How much energy is needed to heat and melt 3.0 kg of copper initially at 83°C
Q = mc ΔT + mL
You'll need to look up specific heat and latent heat of fusion for copper.
And you need to know its melting point.
To determine the energy required to heat and melt a substance, we need to consider the heat required for two processes: heating the substance to its melting point and then melting it.
Step 1: Calculate the energy required to heat the copper from 83°C to its melting point.
The specific heat capacity of copper is 0.385 J/g°C, which means it takes 0.385 Joules of energy to raise the temperature of 1 gram of copper by 1 degree Celsius.
First, we need to determine the temperature change needed to reach the melting point of copper. Copper has a melting point of 1084°C. Therefore, the temperature change required is:
ΔT = (melting point - initial temperature)
ΔT = (1084 - 83)
ΔT = 1001°C
Next, we need to convert the mass of copper from kilograms to grams:
Mass = 3.0 kg * 1000 g/kg = 3000 g
Now, we can calculate the energy required to heat the copper using the formula:
Energy = mass * specific heat capacity * temperature change
Energy = 3000 g * 0.385 J/g°C * 1001°C = 1153650 J
Step 2: Calculate the energy required to melt the copper.
The heat required to melt a substance is known as the heat of fusion. For copper, this value is approximately 205 J/g.
Energy = mass * heat of fusion
Energy = 3000 g * 205 J/g = 615000 J
Step 3: Calculate the total energy required.
To find the total energy required, we add the energy calculated in Step 1 and Step 2:
Total Energy = Energy to heat + Energy to melt
Total Energy = 1153650 J + 615000 J = 1768650 J
Therefore, the total energy required to heat and melt 3.0 kg of copper initially at 83°C is 1,768,650 J.
To calculate the energy required to heat and melt a substance, we need to consider the specific heat capacity and the heat of fusion of the material.
1. Calculate the energy required to raise the temperature of the copper from 83°C to its melting point.
- First, we need to determine the temperature change, which is the final temperature minus the initial temperature:
ΔT = T final - T initial
ΔT = 1084°C - 83°C = 1001°C (Celsius and Kelvin have the same unit size)
- The specific heat capacity of copper is approximately 0.385 J/g°C, meaning it takes 0.385 Joules of energy to raise the temperature of 1 gram of copper by 1 degree Celsius.
- To convert the mass from kilograms to grams, multiply by 1000:
mass = 3.0 kg × 1000 = 3000 g
- Now we can calculate the energy required using the formula:
Energy = mass × specific heat capacity × temperature change
Energy = 3000 g × 0.385 J/g°C × 1001°C
2. Calculate the energy required to melt the copper.
- The heat of fusion for copper is 205 J/g, which means it takes 205 Joules of energy to melt 1 gram of copper without a change in temperature.
- To find the total energy required to melt the copper, multiply the mass by the heat of fusion:
Energy = mass × heat of fusion
Energy = 3000 g × 205 J/g
3. Finally, add the two energies obtained from step 1 and step 2 to get the total energy required:
Total Energy = Energy to raise temperature + Energy to melt
Total Energy = (3000 g × 0.385 J/g°C × 1001°C) + (3000 g × 205 J/g)
By plugging in the values and performing the calculations, you can find the total energy required to heat and melt 3.0 kg of copper initially at 83°C.