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The ideal gas equation Cambridge International AS & A Level Physics revision

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In plain words

Squeeze a gas and its pressure rises. Heat it and it pushes harder, or swells. For a gas that isn't too cold or too squashed, a single equation ties its pressure, its volume, its temperature and the number of molecules together.

4 things to know

  1. For a fixed amount of an ideal gas, pV is proportional to T, with T in kelvin: pV ÷ T is constant.
  2. pV = NkT, where N is the number of molecules and k = 1.38 × 10⁻²³ J/K is the Boltzmann constant.
  3. At constant temperature, pV is constant: halve the volume and the pressure doubles. At constant volume, p is proportional to T. At constant pressure, V is proportional to T.
  4. Follow the pressure of a gas downwards as it cools and it would reach zero at absolute zero, 0 K, which is −273 °C. T in kelvin = θ in °C + 273.

Worked example

A gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K has a volume of 2.0 × 10⁻³ m³. Find the number of molecules in it.

  1. N = pV ÷ kT.
  2. = 1.0 × 10⁵ × 2.0 × 10⁻³ ÷ (1.38 × 10⁻²³ × 300).
  3. = 4.8 × 10²².

Tips and tricks

  • Always change temperatures to kelvin before using a gas equation.
  • For a fixed amount of gas before and after a change: p₁V₁ ÷ T₁ = p₂V₂ ÷ T₂.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

The ideal gas equation: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. In pV = NkT, what is N?
    • the number of molecules (the answer)
    • the number of moles
    • the Avogadro constant
    • the number of newtons

    k is the constant for a single molecule.

  2. The volume of a fixed amount of gas is halved at constant temperature. What happens to its pressure?
    • It doubles. (the answer)
    • It halves.
    • It stays the same.
    • It becomes four times bigger.

    pV is constant.

  3. What is 27 °C in kelvin?
    • 246 K
    • 273 K
    • 300 K (the answer)
    • 327 K

    Add 273.

  4. A fixed amount of gas is heated at constant volume from 300 K to 600 K. What happens to its pressure?
    • It doubles. (the answer)
    • It halves.
    • It stays the same.
    • It rises by 300 Pa.

    At constant volume, p is proportional to T in kelvin.

  5. What is k in pV = NkT?
    • the Boltzmann constant (the answer)
    • the spring constant
    • the Avogadro constant
    • the decay constant

    1.38 × 10⁻²³ J/K.

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