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

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

Step-by-step 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)=(\rho_(cu))/(\rho_w)`

here density of water is 62.4 lbm/ft3

Solving for Density of Copper gives

`S_(cu)=(\rho_(cu))/(\rho_w)\\9=(\rho_(cu))/(62.4)\\\rho_(cu)=9 * 62.4\\\rho_(cu)=561.5 lbm/ft3`

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

`V_(cu)=(m_(cu))/(\rho_(cu))\\V_(cu)=(15)/(561.5)\\V_(cu)=0.0267 ft^3\\\\V_(r)=(m_(r))/(\rho_(r))\\V_(r)=(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)=(V_(cu))/(V_(c))\\c_(cu)=(0.0267)/(1.2409) * 100 \%\\c_(cu)=2.154 \%\\\\c_(r)=(V_(r))/(V_(c))\\c_(r)=(1.214)/(1.2409) * 100 \%\\c_(r)=97.83 \%`

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