Question

James has ten heavily crosslinked epoxy ‘cubic blocks’ with dimensions of 1.0 cm by 1.0 cm by 1.0 cm and a density of 1.05 g/cm3 . Tom has twenty blocks made of the same material by double in length scale of those owned by James. Piter has only one block made of the same material, but his block is five times the length scale of those owned by James. (a) What is the number-average mass of all of the blocks? (b) What is the surface-area-average mass of all of the blocks? (c) What is the volume-average mass of all of the blocks?

Answer 1

(a) Number averaged mass:

# James:

Length of one block = 1 cm

Volume of block = (1*1*1)cm3 = 1 cm3

Mass of one block = volume * density = (1 * 1.05) g = 1.05 g

Number of block = 10

Number averaged mass = 1.05 g per block

# Tom

Length of one block = (2*1) cm = 2 cm

Volume of block = (2*2*2)cm3 = 8 cm3

Mass of one block = volume * density = (8 * 1.05) g = 8,4 g

Number of block = 20

Number averaged mass = 8.4 g per block

# Piter

Length of one block = (5*1) cm = 5 cm

Volume of block = (5*5*5)cm3 = 125 cm3

Mass of one block = volume * density = (125 * 1.05) g = 131.25 g

Number of block = 1

Number averaged mass = 131.25 g per block

(b) Surface area average mass

# James:

Length of one block = 1 cm

Volume of block = (1*1*1)cm3 = 1 cm3

Mass of one block = volume * density = (1 * 1.05) g = 1.05 g

Surface area of one block = 6*length2 = 6*12 cm2 = 6 cm2

Surface area averaged mass = 0.175 g / cm2

# Tom

Length of one block = (2*1) cm = 2 cm

Volume of block = (2*2*2)cm3 = 8 cm3

Mass of one block = volume * density = (8 * 1.05) g = 8,4 g

Surface area of one block = 6*length2 = 6*22 cm2 = 24 cm2

Surface area averaged mass = 0.35 g / cm2

# Piter

Length of one block = (5*1) cm = 5 cm

Volume of block = (5*5*5)cm3 = 125 cm3

Mass of one block = volume * density = (125 * 1.05) g = 131.25 g

Surface area of one block = 6*length2 = 6*52 cm2 = 150 cm2

Surface area averaged mass = 0.875 g / cm2

(c) Volume average mass:

Volume averaged mass is density, which remains the same for all the blocks.

Volume averaged mass = 1.05 g / cm3