Energy is transferred to 15.5kg of ice at 0 ∘ C until it is all melted, but without any temperature change. If the latent heat of fusion of water is 334000J/kg, how much energy is needed to melt the ice?Give your answer in MJ. Ensure your answer is quoted to the correct number of significant figures.
Question
Energy is transferred to 15.5kg of ice at 0 ∘ C until it is all melted, but without any temperature change. If the latent heat of fusion of water is 334000J/kg, how much energy is needed to melt the ice?Give your answer in MJ. Ensure your answer is quoted to the correct number of significant figures.
Solution
The energy required to melt the ice can be calculated using the formula:
Q = m * L_f
where:
- Q is the heat energy required,
- m is the mass of the substance, and
- L_f is the latent heat of fusion.
Substituting the given values:
Q = 15.5 kg * 334000 J/kg = 5177000 J
To convert this to megajoules (MJ), divide by 1,000,000:
Q = 5177000 J / 1,000,000 = 5.177 MJ
So, 5.18 MJ of energy is needed to melt the ice, when rounded to the correct number of significant figures.
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