Heat capacity, specific heat, the principle of mixtures and latent heat.
Heat is energy transferred because of a temperature difference. Heat capacity C = Q/ΔT (J/K). Specific heat capacity c = Q/(m ΔT) (J/kg K), so Q = m c ΔT. Water has c = 4200 J/kg K, which is why it heats up and cools down slowly.
How much heat warms 2 kg of water by 10 °C?
Q = 2 × 4200 × 10 = 84000 J.
An aluminium block of 0.5 kg (c = 900 J/kg K) is heated from 20 °C to 80 °C. Heat needed and its heat capacity?
Q = 0.5 × 900 × 60 = 27000 J. C = m c = 0.5 × 900 = 450 J/K.
If no heat is lost to the surroundings: heat lost by the hot body = heat gained by the cold body.
200 g of water at 80 °C is mixed with 300 g of water at 30 °C. Final temperature?
Let T be final. 200 × (80 − T) = 300 × (T − 30) (c cancels). 16000 − 200T = 300T − 9000, so 500T = 25000 and T = 50 °C.
Latent heat is the heat absorbed or released during a change of state at constant temperature. Specific latent heat of fusion of ice = 336 J/g (3.36 × 10⁵ J/kg). Specific latent heat of vaporisation of water = 2260 J/g (2.26 × 10⁶ J/kg). Q = m L.
Heat to melt 50 g of ice at 0 °C into water at 0 °C?
Q = 50 × 336 = 16800 J.
Heat released when 10 g of steam at 100 °C becomes water at 100 °C?
Q = 10 × 2260 = 22600 J.
Total heat to turn 100 g of ice at −10 °C into steam at 100 °C (c of ice = 2100 J/kg K)?
Ice to 0 °C: 2100 J. Melting: 33600 J. Water 0 to 100 °C: 42000 J. Boiling: 226000 J. Total = 303700 J = 303.7 kJ. Boiling takes most of it.
1. Define specific heat capacity and give its SI unit.
2. Why is water used as a coolant in car radiators?
3. Heat needed to raise 500 g of water by 20 °C?
4. State the principle of calorimetry.
5. Why does the temperature stay constant while ice melts?
6. Heat to melt 2 kg of ice at 0 °C?
7. Why do burns from steam hurt more than from boiling water at the same temperature?
8. Heat capacity of a body is 450 J/K. Heat needed to raise it by 30 K?
9. Name the unit of specific latent heat.
10. Equal masses of water and iron absorb equal heat. Which gets hotter? (c water 4200, c iron 450)