Find the quantity of heat needed to melt 0.5 kg of ice at 0°C (lambda = 3.4e5 J/kg) — Physics problems | PhysLabo
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Heat needed to melt ice

Easy 10 grade Molecular Physics and Thermodynamics / Internal Energy. Heat
Problem statement

Find the quantity of heat needed to melt ice of mass $m = 0.5$ kg at a temperature of $0°$C. The latent heat of fusion of ice is $\lambda = 3.4 \cdot 10^5$ J/kg.

Given
  • $m = 0.5$ kg
  • $\lambda = 3.4 \cdot 10^5$ J/kg
  • $t = 0°$C
  • $Q = ?$
Hints
Hint 1 / 2
During melting the temperature does not change — use $Q = \lambda m$ rather than $cm\Delta t$.
Hint 2 / 2
$\lambda$ is already given in J/kg, so the answer comes out in joules straight away.
Solution

During melting the temperature of the substance does not change, so the heat is found from the latent heat of fusion:

$$Q = \lambda m = 3.4 \cdot 10^{5} \cdot 0.5 = 170\,000 \text{ J} = 170 \text{ kJ}$$

Answer

$Q = 170$ kJ (170 000 J)

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