Read before you practise · 6 min

Use PV = nRT with the Quantity That Actually Changes

Gas-law questions give two states of the same gas, or a gas that leaks, or two vessels joined together. In each case you write PV = nRT (or its ratio form) and decide which of P, V, T and n is actually fixed.

NSEJS · Thermal Physics · 11 linked questions · 100% coverage

Know this first

Ideal Gas Equation and Gas Laws is the central idea in this question pattern. Identify the condition in the stem before applying the method below.

Study deeper: NCERT Science · Thermal Physics

The equation and its ratio form

PV = nRT = (m/M) RT = N kT

For a fixed amount of gas, P1V1 /

T1 = P2V2 / T2, with temperature always in kelvin

A balloon holding 500 m³ of helium at 27 °C (300 K) and 1 atm, taken to -3 °C (270 K) and 0.5 atm, ends with

V2 = 500 x (1/0.5) x (270/300) = 900 m³

Equal volumes of different gases at the same temperature and pressure hold equal numbers of molecules, so the lightest and heaviest gases in equal volumes have equally many molecules.

Fixed volume: pressure is proportional to temperature

In a closed rigid container P is proportional to T.

If heating by 1 °C raises the pressure by 0.4%, then ΔP/

P = ΔT/T = 0.004, so the initial temperature is T = 1 / 0.004 = 250 K

The same reasoning links the final and initial states of any rigid vessel.

When gas leaks or is shared, track the moles

If gas leaks out of a rigid vessel at constant temperature, P is proportional to n, so a pressure that falls to half means half of the gas has gone: a vessel with 6 g of oxygen whose pressure falls to P/2 at the same temperature has lost 3 g. When two bulbs are joined by a thin tube and kept at different temperatures, the pressure is the same in both but the amounts differ, and the total moles stay constant: n1 + n2 is fixed, so P(V/T1 + V/T2) is the same before and after.

Equation of state for a given mass

Convert the mass to moles before writing the equation: 22 g of CO2 is 22/44 = 0.5 mol, so PV = (1/2) RT. When a non-ideal equation of state is given, its isotherms are found by putting T constant and rearranging for P as a function of V.

OlympIQ exam lens

✓Always use kelvin; write the ratio P1V1/T1 = P2V2/T2 for a fixed amount of gas
✓Rigid closed container: P is proportional to T; constant temperature: PV is constant
✓A leak at constant T and V reduces the moles in proportion to the pressure
✓Joined bulbs at different temperatures share the same pressure, with total moles conserved
✓Convert mass to moles with n = m/M before applying PV = nRT

OlympIQ trap

Do not substitute Celsius temperatures into a gas-law ratio. Ratios of Celsius numbers are meaningless; convert every temperature to kelvin and only then compare P, V and T between states.

Ready to try the pattern?

100% coverage across the 11 linked questions.

Practise 11 linked questions

← All NSEJS Prep Paths