A cube of ice whose edges measure 20.0 mm is floating in a glass of ice-cold wat

Question

A cube of ice whose edges measure 20.0 mm is floating in a glass of ice-cold water with one of its faces parallel to the water's surface.

(a) How far below the water surface is the bottom face of the block?
mm

(b) Ice-cold ethyl alcohol is gently poured onto the water's surface to form a layer 5.50 mm thick above the water. The alcohol does not mix with the water. When the ice cube again attains hydrostatic equilibrium, what will be the distance from the top of the water to the bottom face of the block?
mm

(c) Additional cold ethyl alcohol is poured onto the water's surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol?
mm

Explanation / Answer

The depth of the ice below the water level is given by

alcohol depth = d = 5.5 mm
cube length = L = 20 mm
depth below water = h

a) Mass of the ice = mass of water displaced

L*rho(ice) = h*rho(water)

h = [L*rho(ice)] / rho(water)

rho(ice) = 0.917, rho(water) = 1.0

h = 18.34 mm

b) Mass of the ice = mass of water displaced + mass of alcohol displaced.

L*rho(ice) = h*rho(water) + d*rho(alcohol)

h = [L*rho(ice) - d*rho(alcohol)] / rho(water)

rho(ice) = 0.917, rho(ethyl alcohol) = 0.789, rho(water) = 1.0

the distance from the top of the water to the bottom face of the block, h = 14 mm

c) h = 20 - 14 = 6 mm

L = 20 mm

d = [L*rho(ice) - h*rho(water)] / rho(alcohol)

rho(ice) = 0.917, rho(ethyl alcohol) = 0.789, rho(water) = 1.0

thickness requireded for the layer of ethyl alcohol, d = 15.64 mm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.