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1 markThe Kinetic Theory of Gases

CAPE Physics Unit 1 · 2001 · Paper 2 · Question 8(b)(iii)

According to the kinetic theory of gases, the pressure, P, of an ideal gas is related to the mean-square-speed <c²> of its molecules by P = (1/3)(Nm/V)<c²>, where V is the volume, N is the number of molecules, and m is the mass of a molecule.

Hence, show that the average kinetic energy, Eₖ, of a molecule of an ideal gas can be written as Eₖ = (3/2)nRT, where the symbols have their usual meaning.

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Other parts of this question

  1. 8(a)(i)List TWO factors which would affect the rate of evaporation of a liquid.[4 marks]
  2. 8(a)(ii)Explain in terms of the kinetic theory why each of these factors affects the rate of evaporation.[1 mark]
  3. 8(b)(i)State THREE assumptions of the kinetic theory of gases which are used in the derivation of the expression above.[9 marks]
  4. 8(b)(ii)Write down the equation of state for an ideal gas in terms of its thermodynamic temperature T, stating what each symbol represents.[1 mark]
  5. 8(c)(i)Calculate the number of moles of helium in the container.[5 marks]
  6. 8(c)(ii)Calculate the number of helium atoms in the container.[1 mark]
  7. 8(c)(iii)Calculate the average kinetic energy, Eₖ, of an atom of helium in the container.[1 mark]
  8. 8(d)Calculate the final pressure of the gas.[2 marks]

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