Question

The average density of a carbon-fiber-epoxy composite is 1.615 g/cm3. the density of the epoxy resin is 1.21 g/cm3 and that of the carbon fibers is 1.74 g/cm3. (a) what is the volume percentage of carbon fibers in the composite? (b) what are the weight percentages of epoxy resin and carbon fibers in the composite?

Answer 1

The composite material is composed of carbon fiber and epoxy resins. Now, density is an intensive unit. So, to approach this problem, let's assume there is 1 gram of composite material. Thus, mass carbon + mass epoxy = 1 g.

Volume of composite material = 1 g / 1.615 g/cm³ = 0.619 cm³
Volume of carbon fibers = x g / 1.74 g/cm³ 
Volume of epoxy resin = (1 - x) g / 1.21 g/cm³ 

a.) V of composite = V of carbon fibers + V of epoxy resin
0.619 = x/1.74 + (1-x)/1.21
Solve for x,
x = 0.824 g carbon fibers
1-x = 0.176 g epoxy resins

Vol % of carbon fibers = [(0.824/1.74) ÷ 0.619]*100 = 76.5%

b.) Weight % of epoxy = 0.176 g epoxy/1 g composite * 100 = 17.6%
     Weight % of carbon fibers = 0.824 g carbon/1 g composite * 100 = 82.4%