1. The density of solid Cu is 8.96g/cm3 . How many atoms are present per cubic centimeter(cm3) of Cu ?
2. As a solid, Cu adopts a face‑centered cubic unit cell. How many unit cells are present per cubic centimeter(cm3) of Cu ?
3. What is the volume of a unit cell of this metal? What is the edge length of a unit cell of Cu ?

8.5 × 10²² atom / cm³, 2.125 × 10²² unit cells / cm³, 4.7 × 10⁻²³ cm³ / cell unit, 3.61 × 10⁻⁸ cm /cell

Explanation:

The density of the solid Cu = 8.96 g/cm³

a) number of atoms present

mole = mass / molar mass = (8.96 g/cm³) / 63.546 = 0.141 mol

number of atoms = mole × avogadro's constant = 0.141 × 6.02 × 10²³ = 8.5 × 10²² atom / cm³

b) a face-centered cubic unit cell contains 4 atoms

8.5 × 10²² atom / cm³ / 4 = 2.125 × 10²² unit cells / cm³

c) the volume of a unit cell of the metal = reciprocal of  2.125 × 10²² unit cells / cm³  = 1 ÷ ( 2.125 × 10²² unit cells / cm³ ) = 4.7 × 10⁻²³ cm³ / cell unit

the edge length of a cell of cu = ∛(4.7 × 10⁻²³ cm³ / cell unit) = 3.61 × 10⁻⁸ cm /cell

answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.