Calculate the total amount of heat energy required to melt 200 g of ice at 0°C to water at 100°C. (Specific latent heat of ice = 336 J g-1, specific heat capacity of water = 4.2 J g-1°C-1)
Topic: Latent heat and sensible heat
Answer
Given: 200 g of ice at 0 °C to be turned into water at 100 °C
L = 336 J g⁻¹, c_w = 4.2 J g⁻¹ °C⁻¹
The process happens in TWO stages.
Stage 1 — melting the ice at 0 °C (temperature does not change): Q₁ = m L = 200 × 336 = 67 200 J
Stage 2 — heating the water from 0 °C to 100 °C: Q₂ = m c Δθ = 200 × 4.2 × 100 = 84 000 J
Total heat energy required: Q = Q₁ + Q₂ = 67 200 + 84 000 = 151 200 J
Total heat required = 151 200 J (151.2 kJ)
Split the journey at every change of state and write a separate term for each leg. Here there are two: melt at 0 °C, then warm from 0 °C to 100 °C.
The melting stage uses mL with NO temperature term, because the temperature stays at 0 °C the whole time the ice is melting — the energy goes into breaking the bonds of the solid, not into raising the temperature. That is what latent heat means: "hidden" heat, absorbed with no thermometer reading to show for it.
Doing only the second stage gives 84 000 J and misses nearly half the energy. If the question had gone on to steam at 100 °C, a third term — the latent heat of vaporisation — would be needed as well.