Charles’ law

5 min read Last updated April 8, 2026

Why it matters in anaesthesia

  • Explains how gas volumes change with temperature when pressure is held constant (e.g. open to atmosphere).
  • Relevant to gas measurement and delivery systems where temperature differs from calibration conditions (flowmeters, spirometry, gas sampling).
    • Many devices are calibrated at room temperature and atmospheric pressure; patient gas is at ~37°C and saturated with water vapour.
  • Underpins correction factors (ATPS ↔ BTPS ↔ STPD) used in respiratory physiology and equipment specifications.
  • Practical examples: warming/cooling of gas in breathing circuits, respirometer readings, and gas volumes in bags/bellows when temperature changes at atmospheric pressure.

Typical clinical calculations

  • If a gas volume is measured at one temperature and then warmed/cooled at constant pressure, use V2 = V1 × (T2/T1) with temperatures in Kelvin.
    • Convert °C to K: T(K) = T(°C) + 273.
  • Rule of thumb near room temperature: volume changes by ~1/273 per °C (~0.37% per °C) at constant pressure.

Statement and equation

  • For a fixed mass of an ideal gas at constant pressure, volume is directly proportional to absolute temperature.
  • Mathematically: V/T = constant (P constant).
  • Two-point form: V1/T1 = V2/T2 (temperatures in Kelvin).

Derivation from ideal gas law

  • Ideal gas law: PV = nRT.
  • If n and P are constant: V = (nR/P)T → V ∝ T.

Graphical interpretation

  • Plot of V vs T(K) at constant P is a straight line through the origin.
  • Plot of V vs T(°C) extrapolates to zero volume at −273°C (absolute zero).

Conditions and limitations

  • Assumes ideal gas behaviour (negligible intermolecular forces and molecular volume).
  • Best approximation at low pressure and high temperature; deviations occur at high pressure/low temperature (real gases).
  • Must specify constant pressure; if volume is fixed (rigid container), heating increases pressure instead (Gay-Lussac’s/Amontons’ law).

Anaesthetic equipment links

  • Respirometers/volumetric spirometers may read at ambient conditions (ATPS); exhaled gas in the patient is closer to BTPS.
    • If uncorrected, volumes measured at room temperature will be lower than the same gas volume at 37°C (because warming increases volume at constant pressure).
  • Flow measurement and calibration: some flow sensors assume a particular gas temperature; temperature changes can introduce systematic error.
  • Breathing system compliance and reservoir bag volume are not governed by Charles’ law alone (elastic properties matter), but the gas within will expand/contract with temperature if pressure is near atmospheric.

Worked numerical examples (FRCA style)

  • Example 1: 500 mL of gas at 20°C is warmed to 37°C at constant pressure. Find new volume.
    • T1 = 293 K, T2 = 310 K. V2 = 500 × (310/293) ≈ 529 mL.
  • Example 2: A 2.0 L gas volume measured at 15°C (288 K) is delivered to the patient at 37°C (310 K) at constant pressure. What volume would it occupy at 37°C?
    • V2 = 2.0 × (310/288) ≈ 2.15 L.
  • Example 3: A gas volume is 1.0 L at 0°C (273 K). What is the volume at 40°C (313 K) at constant pressure?
    • V2 = 1.0 × (313/273) ≈ 1.15 L.
State Charles’ law and give the mathematical form used in calculations.

Key marks: constant pressure, absolute temperature, proportionality, correct equation.

  • For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature.
  • V/T = constant or V1/T1 = V2/T2 (T in Kelvin).
How can Charles’ law be derived from the ideal gas equation?
  • Start with PV = nRT.
  • At constant n and P: V = (nR/P)T → V ∝ T.
A common FRCA stem: 600 mL of gas at 18°C is warmed to 36°C at atmospheric pressure. What is the new volume?

Convert to Kelvin and apply V2 = V1 × (T2/T1).

  • T1 = 291 K, T2 = 309 K.
  • V2 = 600 × (309/291) ≈ 637 mL.
What does a V vs T(°C) graph look like for Charles’ law and what is the significance of the intercept?
  • Straight line when plotting V against temperature.
  • Extrapolates to V = 0 at −273°C, representing absolute zero (0 K).
In a viva, you are asked: ‘What must be constant for Charles’ law to apply, and what happens if the volume is fixed instead?’
  • Pressure must be constant (and amount of gas fixed).
  • If volume is fixed (rigid container), increasing temperature increases pressure (P ∝ T).
How does Charles’ law contribute to understanding ATPS vs BTPS corrections in spirometry/respirometry?

Examiners want the direction of change and the reason.

  • At constant pressure, warming gas from room temperature to 37°C increases its volume (V ∝ T).
  • Therefore, volumes measured at ambient temperature (ATPS) will be smaller than the volume the same gas would occupy at BTPS, unless corrected.
A previous-style written question: ‘A gas occupies 3.0 L at 25°C. At what temperature (°C) will it occupy 3.3 L at constant pressure?’
  • Use V1/T1 = V2/T2 → T2 = T1 × (V2/V1).
  • T1 = 298 K. T2 = 298 × (3.3/3.0) = 328 K.
  • Convert to °C: 328 − 273 = 55°C.
What are the main limitations of Charles’ law when applied to clinical gases?
  • It assumes ideal gas behaviour; real gases deviate at high pressure and low temperature.
  • In clinical systems, pressure may not be truly constant and water vapour may be present (humidity changes partial pressures and measured volumes).
Viva-style: ‘If you cool a gas-filled reservoir bag left open to atmosphere, what happens to the gas volume and why?’
  • At (approximately) constant atmospheric pressure, cooling decreases absolute temperature, so volume decreases (V ∝ T).
  • In practice the bag’s elastic recoil and any valves/obstruction may affect whether pressure truly remains constant.
A common confusion question: ‘Is Charles’ law the same as Boyle’s law? Contrast them.’
  • Boyle’s law: at constant temperature, P ∝ 1/V (PV = constant).
  • Charles’ law: at constant pressure, V ∝ T (V/T = constant).

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