Unit 5: Thermodynamics

This guide covers sub-topic 5.3 Thermodynamics, the first of four sub-topics in Unit 5: Thermodynamics, Radiation, Oscillations and Cosmology, from the Pearson Edexcel International Advanced Level in Physics (YPH11), Issue 3 specification (first assessment June 2020). Unit 5 is a compulsory, externally assessed IA2 unit examined by a 1 hour 45 minute paper worth 90 marks, and this topic is commonly studied using applications such as space technology.

Before studying this

Unit 5 assumes the mechanics and mathematics developed in Units 1 and 4, and comfort with rearranging equations involving temperature in kelvin.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 5.3

Candidates will be assessed on their ability to: use the equations ΔE = mcΔθ and ΔE = LΔm; CORE PRACTICAL 12: calibrate a thermistor in a potential divider circuit as a thermostat; CORE PRACTICAL 13: determine the specific latent heat of a phase change; understand the concept of internal energy as the random distribution of potential and kinetic energy amongst molecules; understand the concept of absolute zero and how the average kinetic energy of molecules is related to the absolute temperature; use the equation pV = NkT for an ideal gas; CORE PRACTICAL 14: investigate the relationship between pressure and volume of a gas at fixed temperature; and derive and use the equation ½mc̄² = (3/2)kT.

Specific heat capacity and specific latent heat

The energy needed to change an object’s temperature is given by:

ΔE = mcΔθ

where c is specific heat capacity. The energy needed to change a substance’s state at constant temperature is:

ΔE = LΔm

where L is specific latent heat (of fusion, for melting/freezing, or vaporisation, for boiling/condensing). CORE PRACTICAL 12 calibrates a thermistor in a potential divider circuit for use as a thermostat, and CORE PRACTICAL 13 determines the specific latent heat of a phase change experimentally.

Internal energy and absolute zero

Internal energy is the sum of the random distribution of potential energy (from intermolecular bonds/forces) and kinetic energy (from molecular motion) among the particles of a substance — distinct from the macroscopic, ordered kinetic or potential energy of the object as a whole. Absolute zero is the temperature at which molecules have the minimum possible kinetic energy; the average kinetic energy of molecules in a substance is directly proportional to its absolute temperature (in kelvin).

The ideal gas equation

For an ideal gas, pressure, volume, number of molecules and temperature are related by:

pV = NkT

where N is the number of molecules and k is the Boltzmann constant. CORE PRACTICAL 14 investigates the relationship between pressure and volume of a fixed mass of gas at constant temperature (Boyle’s law).

The kinetic theory model of a gas leads to the derived relationship between the mean square speed of gas molecules and absolute temperature:

½m c̄² = (3/2)kT

where m is the mass of one molecule and c̄² is the mean square speed — linking the macroscopic ideal gas equation to the microscopic motion of individual molecules.

Worked example. 0.50 kg of water at 100°C is converted entirely to steam at 100°C. The specific latent heat of vaporisation of water is 2.26 × 10⁶ J/kg. Find the energy required.

ΔE = LΔm = (2.26 × 10⁶) × 0.50 = 1.13 × 10⁶ J (1.13 MJ)

The equation can equally be written in terms of moles rather than molecules:

pV = nRT           n in moles, R = 8.31 J mol⁻¹ K⁻¹

The kinetic theory model

Kinetic theory derives the macroscopic gas laws from the microscopic motion of individual molecules, using several simplifying assumptions: a large number of molecules in random motion; molecular volume negligible compared with the volume of the container; no intermolecular forces except during collisions; collisions are perfectly elastic; and the time of a collision is negligible compared with the time between collisions.

Because an ideal gas has no intermolecular forces, it has no molecular potential energy — its internal energy is entirely kinetic and depends only on temperature, not on pressure or volume.

Mean molecular kinetic energy depends only on absolute temperature, not on pressure, volume, or which gas it is. Helium and xenon at the same temperature have equal mean molecular kinetic energy; the (much heavier) xenon atoms simply move more slowly, since ½m c̄² is the same for both but m differs.

Real gases deviate from ideal behaviour most at high pressure and low temperature, because molecules are then close together, so their own volume becomes significant relative to the container and intermolecular attractions are no longer negligible — exactly the two assumptions that break down. Real gases behave most nearly ideally at low pressure and high temperature, where molecules are far apart.

Common mistakes

Using ΔE = mcΔθ when a substance is changing state at constant temperature — no temperature change occurs during a phase change, so ΔE = LΔm applies instead, and the two must never be added together for the same energy transfer. Forgetting to convert Celsius temperatures to kelvin before using pV = NkT. Confusing internal energy (a property of a substance’s particles) with the object’s overall macroscopic kinetic or potential energy as a whole body.

Quick revision checklist

• Use ΔE = mcΔθ and ΔE = LΔm, and know which applies in a given scenario.
• Describe CORE PRACTICAL 12 (thermistor calibration) and CORE PRACTICAL 13 (specific latent heat).
• Define internal energy and absolute zero, and relate average molecular kinetic energy to absolute temperature.
• Use pV = NkT and describe CORE PRACTICAL 14 (pressure-volume relationship).
• Derive and use ½mc̄² = (3/2)kT.

Related resources

• Unit 5: Nuclear Decay — the next sub-topic
• Unit 1: Mechanics — foundational mechanics this unit builds on
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.