Gas Laws — Quick Summary

Mr Toogood's Physics · Thermal physics

AQA 3.6.2.2
pV = nRT
Moles form
pV = NkT
Molecules form
p₁V₁/T₁=p₂V₂/T₂
Combined law
W = pΔV
Work done

The three experimental laws

  • Boyle's law: p ∝ 1/V (constant T) — squeezing a gas into a smaller volume increases pressure.
  • Charles' law: V/T = constant (constant p) — heating a gas at fixed pressure increases its volume.
  • Pressure law: p/T = constant (constant V) — heating a gas at fixed volume increases its pressure.
Pressure against volume graph for a gas at different temperatures, Boyle's law

pV = constant at fixed T; a higher-temperature gas sits on a higher curve.

Absolute zero

Graph of volume against temperature extrapolated back to absolute zero

Extrapolating V–T (constant p) to V=0 gives −273.15 °C.

Extrapolating a volume–temperature graph (constant pressure) back to zero volume gives −273.15 °C = 0 K, absolute zero — the temperature at which particles theoretically have no kinetic energy left. The pressure–temperature graph extrapolates to the same intercept.

The equation of state

Combining the three laws gives the ideal gas equation, in two equivalent forms:

pV = nRT  (moles)   |   pV = NkT  (molecules)
  • R = molar gas constant = 8.31 J K⁻¹ mol⁻¹
  • k = Boltzmann constant = 1.38×10⁻²³ J K⁻¹ = R/N_A

For comparing two states of the same gas, the constant terms cancel to give the combined gas law:

p₁V₁/T₁ = p₂V₂/T₂
Always use kelvin: T must be in K, not °C, in every gas law equation — add 273 (or 273.15) before substituting.

Work done by an expanding gas

Pressure against volume graph showing the area under the line as the work done by an expanding gas

Work done = area under a p–V graph.

At constant pressure, the work done by an expanding gas is W = pΔV — this is the area under a horizontal line on a p–V graph. For a changing pressure (e.g. isothermal), find the area under the curve instead.

Exam essentials

Key equations

  • pV=nRT   pV=NkT
  • p₁V₁/T₁=p₂V₂/T₂
  • W=pΔV (constant p)

Ideal gas assumptions

  • No long-range forces between particles.
  • Enough particles to treat statistically.
  • All collisions perfectly elastic.
  • Particle volume negligible vs. container.

Common slips

  • Forgetting to convert °C → K before substituting.
  • W=pΔV only holds at constant pressure — otherwise find the area under the curve.
  • Don't confuse n (moles) with N (number of molecules) — and match with R or k accordingly.