Answers · Specific heat capacity
Specific heat capacity — final check key
Check meaning, not exact wording. These are teaching points, not official Cambridge marks.
1. HK1 · Final check
Model answer. (a) At 9.0 kJ the temperature is 60 °C, so the rise is 60 °C − 20 °C = 40 °C. (b) ΔE = 9.0 kJ = 9000 J. c = ΔE / (mΔθ) = 9000 J ÷ (0.50 kg × 40 °C) = 9000 ÷ 20 = 450 J/(kg °C). (c) 450 J/(kg °C) matches iron. (d) As the temperature rises, the internal energy of the block increases. Its particles stay in their fixed positions but vibrate faster, so the average kinetic energy of all the particles increases. (e) Without the jacket the line would start with about the same slope but bend, getting less steep as the block warmed, and end lower. The hotter the block gets compared with the room, the faster energy escapes from it to the air, so less of each kilojoule stays in the block.
A full answer includes
- (a) 60 °C − 20 °C = 40 °C.
- (b) c = 9000 J ÷ (0.50 kg × 40 °C) = 450 J/(kg °C).
- (c) Iron.
- (d) The internal energy increases; the particles vibrate faster, so their average kinetic energy increases.
- (e) The line would bend and become less steep as the block got hotter, because energy escapes to the air faster the hotter the block is, so less of each kilojoule stays in it.
Also accept
- (a) 40 °C; (b) 450 J/(kg °C); (c) iron; (d) internal energy increases, particles vibrate faster, higher average kinetic energy; (e) bends and becomes less steep, because energy escapes faster when the block is hotter.
Watch for
- “(b) c = 9000 ÷ (0.50 × 60) = 300 J/(kg °C).” — 60 °C is the final temperature. Use the rise from 20 °C: 40 °C.
- “(e) Without the jacket the line would be steeper, because the block is open to the air.” — Without a jacket more energy escapes to the air, so less stays in the block and its temperature rises less: the line is less steep, and it bends.
2. HK2 · Final check
Model answer. (a) 1 cm³ of water has a mass of 1 g, so 200 cm³ has a mass of 200 g = 0.200 kg. (b) ΔE = 8.8 kJ = 8800 J. Δθ = 28.0 °C − 18.0 °C = 10.0 °C. c = ΔE / (mΔθ) = 8800 J ÷ (0.200 kg × 10.0 °C) = 4400 J/(kg °C). (c) The joulemeter counted all 8800 J, but some of it escaped to the air and some warmed the cup, the heater and the thermometer. The water’s rise in temperature was therefore smaller than it would have been, and a smaller Δθ gives a bigger c. (d) Weigh the block on a balance instead of measuring a volume. Put the heater in one hole and the thermometer in the other, with a drop of oil in the thermometer’s hole, and wrap the block in an insulating jacket. There is nothing to stir. Then zero the joulemeter, heat, read the energy and the rise, and calculate c = ΔE / (mΔθ) as before. (e) Water has a very high specific heat capacity, so as it cools it gives out a lot of energy for each degree its temperature falls: about 4200 J for each kilogram and each degree. The same mass of a liquid with a lower specific heat capacity would give out less energy while cooling by the same amount, so the bed would not stay warm for as long.
A full answer includes
- (a) 200 cm³ = 200 g = 0.200 kg.
- (b) Δθ = 28.0 °C − 18.0 °C = 10.0 °C; c = 8800 J ÷ (0.200 kg × 10.0 °C) = 4400 J/(kg °C).
- (c) Some energy escaped to the air and some warmed the cup, the heater and the thermometer, so the rise was smaller than it should have been, giving a bigger c.
- (d) Weigh the block; put the heater and the thermometer in its holes (a drop of oil in the thermometer’s hole); wrap it in an insulating jacket; there is nothing to stir; the same readings and calculation.
- (e) Water’s high specific heat capacity: it gives out a lot of energy for each degree it cools, so it keeps a bed warm for longer.
Also accept
- (a) 0.200 kg; (b) 4400 J/(kg °C); (c) energy escaped and warmed the cup and the apparatus, so Δθ too small; (d) weigh the block, heater and thermometer in its holes, a jacket, no stirring; (e) high specific heat capacity, gives out a lot of energy as it cools.
Watch for
- “(b) c = 8800 ÷ (200 × 10.0) = 4.4 J/(kg °C).” — The mass must be in kilograms: 200 cm³ of water is 200 g = 0.200 kg.
- “(e) Water stays hot because it loses less energy to the air.” — Any liquid in the same bottle loses energy to the air in much the same way. Water gives out more energy for each degree it cools, because its specific heat capacity is high.