A-Level Physics October/November 2024 Q2(b)(ii): The ratio mass of block Y / mass of block X is equal to 1.3. The metal in block Y has a…

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  By the principle of conservation of energy, assuming no heat is lost to the surroundings, the heat lost by the hotter block (X) is equal to the heat gained by the colder block (Y).

  Heat lost by X = Heat gained by Y $Q_{lost} = Q_{gained}$ $m_X c_X \Delta\theta_X = m_Y c_Y \Delta\theta_Y$

  From the previous part of the question, the temperature changes are: Change in temperature for block X, $\Delta\theta_X = 45$ K Change in temperature for block Y, $\Delta\theta_Y = 15$ K

  We are given the ratio of masses $m_Y / m_X = 1.3$, so $m_Y = 1.3 m_X$. We are also given $c_Y = 901\,\text{Jkg}^{-1}\text{K}^{-1}$.

  Substituting these values into the energy conservation equation: $m_X \times c_X \times 45 = (1.3 m_X) \times 901 \times 15$

  The mass of block X, $m_X$, cancels from both sides: $c_X \times 45 = 1.3 \times 901 \times 15$

  Rearranging to solve for $c_X$: $c_X = \frac{1.3 \times 901 \times 15}{45}$ $c_X = \frac{17569.5}{45}$ $c_X = 390.433... \,\text{Jkg}^{-1}\text{K}^{-1}$

  Rounding to an appropriate number of significant figures (2 s.f. due to '1.3'): $c_X = 390 \,\text{Jkg}^{-1}\text{K}^{-1}$

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  How the marks are awarded

  • C1 — Correctly identifying the temperature change for block X as 45 K (or °C) and for block Y as 15 K (or °C).
  • C1 — Correctly substituting all values into the energy balance equation, e.g., m * c * 45 = 1.3 * m * 901 * 15, showing the application of the mass ratio.
  • A1 — Calculating the final correct answer of 390 J kg⁻¹ K⁻¹.

  Common mistakes

  • Inverting the mass ratio, for example using m_X = 1.3 * m_Y, which leads to an incorrect answer.
  • Swapping the temperature changes between block X and block Y in the equation.
  • Making a calculation error when rearranging the equation, for example, multiplying by 45 instead of dividing.
  • Stating the final answer to an inappropriate number of significant figures, such as '390.43', which may lose the accuracy mark.

  Examiner tip: Always start thermal exchange problems by equating the heat lost by the hot object to the heat gained by the cold object, ensuring you correctly substitute all given ratios and values.

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