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A2 Daily A Level Physics question

2026-03-02 OCR A Specific heat capacity problems OCR-A 5.1.2 Thermal physics — specific heat capacity; energy, mass and temperature change OCR-A Practical skills — assumptions, energy losses, and proportional reasoning in calorimetry

Two identical 100 W immersion heaters warm 0.50 kg samples of liquids X and Y in identical insulated beakers from the same initial temperature. After 120 s, X has warmed by 8.0 °C and Y by 4.0 °C. The heaters are then switched off, and at that instant each beaker is losing heat to the room at about 10 W (same for both). Which statement must be true about their specific heat capacities and the initial cooling rates just after switch-off?

  1. A X and Y have the same specific heat capacity, and they cool at the same initial rate because the heat loss is the same.
  2. B X has twice the specific heat capacity of Y, and Y’s temperature falls about twice as fast initially.
  3. C Y has twice the specific heat capacity of X, and they cool at the same initial rate because the heat loss is the same.
  4. D Y has twice the specific heat capacity of X, and X’s temperature falls about twice as fast initially. (correct)

Answer

The correct answer is D.

Correct: D — Y has twice the specific heat capacity of X, and X’s temperature falls about twice as fast initially. Same energy is delivered to equal masses, so the larger temperature rise means the smaller specific heat capacity: 8 °C vs 4 °C gives c_Y = 2 c_X. With equal heat loss (about 10 W) just after switch-off, the temperature drop per second is inversely proportional to mc, so the smaller c (X) cools faster; numerically about 0.0067 K s⁻1 for X and 0.0033 K s⁻1 for Y. A is wrong because equal power loss does not mean equal temperature-change rate; for the same watts out, a larger c gives a smaller change per second. B is wrong because it inverts the ratio (X would then have warmed less, not more) and also picks the wrong beaker to cool faster. C is wrong because, although c_Y = 2 c_X is correct, equal heat loss does not produce equal cooling rates; in the limiting case of extremely large c the temperature would barely change at all. D is correct for both the capacity ratio and the relative initial cooling rates.

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