NDA (I) 2017 General Ability Test · Question 124 of 149

Correct — D, Their containers also expand when heated. A solid can be heated on its own and its expansion measured directly, but a liquid has no shape of its own and must be held in a vessel. Heat the vessel and its walls expand too, so its internal volume grows at the same time as the liquid inside it. What you actually see rising in the stem of the flask is therefore not the liquid's full expansion but only the excess of it over the vessel's — the apparent expansion. The real expansion is recovered by adding the vessel's own coefficient back in, so the coefficient of real expansion equals the coefficient of apparent expansion plus that of the container. That extra correction, needed for no solid, is what makes the liquid measurement the harder one.

• (a)Liquids tend to evaporate at all temperatures — Evaporation is a real nuisance in the laboratory and it does remove some liquid, but it is a difficulty that can be dealt with by closing the vessel or by working well below the boiling point. It is not the reason the measurement is awkward in principle, and it says nothing about why the reading you take is not the expansion you want.
• (b)Liquids conduct more heat — Most liquids are in fact poor conductors of heat compared with metals, mercury being the well-known exception, so the premise is shaky. In any case the rate at which heat spreads affects only how long you must wait for the liquid to reach a uniform temperature, not the accuracy of the expansion you finally measure.
• (c)Liquids expand too much when heated — Liquids do expand far more than solids — that is why a thin capillary stem is enough to show the change — but a large effect is easier to measure, not harder. The trouble is not the size of the expansion; it is that part of it is masked by the vessel.

Solids can expand in length, in area or in volume, so they have three coefficients, related as roughly one to two to three. A liquid has no fixed shape, so only volume expansion is meaningful for it, and there is only one coefficient. Measuring it means separating two effects that happen together — the liquid's own expansion and the enlargement of the container. The relation γ_real = γ_apparent + γ_vessel does that separation, and the classical way of side-stepping the problem altogether is Dulong and Petit's method, which balances two columns of the same liquid at different temperatures so that the vessel's expansion drops out of the comparison.

The examiner is asking about the logic of a measurement, not about a formula, so the useful question to put to each option is whether it explains why the reading you take differs from the quantity you want. Only one option does. The rest describe genuine properties of liquids that make laboratory work fiddly without corrupting the result. This is also the idea behind the everyday behaviour you already know — a thermometer works because mercury or alcohol expands much more than the glass around it, so the apparent expansion is large enough to read on a scale.

• Liquids have only a coefficient of volume expansion, since they take the shape of their container.
• The coefficient of real expansion equals the coefficient of apparent expansion plus the coefficient of expansion of the vessel.
• Liquids typically expand several times as much as solids for the same rise in temperature.
• Water is anomalous between 0 °C and 4 °C, contracting as it warms and reaching its maximum density at about 4 °C.

• Choosing evaporation, which is a practical nuisance rather than the reason the reading is incomplete.
• Assuming a large expansion is harder to measure than a small one.
• Forgetting that a liquid has no linear or areal coefficient, only a volume one.

NDA asks why liquid expansion is measured as apparent expansion, or sets a numerical question linking real, apparent and vessel coefficients.

• practice — not a real PYQ

  The coefficient of real expansion of a liquid is equal to

  • (a)the coefficient of apparent expansion minus that of the vessel
  • (b)the coefficient of apparent expansion plus that of the vessel
  • (c)the coefficient of apparent expansion divided by that of the vessel
  • (d)the coefficient of apparent expansion alone

  Answer(b) the coefficient of apparent expansion plus that of the vessel — the container's expansion is added back because it hid part of the liquid's.

• practice — not a real PYQ

  Water is unusual among liquids because between 0 °C and 4 °C it

  • (a)expands as it is warmed
  • (b)contracts as it is warmed
  • (c)neither expands nor contracts
  • (d)changes into vapour

  Answer(b) contracts as it is warmed — its density is highest at about 4 °C, which is why ice forms on the surface of a lake first.