How much energy is needed to heat and melt 3.0 kg of copper initially at 83°C?
Be mindful of significant figure rules for both multiplication and addition
melting point of copper = 1083.0 °C
heat capacity of copper = .39 kJ/kg-K
heat of fusion of copper = 207 kJ/kg
so to warm it up
Qin = .39 kJ/kgK(1083-83)K(3kg) = 1170 kJ
then to melt it
Qin = 207kJ/kg (3 kg) = 621 kJ
total Qin = 1791 kJ or 179,100 J
To determine the amount of energy needed to heat and melt 3.0 kg of copper initially at 83°C, we'll need to consider two separate processes: heating the copper and then melting it.
First, let's calculate the energy required to heat the copper from its initial temperature to its melting point. The specific heat capacity of copper is 0.39 J/g°C.
Step 1: Convert the mass from kilograms to grams:
Mass of copper = 3.0 kg = 3000 g
Step 2: Calculate the temperature change:
Temperature change = Final temperature - Initial temperature
Temperature change = (melting point of copper) - 83°C = (1083°C) - 83°C = 1000°C
Step 3: Calculate the energy required to heat the copper:
Energy = mass × specific heat capacity × temperature change
Energy = 3000 g × 0.39 J/g°C × 1000°C = 1,170,000 J
So, the energy required to heat the copper from 83°C to its melting point is 1,170,000 J.
Next, let's calculate the energy required to melt the copper. The heat of fusion for copper is 205 J/g.
Step 4: Calculate the energy required to melt the copper:
Energy = mass × heat of fusion
Energy = 3000 g × 205 J/g = 615,000 J
Therefore, the energy required to heat and melt 3.0 kg of copper initially at 83°C is the sum of the energies calculated in Step 3 and Step 4:
Total Energy = Energy required to heat + Energy required to melt
Total Energy = 1,170,000 J + 615,000 J = 1,785,000 J
So, the total energy needed is 1,785,000 J (rounded to the appropriate significant figures based on the significant figure rules).
To calculate the energy needed to heat and melt copper, we need to consider two processes: heating the copper to its melting point and then melting it.
1. Heating the copper:
The specific heat capacity of copper is 0.39 J/g°C.
To convert the mass of copper from kg to grams, we multiply by 1000:
3.0 kg x 1000 g/kg = 3000 g.
To calculate the change in temperature, we subtract the initial temperature (83°C) from the melting point of copper (1085°C):
1085°C - 83°C = 1002°C.
Next, we calculate the energy required to heat the copper using the formula:
Energy = mass x specific heat capacity x change in temperature.
Energy = 3000 g x 0.39 J/g°C x 1002°C.
Energy = 1,173,180 J.
2. Melting the copper:
The latent heat of fusion for copper is 205 J/g.
To calculate the energy required to melt the copper, we multiply the mass of copper by the latent heat of fusion:
Energy = mass x latent heat of fusion.
Energy = 3000 g x 205 J/g.
Energy = 615,000 J.
Therefore, the total energy needed to heat and melt 3.0 kg of copper initially at 83°C is the sum of the energy required for heating and melting:
Total energy = 1,173,180 J + 615,000 J.
Total energy = 1,788,180 J.