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Difficulty: MediumLatent Heat and Changes of State

An ice block of mass 0.15 kg0.15\text{ kg} at −10∘C-10^\circ\text{C} absorbs thermal energy until it turns completely into liquid water at 0∘C0^\circ\text{C}. Taking the specific heat capacity of ice as 2100 J kg−1 K−12100\text{ J kg}^{-1}\text{ K}^{-1} and the specific latent heat of fusion of ice as 3.36×105 J kg−13.36 \times 10^5\text{ J kg}^{-1}, what is the total thermal energy supplied in joules?

Answer: 53550 J

Answer

The total thermal energy supplied is 53,550 J.
To transform sub-zero ice into liquid water at its melting point, thermal energy is absorbed in two distinct stages: warming the ice from −10∘C-10^\circ\text{C} to 0∘C0^\circ\text{C} (Q1=0.15×2100×10=3150 JQ_1 = 0.15 \times 2100 \times 10 = 3150\text{ J}) and melting the ice completely at 0∘C0^\circ\text{C} (Q2=0.15×3.36×105=50400 JQ_2 = 0.15 \times 3.36 \times 10^5 = 50400\text{ J}). Adding these yields a total energy of 53550 J53550\text{ J}.

Step-by-Step Solution

1
Calculate the thermal energy required to warm the solid ice from −10∘C-10^\circ\text{C} to its melting point (0∘C0^\circ\text{C}).
Q1=3150 JQ_1 = 3150\text{ J}
Before the phase transition can begin, sensible heat must be supplied to raise the ice temperature using Q1=mciceΔTQ_1 = m c_{\text{ice}} \Delta T.
2
Calculate the thermal energy required to melt the ice at constant temperature (0∘C0^\circ\text{C}).
Q2=50400 JQ_2 = 50400\text{ J}
Phase transformation at constant temperature requires latent heat of fusion using Q2=mLfQ_2 = m L_f.
3
Sum the energy required for both stages to determine total energy.
Qtotal=53550 JQ_{\text{total}} = 53550\text{ J}
The total energy supplied is the sum of sensible warming heat (Q1Q_1) and latent melting heat (Q2Q_2).

Key Concept

Multi-step heat energy calculation involving sensible heat (mcΔTm c \Delta T) and latent heat of fusion (mLfm L_f).
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Topics

Latent Heat and Changes of State

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