A block of solid gold is at its melting point of 1064 ∘ C. It has a specific latent heat of fusion of 63kJ/kg. If the block is completely melted by supplying 2.0kJ of thermal energy, what is its mass, assuming that there is no resulting temperature change?
Question
A block of solid gold is at its melting point of 1064 ∘ C. It has a specific latent heat of fusion of 63kJ/kg. If the block is completely melted by supplying 2.0kJ of thermal energy, what is its mass, assuming that there is no resulting temperature change?
Solution
The specific latent heat of fusion (L) is the amount of heat required to change 1 kg of a substance from the solid state to the liquid state without any change in temperature. It is given by the formula:
Q = mL
where: Q is the heat supplied, m is the mass of the substance, and L is the specific latent heat of fusion.
In this case, we are given: Q = 2.0 kJ = 2000 J (since 1 kJ = 1000 J), and L = 63 kJ/kg = 63000 J/kg.
We are asked to find the mass (m). We can rearrange the formula to solve for m:
m = Q / L
Substituting the given values:
m = 2000 J / 63000 J/kg = 0.0317 kg
So, the mass of the gold block is approximately 0.0317 kg.
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