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Difficulty: EasyLatent Heat and Changes of State

Calculate the thermal energy, in joules, required to completely melt 0.50 kg0.50\text{ kg} of ice at its melting point of 0∘C0^\circ\text{C}. (Take the specific latent heat of fusion of ice as 3.36×105 J kg−13.36 \times 10^5\text{ J kg}^{-1}).

Answer: 168000 J

Answer

The total heat required to completely melt the ice is 168,000 J168,000\text{ J}.
During a state change from solid to liquid at constant temperature, the thermal energy absorbed is given directly by Q=mLfQ = m L_f. Multiplying mass (0.50 kg0.50\text{ kg}) by specific latent heat (3.36×105 J kg−13.36 \times 10^5\text{ J kg}^{-1}) gives 168,000 J168,000\text{ J}.

Step-by-Step Solution

1
Identify the given values and formula
Mass m=0.50 kgm = 0.50\text{ kg}, Specific latent heat of fusion Lf=3.36×105 J kg−1L_f = 3.36 \times 10^5\text{ J kg}^{-1}, Formula: Q=mLfQ = m L_f
Since the phase change occurs at constant temperature (0∘C0^\circ\text{C}), sensible heat calculation (mcΔTmc\Delta T) is zero and only latent heat is needed.
2
Substitute values into the formula and calculate
Q=0.50 kg×3.36×105 J kg−1=168,000 JQ = 0.50\text{ kg} \times 3.36 \times 10^5\text{ J kg}^{-1} = 168,000\text{ J}
Direct multiplication of mass and specific latent heat yields the energy required in Joules.

Key Concept

Specific Latent Heat of Fusion
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Topics

Latent Heat and Changes of State

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