an iron sphere weighting 100kg is cast in a mold If an iron

an iron sphere weighting 100kg is cast in a mold. If an iron cube (side 15 cm) is cast under identical conditions, what will be its solidification time? density of iron 7800 kg/m^3

Solution

>> As, Solidification time , t = B*(V/A)² [ According to Chvorinov\'s Rule ]

>> Now, Considering Sphere.

Weight = 100 kg = m

and, density = 7800 Kg/m³

As, Mass = Volume*Density

=> Volume = 100/7800 = 0.0128 m³

Let, radius of ion sphere = \"R\"

=> (4/3)pi*R³ = 0.0128

>> Solving, R = 0.145 m   

So, A = Surface Area = 4*pi*R² = 0.265 m²

So, t1 = Solidification Time of Iron Sphere = B*(0.0128/0.265)² = 2.333*10^-3*B ......(1).........

>> Considering Iron Cube

Side, a = 15 cm = 0.15 m

So, Volume, V = a³ = 3.375*10^-3 m³

and, A = Surface Area = 6*a² =0.135 m²

So, t2 = Solidification Time of Iron Cube = B*(3.375*10^-3 /0.135)² = 6.25*10^-4*B ......(2).........

Doing (2) / (1),

=> t2 /t1 = (6.25*10^-4/2.333*10^-3) = 0.268

=> t2 = 0.268*t1 ,

i.e. SOlidification time of Iron Cube = 0.268 times of Solidification Time of Iron Sphere.........