Equation of state

Physics A2 · Ideal gases. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic freeAll Physics A2 topics

The idea

An ideal gas is a gas that obeys pV ∝ T, where p is the pressure, V is the volume and T is the thermodynamic temperature in kelvin. Real gases behave almost like this at low pressure and well above their boiling point.

The equation of state turns the proportionality into an equation. It can be written with the amount of gas in moles, pV = nRT, or with the number of molecules, pV = NkT. The two forms are the same, because N = nNA and the Boltzmann constant is k = R/NA.

For a fixed mass of gas, pV/T stays constant. This lets you compare two states without finding n.

Rules to remember

Common mistake

Students put the Celsius temperature into the equation. Always change to kelvin first: 27 °C is 300 K, so heating from 27 °C to 327 °C doubles T, it does not multiply it by 12.

Worked example

A balloon of volume 0.015 m3 holds an ideal gas at a pressure of 1.1 × 105 Pa and a temperature of 17 °C. How many molecules does it contain?

  1. Temperature: T = 17 + 273 = 290 K.
  2. pV = 1.1 × 105 × 0.015 = 1650 J.
  3. Rearrange pV = NkT: N = pV ÷ (kT) = 1650 ÷ (1.38 × 10−23 × 290).
  4. kT = 4.00 × 10−21 J, so N = 1650 ÷ 4.00 × 10−21 = 4.1 × 1023.

Answer: About 4.1 × 1023 molecules.

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Read the full notes

Keep going

← The moleKinetic theory of gases →Take a Physics A2 test