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3 marksThe Kinetic Theory of Gases

CAPE Physics Unit 1 · 2013 · Paper 2 · Question 3(d)

1.12 moles of gas in a closed container at a temperature of 273 K exert a pressure of 1.01 × 10⁵ Nm⁻² on the walls of the container. Air is then extracted from the container so that the temperature is reduced to 223 K and the pressure reduced to 1.33 × 10⁴ N m⁻². Determine the number of moles in the container under these new conditions.

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  1. 3(a)Show that both sides of the relation PV = (1/3) N mc² have the same fundamental units.[2 marks]
  2. 3(b)Using the equation in (a) above, show that the mean kinetic energy of the molecules in 1 mole of an ideal monatomic gas is equal to (3/2) kT, where k is the…[3 marks]
  3. 3(c)Given that the root-mean-square (rms) speed of the molecules in a gas is inversely proportional to the square root of its molar mass, show that the ratio of…[2 marks]
  4. 3(e)Use the graph to determine the work done in this expansion.[3 marks]
  5. 3(f)If the expansion along AB had continued with no change in direction, what would be the volume of the gas at a pressure of 2 × 10⁵ Nm⁻²?[2 marks]

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