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Ideal Gases and Kinetic Theory (A level)

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For A level physics (AQA 7408, with OCR A and Edexcel). Squash and heat an animated gas: move the piston, use the heater, hold T, V or p constant and plot p–V, p–T or V–T live. Then practise the gas laws, moles and molecules, r.m.s. speed, mean kinetic energy, internal energy, absolute zero and Brownian motion.

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Worked solution

    Key facts

    T / K = θ / °C + 273

    Boyle’s law (constant T): pV = constant. Charles’s law (constant p): V/T = constant. Pressure law (constant V): p/T = constant. All need T in kelvin and a fixed mass of gas.

    pV = nRT    pV = NkT    N = n NA    k = R / NA

    pV = ⅓ N m (crms)²    ½ m (crms)² = 3/2 kT = 3RT / 2NA

    crms = √[(c₁² + c₂² + … + cN²) / N]

    Internal energy of an ideal gas: there are no forces between the molecules, so it is all random kinetic energy, U = 3/2 nRT. Absolute zero (0 K, −273 °C) is where an ideal gas would have zero pressure and its molecules minimum kinetic energy. Brownian motion of smoke particles is evidence for fast, randomly moving molecules.

    AQA data sheet values: R = 8.31 J mol−1 K−1, k = 1.38 ×10−23 J K−1, NA = 6.02 ×1023 mol−1. 1 cm³ = 10−6 m³.

    Calculated answers within 2% are marked correct (0.5% for r.m.s. speeds from a list, 1% for factors). Readings from a graph count within 3%, and absolute zero from your own extrapolated line within 10 °C.

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