The melting point of a solid is 90.0ºC. What is the heat required to change 2.5 kg of this solid at 30.0ºC to a liquid? The specific heat of the solid is 390 J/kg K and its heat of fusion is 4000 J/kg.
The melting point of a solid is 90°C. What is the heat required to change 2.5 kg of this solid at 30°C to a liquid?
The specific heat of the solid is (390 J/(kg.K)) and its heat of fusion is (4000 J/kg).
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To find the heat required to change the solid to a liquid, we need to first determine the heat required to raise the temperature of the solid from 30.0ºC to its melting point, and then add the heat of fusion to account for the phase change.
1. Calculate the heat to raise the temperature of the solid from 30.0ºC to its melting point:
Heat = mass × specific heat × temperature change
The mass is given as 2.5 kg, the specific heat is 390 J/kg K, and the temperature change is the difference between the melting point (90.0ºC) and the initial temperature (30.0ºC):
Heat = 2.5 kg × 390 J/kg K × (90.0ºC - 30.0ºC)
2. Calculate the heat of fusion:
Heat of fusion is given as 4000 J/kg.
3. Add the two heats together to get the total heat required:
Total Heat = Heat to raise temperature + Heat of fusion
Using these steps, we can now calculate the total heat required.
first the 60 degree rise from 30 to 90
390 J/kg deg * 2.5 kg * 60 deg = 58,500 Joules
now the melt
2.5 kg * 4,000 J/kg = 10,000 Joules
sum = 68,500 Joules