A-LevelPhysicsIdeal gases9702/42 · Feb/Mar 2018 · Q210 Marks

A cylinder contains 5.12 mol of an ideal gas at pressure of 5.60 × 10⁵ Pa and volume 3.80 × 10⁴ cm³.

(a)Determine the temperature of the gas. temperature = .............................................................. K[2]
(b)(i)The average kinetic energy Ek of a molecule of the gas is given by the expression Ek = ³/₂ kT where k is the Boltzmann constant and T is the thermodynamic temperature. The gas is heated at constant pressure so that its temperature rises by 125 K. Use your answer in (a) to determine the new volume of the gas. volume = ........................................................... cm³[2]
(b)(ii)Calculate the increase in internal energy of the gas. Explain your working. increase in internal energy = ........................................................... J[3]
(c)(i)Use your answer in (b)(i) to determine the external work done during the expansion of the gas. work done = ........................................................... J[2]
(c)(ii)Calculate the total thermal energy required to heat the gas in (b). energy = .............................................................. J[1]

Mark scheme

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

[C1] pV = nRT
[A1] T = (5.60 × 10⁵ × 3.80 × 10⁻²)/(5.12 × 8.31)
[A1] T = 500 K
[C1] V/T is constant
[A1] V = (3.80 × 10⁴) × (500 + 125)/500
[A1] V = 4.75 × 10⁴ cm³
[B1] (for ideal gas,) change in internal energy is change in (total) kinetic energy (of molecules)
[C1] ΔU = 3/2 × 1.38 × 10⁻²³ x 125 x 5.12 × 6.02 × 10²³
[A1] = 7980 J
[C1] W = pΔV
[A1] = 5.60 × 10⁵ × (4.75 – 3.80) × 10⁻²
[A1] = 5320 J
[A1] total = 7980 + 5320
[A1] = 13300 J

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