 1. Equate the two expressions for pressure, cancelling $V$ from both sides:

   $$p = \frac{Nm\langle c^2 \rangle}{3V} = \frac{NkT}{V} \implies \frac{1}{3}m\langle c^2 \rangle = kT$$
2. 2. Multiply both sides by $\frac{3}{2}$ to get average kinetic energy on the left:

   $$\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT$$

*Conclusion:* The average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas.

**Worked example:** Calculate the mean square speed of oxygen molecules at a temperature of 27 °C. Mass of an oxygen molecule = $5.31 \times 10^{-26}$ kg, $k = 1.38 \times 10^{-23} J K^{-1}$.

1. 1. Convert temperature to Kelvin:

   $$T = 27 + 273 = 300 K$$
2. 2. Rearrange the kinetic theory equation for $\langle c^2 \rangle$:

   $$\langle c^2 \rangle = \frac{3kT}{m}$$
3. 3. Substitute values and calculate:

   $$\langle c^2 \rangle = \frac{3 \times 1.38 \times 10^{-23} \times 300}{5.31 \times 10^{-26}} \approx 2.3 \times 10^5 m^2 s^{-2} (2 s.f.)$$

> **Exam tip:** Do not confuse mean square speed $\langle c^2 \rangle$ with root mean square (r.m.s.) speed: if a question asks for r.m.s speed, take the square root of your calculated $\langle c^2 \rangle$ value, but always check the question carefully first.

*Calculator:* allowed

## Core Practicals for Thermodynamics

There are three core practicals assessed in this topic, and you will be expected to describe procedures, analyse data, and identify sources of error for each in exam questions:

- **Core Practical 12 (Thermostat):** Connect a thermistor in a potential divider circuit, calibrate output voltage against temperature to create a temperature-controlled switch.
- **Core Practical 13 (Specific Latent Heat):** Heat a substance to its melting/boiling point, measure energy supplied and mass of substance that changes state, calculate $L = \Delta E / \Delta m$, accounting for heat loss to surroundings.
- **Core Practical 14 (p-V at fixed T):** Trapped air in a syringe, apply different pressures, measure corresponding volume at constant temperature, plot $p$ against $1/V$ to verify Boyle's law ($pV = constant$).

**Worked example:** In a specific latent heat of fusion of ice experiment, 100 g of ice melts in 5 minutes when connected to a 12 V, 2 A power supply. Calculate the experimental value of specific latent heat of fusion, and suggest one source of error with its effect.

1. 1. Calculate total energy supplied by the power supply:

   $$\Delta E = VIt = 12 \times 2 \times (5 \times 60) = 7200 J$$
2. 2. Convert mass of ice to kg: $\Delta m = 0.1 kg$
3. 3. Calculate latent heat:

   $$L = \frac{\Delta E}{\Delta m} = \frac{7200}{0.1} = 7.2 \times 10^4 J kg^{-1}$$
4. 4. Source of error: Heat absorbed from the surroundings melts extra ice, leading to an artificially low calculated value of $L$.

> **Exam tip:** When evaluating practicals, always link sources of error to their effect on the final calculated value, not just list the error, to gain full evaluation marks.

## Common pitfalls

- **Wrong:** Using Celsius temperature in ideal gas or kinetic theory calculations
  - Why it fails: The proportionality between molecular KE and temperature only applies to the absolute Kelvin scale; negative Celsius values lead to invalid negative energy results.
  - Correct: Always convert Celsius to Kelvin using $T(K) = \theta(°C) + 273$ before substituting into gas equations.
- **Wrong:** Using $pV=nRT$ with the molar gas constant R
  - Why it fails: Edexcel IAL Physics does not assess moles, R, or Avogadro's number in this topic, so this form of the gas law is not accepted.
  - Correct: Use only $pV=NkT$ where $N$ is the number of molecules, and $k$ is the Boltzmann constant given on the data sheet.
- **Wrong:** Combining specific heat and latent heat calculations into one step
  - Why it fails: Temperature remains constant during a state change, so the two energy transfers are independent and cannot be calculated with a single formula.
  - Correct: Calculate energy for temperature change and state change separately, then sum the values to get total energy transferred.
- **Wrong:** Confusing mean square speed $\langle c^2 \rangle$ with root mean square speed
  - Why it fails: The kinetic theory equation uses mean square speed, so using r.m.s speed will give a value orders of magnitude incorrect.
  - Correct: Check the question carefully: if it asks for $\langle c^2 \rangle$, do not take the square root; if it asks for r.m.s speed, calculate $\sqrt{\langle c^2 \rangle}$.
- **Wrong:** Stating that kinetic energy changes during a constant-temperature state change
  - Why it fails: Temperature is a measure of average molecular KE, so constant temperature means constant average KE.
  - Correct: Explain that internal energy changes during state changes come from changes in molecular potential energy, not kinetic energy.

## Cheatsheet

| Formula/Concept | Key Variables | Exam Note |
| --- | --- | --- |
| $\Delta E = mc\Delta\theta$ | $\Delta E$ = energy (J), $m$ = mass (kg), $\Delta\theta$ = temp change (K/°C) | For temperature changes, no state change |
| $\Delta E = L\Delta m$ | $L$ = latent heat ($J kg^{-1}$), $\Delta m$ = mass changing state (kg) | For state changes, constant temperature |
| $pV = NkT$ | $p$ = pressure (Pa), $V$ = volume ($m^3$), $T$ = temp (K) | $k = 1.38 \times 10^{-23} J K^{-1}$, given in exam |
| $\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT$ | $\langle c^2 \rangle$ = mean square speed ($m^2 s^{-2}$) | Average KE ∝ absolute temperature |
| Core Practical 12 | Thermistor potential divider | Calibrate voltage to temperature for thermostat |
| Core Practical 13 | Specific latent heat | Correct for heat loss to reduce systematic error |
| Core Practical 14 | p-V at fixed T | Plot $p$ vs $1/V$ to verify Boyle's law |

## What's next

Now that you have mastered thermodynamics for Edexcel IAL Physics Unit 5, you are ready to move on to the other WPH15 unit topics. The next topic is nuclear radiation, where you will learn about radioactive decay, half-life, and nuclear reactions, building on your understanding of energy transfer from this topic. Following radiation, you will study oscillations, including simple harmonic motion, damping, and resonance, before moving on to cosmology, the final Unit 5 topic covering stellar evolution, the Big Bang theory, and Hubble's law. Make sure you practice past paper questions on thermodynamics to consolidate your understanding, as this topic is frequently tested in both multiple choice and long answer sections of the WPH15 exam, often combined with practical analysis questions worth 6+ marks.

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