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Detailed notes on Thermal Physics for Cambridge IGCSE Coordinated Science, covering key concepts, explanations, examples, and exam-focused revision points.
Gas pressure, volume, and temperature are related by the gas laws. Cambridge tests Boyle's Law (P ∝ 1/V at constant T), the pressure law (P ∝ T at constant V), and qualitative understanding of Charles' Law.
Mapped to the Cambridge IGCSE 0654 syllabus (2025-2027).
At constant temperature, doubling pressure halves volume. PV = constant.
Boyle's Law:
P₁V₁ = P₂V₂ (constant temperature, fixed amount of gas) P ∝ 1/V
Graphs:
Kinetic explanation:
Example: A gas has P₁ = 100 kPa and V₁ = 3.0 L. Volume is compressed to V₂ = 1.5 L. Find P₂.
P₂ = P₁V₁/V₂ = 100 × 3.0 / 1.5 = 200 kPa
Applications:
At constant volume, pressure is proportional to absolute (Kelvin) temperature.
Kelvin (absolute) temperature scale:
T (K) = T (°C) + 273
Pressure Law (Gay-Lussac's Law):
P/T = constant (constant volume, fixed amount of gas) P₁/T₁ = P₂/T₂
Kinetic explanation of pressure law:
Graph: P vs T(K): straight line through the origin (directly proportional)
Example: A gas at 300 K has pressure 150 kPa. What is the pressure at 450 K (constant volume)?
P₂ = P₁ × T₂/T₁ = 150 × 450/300 = 225 kPa
Charles' Law (qualitative):
V ∝ T at constant pressure
Verbatim phrases and definitions Cambridge mark schemes credit.
Paper 4: 'A sealed gas has volume 2.0 L at pressure 100 kPa. Calculate the pressure when volume is reduced to 0.8 L at the same temperature' (2 marks — P₂ = 100 × 2.0/0.8 = 250 kPa). 'A gas at 27°C has pressure 200 kPa. Calculate the pressure at 127°C (constant volume)' (3 marks — T₁ = 300 K; T₂ = 400 K; P₂ = 200 × 400/300 = 267 kPa). 'Explain using particle theory why increasing temperature at constant volume increases pressure' (3 marks).
Sources: Cambridge IGCSE Coordinated Sciences 0654 syllabus 2025-2027 (P3); 0654 Examiner Reports 2022-2024. Last reviewed 2026-05-14.
Step-by-step solutions to past-paper-style questions on pressure changes, written exactly the way a tutor would explain them at the board.
Question
A gas occupies 2.0L at a pressure of 100kPa at constant temperature. The gas is compressed to 0.5L. Find the new pressure.
Step-by-step solution
Step 1
Boyle's law: p1V1=p2V2 at constant temperature.
100×2.0=p2×0.5
Step 2
Solve for p2.
p2=0.5100×2.0=400kPa
Answer
p2=400kPa
Examiner tip
Units cancel as long as both pressures are in the same unit and both volumes are in the same unit. No conversion needed if consistent.
Question
A diver is 25m below the surface of the sea. The density of sea water is 1025kg/m3. Take g=10N/kg. Calculate the pressure due to the water at this depth.
Step-by-step solution
Step 1
Use p=hρg.
p=25×1025×10=256250Pa≈256kPa
Answer
p≈256kPa (pressure due to the water column only).
Examiner tip
Total pressure on the diver = water pressure + atmospheric pressure (≈101kPa). Read the question carefully for what it asks.
Question
A gas at 27°C and 150kPa has a volume of 3.0m3. It is heated to 127°C and compressed to 2.0m3. Find the new pressure.
Step-by-step solution
Step 1
Convert temperatures to kelvin: T(K)=T(°C)+273.
T1=27+273=300K;T2=127+273=400K
Step 2
Apply the combined gas law.
T1p1V1=T2p2V2⟹p2=T1V2p1V1T2
Step 3
Substitute values.
p2=300×2.0150×3.0×400=600180000=300kPa
Answer
p2=300kPa
Examiner tip
ALWAYS convert Celsius to kelvin before using any gas law. T=0°C is NOT the same as 0K.
The formulae you need to memorise for pressure changes on the Cambridge IGCSE 0654 paper, with every variable defined in plain English and a note on when to use it.
p1V1=p2V2(constant T)
When to use
When temperature is constant and pressure or volume changes.
T1p1=T2p2(constant V)
When to use
When volume is constant and pressure and temperature change.
T1p1V1=T2p2V2
When to use
When all three gas variables change simultaneously.
p=hρg
When to use
Finding pressure at a given depth in a static liquid.
Definitions to memorise and the exact keywords mark schemes credit for pressure changes answers — sharpened from recent examiner reports for the 2026 0654 sitting.
At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: pV=constant.
The lowest possible temperature, 0K (−273°C), at which particles have minimum internal energy. Gas pressure and volume are theoretically zero at absolute zero.
The absolute temperature scale. T(K)=T(°C)+273. Must be used in all gas law calculations.
The SI unit of pressure. 1Pa=1N/m2.
The traps other students keep falling into on pressure changes questions — taken from recent Cambridge IGCSE 0654 examiner reports and mark schemes — and how to avoid them.
Why it happens
Students forget to convert, especially when the temperature change is small.
How to avoid it
Always add 273 to convert °C to K before substituting into any gas law. Celsius temperatures give wrong ratios.
Why it happens
Algebraic rearrangement error.
How to avoid it
Rearrange carefully: p2=p1V1/V2. If pressure increases, volume must decrease — check this sense before accepting your answer.
Why it happens
p=hρg gives only the pressure due to the liquid column.
How to avoid it
Total pressure = liquid pressure + atmospheric pressure. Read the question: if it asks for pressure 'due to the water', use hρg only.
The things students keep getting wrong in this sub-topic, answered.