A-LevelPhysicsThermodynamics9702/42 · Oct/Nov 2020 · Q210 Marks

The atoms of an ideal gas occupy a container of volume 2.30 x 10⁻³m³ at pressure 2.60 x 10⁵ Pa and temperature 180K, as illustrated in [Figure 2.1]. The gas is heated at constant pressure so that its volume becomes 3.80 × 10⁻³m³ at a temperature T. For the fixed mass of gas, calculate:

(a)State what is meant by the internal energy of a system.[2]
(b)(i)the amount of substance, in mol[2]
(b)(ii)the temperature T, in K.[2]
(c)(i)Determine the work done on the gas during this change. Explain your working.[3]
(c)(ii)Determine the change ∆U in internal energy of the gas.[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] sum of potential energy and kinetic energy (of particles)
[B1] (total) energy of random motion of particles
[C1] pV = nRT
[A1] 2.60 x 10⁵ x 2.30 × 10⁻³ = n x 8.31 × 180, n = 0.400 mol
[C1] (2.30 × 10⁻³) / 180 = (3.80 × 10⁻³) / T OR 2.60 x 10⁵ x 3.80 × 10⁻³ = 0.400 × 8.31 × T
[A1] T = 297 K
[C1] ΔW = pΔV
[A1] = 2.60 × 10⁵ × (2.30 – 3.80) × 10⁻³, = (-)390 J
[B1] negative because work is done by gas / negative because work is done against atmospheric pressure / negative because volume of gas increases
[A1] ΔU = (980 – 390) = 590 J

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