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Difficulty: MediumLatent Heat and Changes of State

A solid sample of mass 0.25 kg0.25\text{ kg} at its melting point is completely melted by an electric heater rated at 700 W700\text{ W}. If the specific latent heat of fusion of the substance is 3.36×105 J kg−13.36 \times 10^5\text{ J kg}^{-1}, what is the time taken to melt the sample completely at a constant temperature?

  1. 120 s120\text{ s}Answer
  2. B
    420 s420\text{ s}
  3. C
    210 s210\text{ s}
  4. D
    1200 s1200\text{ s}

Answer

The time taken to completely melt the block is 120 s120\text{ s}.
The thermal energy required to melt a substance at its melting point depends solely on its mass and specific latent heat of fusion (Q=mLfQ = m L_f). Calculating Q=0.25 kg×3.36×105 J kg−1=84,000 JQ = 0.25\text{ kg} \times 3.36 \times 10^5\text{ J kg}^{-1} = 84,000\text{ J} and dividing by heater power 700 W700\text{ W} yields exactly 120 s120\text{ s}.

Step-by-Step Solution

1
Calculate the total thermal energy required for phase change.
Q=mLf=0.25 kg×3.36×105 J kg−1=84,000 JQ = m L_f = 0.25\text{ kg} \times 3.36 \times 10^5\text{ J kg}^{-1} = 84,000\text{ J}
During a change of state at constant temperature, thermal energy is given by Q=mLfQ = m L_f.
2
Relate energy supplied by the electrical heater to time using power formula.
Q=P×t  ⟹  t=QPQ = P \times t \implies t = \frac{Q}{P}
Power is the rate of energy transfer per unit time (P=QtP = \frac{Q}{t}).
3
Substitute the energy and power values to solve for time tt.
t=84,000 J700 W=120 st = \frac{84,000\text{ J}}{700\text{ W}} = 120\text{ s}
Dividing total energy required by power gives time in seconds.

Key Concept

Latent Heat of Fusion and Electrical Thermal Energy
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Topics

Latent Heat and Changes of State

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