Capillary diameter controls liquid rise for a given expansion

Steps:

• Thermometer range is the temperature span until liquid reaches capillary top.
• Liquid expansion volume = α × V_bulb × ΔT, where α is expansion coefficient.
• Rise height h = expansion volume / (π r² L), but for fixed L, range ΔT ∝ 1 / (π r²).
• Increasing r (diameter) increases cross-sectional area, reducing h for same ΔT, thus extending range.

Why C is correct:

• Larger capillary diameter increases bore area (∝ r²), so same expansion volume causes less rise, allowing greater ΔT before overflow (from volume flow formula).

Why the others are wrong:

• A: Shorter capillary reduces total length, so liquid reaches top sooner, decreasing range.
• B: Thinner glass affects heat transfer but not expansion volume or capillary capacity, so range unchanged.
• D: More bulb liquid increases expansion volume for same ΔT, causing faster rise and shorter range.

Final answer: C