A-Level Physics May/June 2024 Q2(b)(ii): Determine the number N of molecules of the gas in Y. Explain your reasoning.

1 answer

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  Reasoning

  Since the two containers are in thermal equilibrium, the temperature of the gas in container Y is the same as the temperature of the gas in container X. Therefore, the temperature of gas Y is $T = 507$ K.

  Calculation

  The ideal gas equation in terms of the number of molecules $N$ is: $pV = NkT$

  Rearranging for $N$ and substituting the values for gas Y: $N = \frac{pV}{kT}$

  $N = \frac{(2.90 \times 10^5) \times (0.0430)}{(1.38 \times 10^{-23}) \times (507)}$

  $N = 1.781... \times 10^{24}$

  $N \approx 1.78 \times 10^{24}$

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  How the marks are awarded

  • B1 — Explaining that thermal equilibrium means the temperatures of the gases in X and Y are equal, thus justifying the use of T = 507 K for gas Y.
  • C1 — Correctly stating the ideal gas equation in terms of the number of molecules, N, and the Boltzmann constant, k: pV = NkT.
  • A1 — Correctly substituting all values for gas Y into the rearranged equation and calculating the final answer for N to an appropriate number of significant figures.

  Common mistakes

  • Using the molar gas constant R (in pV = nRT) instead of the Boltzmann constant k, which requires an extra conversion step that is often forgotten or done incorrectly.
  • Forgetting to explain the reasoning for the temperature, thereby losing the first mark. The question explicitly asks for an explanation.
  • Using the pressure or volume values for container X instead of container Y.
  • Making a calculator error with the powers of 10, leading to an answer with an incorrect order of magnitude.

  Examiner tip: Always explicitly state the physical principle (e.g., thermal equilibrium) that justifies the value you are using in a calculation, especially when the question asks you to 'explain'.

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