A cube of ice whose edges measure 22.0 mm is floating in a glass of ice-cold wat

Question

A cube of ice whose edges measure 22.0 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?

(b) Ice-cold ethyl alcohol is gently poured onto the water's surface to form a layer 6.00 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?

(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?

Explanation / Answer

(a)

Mass of water displaced = mass of the ice

Volume of water desplaced*density of water=Volume of ice*density of ice

22*22*h*998 =22^3*916.7

water surface is the bottom face of the block, h = 20.21 mm

(b)

Mass of water displaced = mass of the ice+ mass of ethyl alchohol

Volume of water desplaced*density of water=Volume of ice*density of ice + Volume of ethyl alchohol*density of ethyl alchohol

22*22*h*998 =22^3*916.7+22*22*6*789

water surface is the bottom face of the block: h=24.95 mm.

(c)

Mass of water displaced = mass of the ice+ mass of ethyl alchohol

Volume of water desplaced*density of water=Volume of ice*density of ice + Volume of ethyl alchohol*density of ethyl alchohol

22*22*22*998 =22^3*916.7+22*22*x*789

thichness of the layer: h=2.27 mm.

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