A spherical drop of molten metal of radius 5 mm was found to solidify in 12 s. In how much time will a similar drop of radius 10 mm solidify?

Concept:

Solidification time:

It is the time required for a casting to solidify after pouring. This time is dependent on the size and shape of the casting.

There is an empirical relationship known as Chvorinov’s rule –

where t_s = solidification time of casting, V = volume of casting, A_s = surface area of casting and K = solidification factor.

Calculation:

Given:

R₁ = 5 mm, R₂ = 10 mm ⇒ R₂ = 2R₁

t_S1 = 12 sec ⇒ time required for the sphere of radius 5 mm to solidify., t_S2 = time required for the sphere of radius 10 mm to solidify.

∴ t_S2 = 48 sec.