How much heat, in kilojoules, is evolved when a 3.70 kg sample of molten Cu freezes?
The normal boiling point is 1357 K, and heat of fusion is 13.05 KJ/mol.
2.) How much heat must be absorbed at 1357 K to melt a bar of copper (80 * 10 * 12 cm) assume d = 8.93 g/cm^3.
Andrew, I think I answered #1 earlier.
#2.
First calculate the volume of a bar of Cu that is 80 cm x 10 cm x 12 cm.
Volume = Length x width x depth. in cubic centimeters.
mass = density x volume. You have the density and you know the volume, you can calculate mass.
heat to melt = mass x heat of fusion.
Since the heat of fusion is listed in J/mole, you must change the mass of copper to moles from grams. moles = grams/molar mass.
To find the heat evolved when a sample of molten Cu freezes, we need to calculate the heat of fusion for the given mass of copper. The heat of fusion (ΔHfus) is the amount of energy required to change a substance from a solid to a liquid state at a constant temperature.
1) First, convert the given mass of copper from kilograms to grams:
Mass = 3.70 kg = 3.70 * 1000 g = 3700 g
2) Use the molar mass of copper (63.55 g/mol) to determine the number of moles:
Moles = Mass / Molar mass
Moles = 3700 g / 63.55 g/mol ≈ 58.16 mol
3) Calculate the heat evolved by multiplying the number of moles by the heat of fusion:
Heat evolved = Moles * Heat of fusion
Heat evolved = 58.16 mol * 13.05 kJ/mol = 758.59 kJ
Therefore, when a 3.70 kg sample of molten Cu freezes, approximately 758.59 kilojoules of heat is evolved.
Now let's move on to the second question:
To find the heat absorbed when melting a bar of copper, we can use the formula:
Heat absorbed = Mass * Specific heat capacity * Temperature change
Specific heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius or one Kelvin per unit mass.
1) Determine the mass of the copper bar using the given dimensions and density:
Volume = Length * Width * Height
Volume = 80 cm * 10 cm * 12 cm = 9600 cm^3
Convert the volume to cubic meters:
Volume = 9600 cm^3 * (0.01 m / 1 cm)^3 = 0.96 m^3
Mass = Volume * Density
Mass = 0.96 m^3 * 8.93 g/cm^3 = 8568.48 g
2) Convert the mass from grams to kilograms:
Mass = 8568.48 g * (1 kg / 1000 g) = 8.57 kg
3) Use the specific heat capacity of copper (0.39 kJ/kg·K) and the temperature change (ΔT) to calculate the heat absorbed:
Temperature change = Normal boiling point - Melting point
ΔT = 1357 K - 0 K = 1357 K
Heat absorbed = Mass * Specific heat capacity * Temperature change
Heat absorbed = 8.57 kg * 0.39 kJ/kg·K * 1357 K ≈ 4521.75 kJ
Therefore, to melt the bar of copper, approximately 4521.75 kilojoules of heat must be absorbed at 1357 K.