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.
450 kcal
430 kcal
280 kcal
130 kcal
ok, thank you. :)
To determine the energy needed to heat and melt copper, we need to consider two processes: heating the copper from 83°C to its melting point, and then melting the copper.
1. First, we calculate the energy required to heat the copper from 83°C to its melting point.
The specific heat capacity of copper is approximately 0.39 J/g°C. The formula for calculating the energy required to heat a substance is:
Q = m * c * ΔT
Where:
Q = energy
m = mass
c = specific heat capacity
ΔT = change in temperature
Converting the mass to grams: 3.0 kg = 3000 g
Calculating the energy required to heat the copper:
Q1 = (3000 g) * (0.39 J/g°C) * (Tf - Ti)
Q1 = 1170 * (Tf - 83)
2. Next, we calculate the energy required to melt the copper.
The heat of fusion for copper is approximately 205 J/g. The formula for calculating the energy required to melt a substance is:
Q = m * ΔHf
Where:
Q = energy
m = mass
ΔHf = change in enthalpy of fusion
Calculating the energy required to melt the copper:
Q2 = (3000 g) * (205 J/g)
Q2 = 615000 J
Now, we add the energies from heating and melting together to get the total energy required:
Total energy = Q1 + Q2
Total energy = 1170 * (Tf - 83) + 615000 J
Since we are given the answer choices in kilocalories (kcal), we need to convert the total energy to kcal:
Total energy = (1170 * (Tf - 83) + 615000 J) / 4184 J/kcal
Now we can substitute the given values for Tf:
a. Substituting Tf = 1084°C
Total energy = (1170 * (1084 - 83) + 615000) / 4184
Total energy ≈ 279.91 kcal
b. Substituting Tf = 1374°C
Total energy = (1170 * (1374 - 83) + 615000) / 4184
Total energy ≈ 449.36 kcal
c. Substituting Tf = 2535°C
Total energy = (1170 * (2535 - 83) + 615000) / 4184
Total energy ≈ 565.04 kcal
d. Substituting Tf = 331°C
Total energy = (1170 * (331 - 83) + 615000) / 4184
Total energy ≈ 129.69 kcal
Among the answer choices, the closest value to the calculated total energy is 130 kcal (answer d). Therefore, the answer is 130 kcal.
To calculate the total energy required to heat and melt a substance, we need to consider two separate processes:
1. Heating the substance from its initial temperature to its melting point
2. Melting the substance at its melting point
First, we need to determine the energy required to heat the 3.0 kg of copper from 83°C to its melting point.
The specific heat capacity of copper is 0.387 J/g°C (or 0.387 kcal/kg°C).
To convert 3.0 kg to grams:
3.0 kg = 3,000 g
The formula to calculate the energy required to heat a substance is:
Energy = mass × specific heat capacity × temperature change
Temperature change = final temperature - initial temperature
Temperature change = melting point of copper - initial temperature
The melting point of copper is approximately 1084°C.
Temperature change = 1084°C - 83°C
Temperature change = 1001°C
Now we can calculate the energy required to heat the copper:
Energy = 3,000 g × 0.387 kcal/kg°C × 1001°C
Energy = 1,161,000 kcal
Next, we need to determine the energy required to melt the copper at its melting point. The heat of fusion (also known as the enthalpy of fusion) for copper is approximately 13.1 kcal/kg.
Energy = mass × heat of fusion
Energy = 3,000 g × 13.1 kcal/kg
Energy = 39,300 kcal
Now, we can find the total energy required:
Total energy = energy required to heat + energy required to melt
Total energy = 1,161,000 kcal + 39,300 kcal
Total energy = 1,200,300 kcal
When considering significant figures, we need to adhere to the least precise measurement. In this case, the value 3.0 kg has two significant figures, so we should round the final answer to two significant figures:
Total energy = 1,200,000 kcal
Therefore, the correct answer is 1,200,000 kcal.
q1 = heat needed to raise T Cu from 83 C to it's melting point (you will look that up) is
q1 = mass Cu x specific heat Cu x (Tfinal-Tinitial) where Tf is the melting point and Ti is 83C.
q2 = heat needed to melt Cu at its melting point is
q2 = mass Cu x heat fusion
You will need to look up the heat fusion for Cu.
Then qtotal = q1 + q2
Post your work if you get stuck.