A piece of ice is dropped in a vessel containing kerosene oil. When ice melts,…
2023
A piece of ice is dropped in a vessel containing kerosene oil. When ice melts, the level of kerosene oil will
Answer: B. fall — Concept: A solid placed inside a liquid pushes the liquid surface up by exactly the volume that the solid occupies below that surface. How much volume that is…
- A.
rise
- B.
fall
- C.
remain same
- D.
More than one of the above
- E.
None of the above
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept: A solid placed inside a liquid pushes the liquid surface up by exactly the volume that the solid occupies below that surface. How much volume that is depends on whether the solid sinks or floats, and that is settled by comparing densities: a solid denser than the liquid sinks and occupies its own entire volume, while a solid lighter than the liquid floats and pushes aside only its own weight of liquid. When such a solid later melts, the surface moves by the difference between the volume the solid occupied and the volume its melt occupies.
Substance | Approximate density (g/cm³) | Behaviour in kerosene oil |
|---|---|---|
Kerosene oil | 0.80 | the surrounding liquid |
Ice | 0.92 | denser than kerosene, so it sinks |
Water (the melt) | 1.00 | denser than kerosene and does not mix with it, so it settles below |
Application:
Let the piece of ice have mass m grams.
Ice at about 0.92 g/cm³ is denser than kerosene oil at about 0.80 g/cm³, so the ice does not float: it sinks and rests fully submerged at the bottom of the vessel.
A fully submerged solid pushes aside its own whole volume, so the kerosene surface is raised by Vice = m / 0.92 ≈ 1.09 m cm³.
The ice now melts into water of the same mass m. Water at 1.00 g/cm³ is denser than kerosene and does not mix with it, so the melt gathers as a layer at the bottom and occupies Vwater = m / 1.00 = 1.00 m cm³.
The volume sitting beneath the kerosene therefore changes by Vwater − Vice = 1.00 m − 1.09 m ≈ −0.09 m cm³, i.e. about 8% less volume than before melting.
With less volume underneath it, the kerosene column is held up from below by a smaller amount, so its surface settles lower than where it began.
Cross-check:
Height check on a vessel of uniform cross-section A: the change in surface height is (Vwater − Vice) / A = −0.09 m / A, a negative number, so the surface ends below its starting position.
Contrast with ice floating in water, the case students usually remember: there the floating ice pushes aside exactly the mass of water it is about to become, so the volume it displaces equals the volume of its melt and the level is unchanged. That equality needs the ice to float, which it cannot do in a liquid as light as kerosene oil.
A higher final surface would need the melt to take up more room than the ice did, which happens only for a substance whose liquid form is lighter than its solid form. Water is the opposite: it contracts by roughly 8% as ice turns into water.
Result: the kerosene oil level falls.