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Difficulty: EasyLatent Heat and Changes of State

A sample of ice with a mass of 0.20 kg0.20\text{ kg} at 0∘C0^\circ\text{C} absorbs 67,200 J67,200\text{ J} of thermal energy to melt completely into water at 0∘C0^\circ\text{C}. What is the specific latent heat of fusion of ice in J kg−1\text{J kg}^{-1}?

Answer: 336000 J kg^-1

Answer

The specific latent heat of fusion of ice is 336,000 J kg−1336,000\text{ J kg}^{-1}.
For a change of state from solid to liquid at constant temperature, the thermal energy transferred is related to mass by Q=mLfQ = m L_f. Dividing the absorbed energy (67,200 J67,200\text{ J}) by the mass (0.20 kg0.20\text{ kg}) yields the specific latent heat of fusion, 336,000 J kg−1336,000\text{ J kg}^{-1}.

Step-by-Step Solution

1
Identify the given values from the problem statement
Heat energy Q=67,200 JQ = 67,200\text{ J}, Mass m=0.20 kgm = 0.20\text{ kg}
These parameters are required to calculate the specific latent heat.
2
Apply the energy formula for phase transition at constant temperature
Q=mLfQ = m L_f
During melting, temperature remains constant at 0∘C0^\circ\text{C}, so heat absorbed depends only on mass and specific latent heat of fusion.
3
Solve for the specific latent heat of fusion LfL_f
Lf=Qm=67,2000.20=336,000 J kg−1L_f = \frac{Q}{m} = \frac{67,200}{0.20} = 336,000\text{ J kg}^{-1}
Dividing total energy by mass gives heat required per kilogram.

Key Concept

Specific Latent Heat of Fusion
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Topics

Latent Heat and Changes of State

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