A-LevelPhysicsIdeal gases9702/41 · May/June 2018 · Q38 Marks

3 (a) (i) State what is meant by the internal energy of a system. (ii) Explain why, for an ideal gas, the change in internal energy is directly proportional to the change in thermodynamic temperature of the gas. (b) A cylinder of volume 1.8 × 10⁴ cm³ contains helium gas at pressure 6.4 × 10⁸ Pa and temperature 25 °C. Helium gas may be considered to be an ideal gas consisting of single atoms. Calculate the number of helium atoms in the cylinder. number = ..............................................

(a)(i)State what is meant by the internal energy of a system.[2]
(a)(ii)Explain why, for an ideal gas, the change in internal energy is directly proportional to the change in thermodynamic temperature of the gas.[3]
(b)Calculate the number of helium atoms in the cylinder. number = ..............................................[3]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[B1] sum of potential and kinetic energies (of molecules/atoms/particles)
[B1] (energy of) molecules/atoms/particles in random motion
[B1] (in ideal gas) no intermolecular forces so no potential energy
[B1] internal energy is (solely) kinetic energy (of particles)
[B1] (mean) kinetic energy (of particles) proportional to (thermodynamic) temperature of gas
[C1] pV = NkT
[C1] 6.4 x 10⁸ x 1.8 x 10⁴ x 10⁻⁶ = N x 1.38 × 10⁻²³ × 298
[C1] OR pV=nRT and N = n × NA
[C1] OR 6.4 x 10⁸ x 1.8 × 10⁴ × 10⁻⁶ = n x 8.31 × 298
[C1] OR n = 46.5 (mol)
[C1] OR N = 46.5 × 6.02 × 10²³
[A1] N = 2.8 x 10²⁵

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