Answer:
The specific heat of copper is  [tex]C= 392 J/kg\cdot ^o K[/tex]
Explanation:
From the question we are told that
The amount of energy contributed by each oscillating lattice site  is  [tex]E =3 kT[/tex]
    The atomic mass of copper  is  [tex]M = 63.6 g/mol[/tex]
    The atomic mass of aluminum is  [tex]m_a = 27.0g/mol[/tex]
    The specific heat of aluminum is  [tex]c_a = 900 J/kg-K[/tex]
 The objective of this solution is to obtain the specific heat of copper
    Now specific heat can be  defined as the heat required to raise the temperature of  1 kg of a substance by  [tex]1 ^o K[/tex]
 The general equation for specific heat is Â
          [tex]C = \frac{dU}{dT}[/tex]
Where [tex]dT[/tex] is the change in temperature
       [tex]dU[/tex] is the change in internal energy
The internal energy is mathematically evaluated as
            [tex]U = 3nk_BT[/tex]
   Where  [tex]k_B[/tex] is the Boltzmann constant with a value of [tex]1.38*10^{-23} kg \cdot m^2 /s^2 \cdot ^o K[/tex]
          T is the room temperature
           n is the number of atoms in a substance
Generally number of  atoms in mass of an element can be obtained using the mathematical operation
           [tex]n = \frac{m}{M} * N_A[/tex]
Where [tex]N_A[/tex] is the Avogadro's number with a constant value of  [tex]6.022*10^{23} / mol[/tex]
     M is the atomic mass of the element
      m actual mass of the element
 So the number of atoms in 1 kg of copper is evaluated as Â
       [tex]m = 1 kg = 1 kg * \frac{10000 g}{1kg } = 1000g[/tex]
The number of atom is Â
            [tex]n = \frac{1000}{63.6} * (6.0*0^{23})[/tex]
             [tex]= 9.46*10^{24} \ atoms[/tex]
Now substituting the equation for internal energy into the equation for specific heat
     [tex]C = \frac{d}{dT} (3 n k_B T)[/tex]
       [tex]=3nk_B[/tex]
Substituting values
     [tex]C = 3 (9.46*10^{24} )(1.38 *10^{-23})[/tex]
      [tex]C= 392 J/kg\cdot ^o K[/tex]
