Question:

At ship floats with 40% submerged when at 100K and 80% submerged when at 150K. Coeff of volume expansion of liquid is?

• 0.02
• 0.005
• 0.0075

Soltuion

This is a simple question about the expansion of liquids, we know the two temperatures, so we know the initial volume and final volume of the liquid we will be able to solve the question.

Let the mass of the ship be M. Since the ship is floating the mass of liquid displaced is equal to the mass of the ship.

If V is the volume of ship, the volume of liquid displaced at 100K and 150K is 0.4V and 0.8V.

So 0.4V is expanding into 0.8V.

Hence we get 0.8V=0.4V(1+DeltaT alpha)

=>2=1+(150-100)alpha

=> alpha=1/50=0.02