Question

I am making composites of silicone rubber and copper particles; by mixing thermally conductive particles into the thermally insulating rubber, I can increase the thermal conductivity of the mixture over that of the ‘neat’ rubber. The density of the rubber is 70 lbm/ft3 and the specific gravity of the copper is 9. If my composite is 15 mass percent copper, what is the composition on a volume basis?

Answer 1

Answer:

The composition of Composite of Volume basis is 2.154% Copper and 97.83% Rubber.

Explanation:

Let us assume that the total mass of composite is 100 lbm So as per the given conditions

• 15 lbm is copper and 85 lbm is rubber.
• Density of rubber is 70 lbm/ft3
• Specific gravity of Copper is 9

So As per the formula of specific gravity

                                         $S_{cu}=\frac{\rho_{cu}}{\rho_w}$

here density of water is 62.4 lbm/ft3

Solving for Density of Copper gives

                                        $S_{cu}=\frac{\rho_{cu}}{\rho_w}\\9=\frac{\rho_{cu}}{62.4}\\\rho_{cu}=9 \times 62.4\\\rho_{cu}=561.5 lbm/ft3$

For composition on volume basis, volume of individual components and composite are calculated as

                                          $V_{cu}=\frac{m_{cu}}{\rho_{cu}}\\V_{cu}=\frac{15}{561.5}\\V_{cu}=0.0267 ft^3\\\\V_{r}=\frac{m_{r}}{\rho_{r}}\\V_{r}=\frac{85}{70}\\V_{r}=1.214 ft^3\\\\V_{c}=V_{r}+V_{cu}\\V_{c}=1.214+0.0267 \\V_{c}=1.2409 ft^3$

The composition is given as

$c_{cu}=\frac{V_{cu}}{V_{c}}\\c_{cu}=\frac{0.0267}{1.2409} \times 100 \%\\c_{cu}=2.154 \%\\\\c_{r}=\frac{V_{r}}{V_{c}}\\c_{r}=\frac{1.214}{1.2409} \times 100 \%\\c_{r}=97.83 \%$

So the composition of Composite of Volume basis is 2.154% Copper and 97.83% Rubber.