Parameters: Aluminum --- Density = 2700 kg/m^3 Specific Heat = 900 J/kgK Thermal

Question

Parameters:

Aluminum ---

Density = 2700 kg/m^3
Specific Heat = 900 J/kgK
Thermal Conductivity = 235 W/mK

Copper ---

Density = 8900 kg/m^3
Specific Heat = Unknown
Thermal Conductivity = 401 W/mK

For most solids at room temperature, the specific heat is determined by oscillations of the atom cores in the lattice (each node of which contributes 3kT of energy, by equipartition), as well as a contribution from the electrons (if it's a metal). At room temperature, the latter contribution is typically much smaller than the former, so we will ignore it here. In other words, you can resonably estimate the specific heat simply by counting the number of atoms. Use this fact to estimate the specific heat of copper (atomic mass = 63.6), given that the specific heat of aluminum (atomic mass = 27) is 900 J/kg K

Please show all work, thanks!

Explanation / Answer

Here, average energy = 3KT

                                     = (6.023 * 1023) * (3) * (1.38 * 10-23) * (293)

                                    = 7306.019 J

=>    specific heat of copper   =   (7306.019)/(0.0636 * 293)

                                                = 392 J/kg K

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