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Difficulty: MediumLatent Heat and Changes of State

A solid substance of mass 0.50 kg0.50\text{ kg} at its melting point is supplied with thermal energy by an electric heater operating at a constant rate of 150 W150\text{ W}. If it takes 4.0 minutes4.0\text{ minutes} for the solid to melt completely without any change in temperature, what is the specific latent heat of fusion of the substance?

  1. A
    1.8×104 J kg−11.8 \times 10^4\text{ J kg}^{-1}
  2. 7.2×104 J kg−17.2 \times 10^4\text{ J kg}^{-1}Answer
  3. C
    3.6×104 J kg−13.6 \times 10^4\text{ J kg}^{-1}
  4. D
    1.2×103 J kg−11.2 \times 10^3\text{ J kg}^{-1}

Answer

The specific latent heat of fusion of the substance is 7.2×104 J kg−17.2 \times 10^4\text{ J kg}^{-1}.
During a change of phase at constant temperature, the thermal energy supplied is used exclusively to weaken intermolecular bonds without increasing kinetic energy or temperature. The heat supplied is Q=P×t=150 W×240 s=36 000 JQ = P \times t = 150\text{ W} \times 240\text{ s} = 36\,000\text{ J}. Using Q=mLQ = mL, the specific latent heat L=Qm=36 000 J0.50 kg=7.2×104 J kg−1L = \frac{Q}{m} = \frac{36\,000\text{ J}}{0.50\text{ kg}} = 7.2 \times 10^4\text{ J kg}^{-1}.

Step-by-Step Solution

1
Convert the given heating duration into SI units (seconds).
t=4.0 minutes=4.0×60 s=240 st = 4.0\text{ minutes} = 4.0 \times 60\text{ s} = 240\text{ s}.
Standard calculation of thermal energy requires time to be in seconds when power is given in Watts.
2
Calculate the total thermal energy supplied by the heater.
Q=P×t=150 W×240 s=36 000 J=3.6×104 JQ = P \times t = 150\text{ W} \times 240\text{ s} = 36\,000\text{ J} = 3.6 \times 10^4\text{ J}.
Electrical energy supplied is completely converted into heat energy.
3
Apply the latent heat formula to find the specific latent heat of fusion.
L=Qm=36 000 J0.50 kg=72 000 J kg−1=7.2×104 J kg−1L = \frac{Q}{m} = \frac{36\,000\text{ J}}{0.50\text{ kg}} = 72\,000\text{ J kg}^{-1} = 7.2 \times 10^4\text{ J kg}^{-1}.
During a change of state at constant temperature, heat absorbed is given by Q=mLQ = mL.

Key Concept

Latent Heat of Fusion
Estimated Time:1m 30s
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Topics

Latent Heat and Changes of State

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