A cube of aluminum 24.0 cm on each side is cooled from 128 °C to 20 °C. If the energy removed from the aluminum cube were added to a copper cube of the same size at 30 °C, what would be the final temperature of the copper cube?(ρAl = 2700 kg/m³; ρcopper = 8890 kg/m³)
volume Al or Cu cube = 24 x 24 x 24 = ?cc.
mass Al = volume x density = ?
mass Cu = volume x density = ?
Look up specific heat Al
Look up specific heat Cu
Energy removed from Al + energy added to Cu = 0
[mass Al x specific heat Al x (Tfinal-Tinitial)] + [mass Cu x specific heat Cu x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal Cu.
To find the final temperature of the copper cube, we can use the principle of conservation of energy.
The energy removed from the aluminum cube can be calculated using the formula:
Q = mcΔT
Where:
Q is the heat energy removed
m is the mass of the aluminum cube
c is the specific heat capacity of aluminum
ΔT is the change in temperature of the aluminum cube
The mass of the aluminum cube can be calculated using the formula:
m = ρV
Where:
ρ is the density of aluminum
V is the volume of the cube
Substituting the given values, we have:
ρAl = 2700 kg/m³
V = (24 cm)^3 = (0.24 m)^3 = 0.013824 m³
So, the mass of the aluminum cube is:
m = 2700 kg/m³ * 0.013824 m³ = 37.3488 kg
Now, let's calculate the energy removed from the aluminum cube using the specific heat capacity of aluminum:
c = 900 J/kg°C (approximate value for aluminum)
ΔT = (128 °C - 20 °C) = 108 °C
Q = mcΔT
Q = 37.3488 kg * 900 J/kg°C * 108 °C = 363,399.168 J
Now, we can add this energy to the copper cube and calculate its final temperature using the formula:
Q = mcΔT
Given that the copper cube is at 30 °C:
ΔT = Tf - 30 °C
Where Tf is the final temperature of the copper cube.
If we assume that the specific heat capacity and density of copper are the same as those of aluminum (which is not exactly true but gives a rough estimate), then we have:
m = ρV (using the same volume as the aluminum cube)
m = 2700 kg/m³ * 0.013824 m³ = 37.3488 kg
Q = mcΔT
363,399.168 J = 37.3488 kg * 900 J/kg°C * (Tf - 30 °C)
Simplifying the equation:
Tf - 30 °C = (363,399.168 J) / (37.3488 kg * 900 J/kg°C)
Tf - 30 °C = 13.965 °C
Tf = 13.965 °C + 30 °C = 43.965 °C
Therefore, the final temperature of the copper cube would be approximately 43.965 °C.