Answer:
as the exercise is incomplete, I add the information that is missing:
Consider a packed bed of 75-mm-diameter aluminum spheres ? = 2700 kg/m3, and c = 950 J/kg
Answer: The copper can store 34.1% more thermal energy at 272.42ºC
Explanation:
Given:
Diameter packed bed = 75 mm
Density = 2700 kg/m³
specific heat = 950 J/kg K
initial temperature sphere = 25ºC
thermal conductivity = 240 W/m K
temperature of gas = 300ºC
convection coefficient = 75 W/m²K
The characteristic length is
The Biot number is equal to
Bi < 1, we will use the lumped capacitance method
The energy transfer is equal to:
(eq. 1)
Replacing in eq. 1
The temperature at the center of sphere is
We obtain the percentage increase
Cpcu = 385 J/kg K
(pCp)cu = 8933 * 385 = 3439205 J/m³K
from water:
(pCp)wa = 2700 * 950 = 2565000 J/m³K
the percentage increase is
%P = (3439205 - 2565000)/2565000 = 34.1%
The copper can store 34.1% more thermal energy.