A student places 0.050 kg of ice at 0 °C into a well-insulated container. She supplies energy at a steady rate of 200 W. The graph shows the temperature ris...
Question 1 Report
A student places 0.050 kg of ice at 0 °C into a well-insulated container. She supplies energy at a steady rate of 200 W. The graph shows the temperature rising from 0 °C after all the ice has melted.
The flat section from 0 to t₁ lasts 83.5 s. What is the specific latent heat of fusion of ice, based on these data?
Answer Details
During the flat section from 0 to \( t_1 \), the ice is melting at a constant temperature of 0 degrees C. All the energy supplied by the heater goes into breaking the bonds between water molecules in the solid lattice, not into raising the temperature. This energy is the latent heat of fusion.
The energy supplied during this time is:
\[ E = Pt = 200 \times 83.5 = 16\,700 \text{ J} \]
The specific latent heat of fusion is defined as the energy required per kilogram to change a substance from solid to liquid at constant temperature:
\[ L_f = \frac{E}{m} = \frac{16\,700}{0.050} = 334\,000 \text{ J/kg} = 3.34 \times 10^5 \text{ J/kg} \]
If you accidentally divide by the mass in grams (50) instead of kilograms (0.050), you would get 334 J/kg, which is far too small. If you forget to multiply by time and just use the power (200 J), you would get 4000 J/kg. The key steps are: calculate total energy first (power multiplied by time), then divide by the mass in kilograms.
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