Expansion — Set 3

Correct Answer: D. 4°C

• **4°C** = Water reaches its maximum density (~1000 kg/m³) at approximately 4°C due to its anomalous expansion — below 4°C the density decreases again as water expands on cooling toward the ice point. • **Anomalous expansion** — From 0°C to 4°C, water contracts on heating; above 4°C, it expands normally; this unique behaviour is caused by hydrogen bonding in the water structure. • 💡 Wrong-option analysis: 100°C: the boiling point of water; density is much lower than maximum at this temperature; 0°C: the freezing point; water has lower density at 0°C than at 4°C; 10°C: water is already expanding normally above 4°C.

Correct Answer: D. Has a low freezing point

• **Has a low freezing point** = Ethyl alcohol freezes at about −114°C, far below mercury's freezing point (−39°C) and water's freezing point (0°C), keeping it liquid at very low temperatures. • **Freezing point: alcohol ≈ −114°C vs mercury ≈ −39°C** — This allows alcohol thermometers to function at temperatures that would solidify mercury, making them ideal for polar and high-altitude measurements. • 💡 Wrong-option analysis: Does not expand with heat: alcohol does expand with heat — that is how the thermometer works; Has extremely high boiling point: alcohol boils at only 78°C, far below mercury's 357°C; Is a metal: alcohol (ethanol) is a liquid organic compound, not a metal.

Correct Answer: A. Invar

• **Invar** = Invar alloy (64% Fe, 36% Ni) has an extremely small coefficient of linear expansion (α ≈ 1.2×10⁻⁶ K⁻¹), making it ideal for precision measuring instruments, pendulums, and standards. • **α(Invar) ≈ 1.2×10⁻⁶ K⁻¹** — Contrast with brass (≈19×10⁻⁶) and aluminium (≈23×10⁻⁶); invar changes length ~15–20 times less for the same temperature rise. • 💡 Wrong-option analysis: Aluminium: has a high α (≈23×10⁻⁶ K⁻¹), not known for low expansion; Lead: also has relatively high α (≈29×10⁻⁶ K⁻¹); Brass: has moderate-to-high α (≈19×10⁻⁶ K⁻¹).

Correct Answer: B. Lower expansion coefficient

• **Lower expansion coefficient** = The metal with higher α expands more and occupies the outer (longer) arc; the strip bends toward the side with lower α because that side is shorter. • **Inward bending rule** — If brass (higher α) is on top and invar (lower α) is below, heating makes the strip curve downward (toward invar side). • 💡 Wrong-option analysis: Higher density: density does not determine which way the strip bends; Lower melting point: melting point is irrelevant to bending direction; Higher expansion coefficient: the strip bends away from the higher-expansion metal, not toward it.

Correct Answer: D. Apparent = Real − Container expansion

• **Apparent = Real − Container expansion** = The real expansion is the true volume increase of the liquid; the container also expands, providing more space; so the observed (apparent) rise = real expansion − container expansion. • **γ_apparent = γ_liquid − γ_container** — If the container expands as much as the liquid, the apparent expansion is zero even though real expansion occurs. • 💡 Wrong-option analysis: Real = Container expansion only: real expansion is a property of the liquid, not just the container; Apparent = Real + Container expansion: adding would overestimate; Real = Apparent − Container expansion: this has the relationship inverted.

Correct Answer: D. Contracts on heating from 0°C to 4°C

• **Contracts on heating from 0°C to 4°C** = The anomalous expansion of water means that between 0°C and 4°C, heating causes contraction (increase in density) rather than expansion; maximum density is at 4°C. • **Molecular explanation** — As ice melts and warms from 0°C, open hydrogen-bonded structures collapse, reducing volume; above 4°C, normal kinetic expansion dominates. • 💡 Wrong-option analysis: Expands on cooling from 100°C to 0°C uniformly: above 4°C water expands normally; Stops expanding above 4°C: above 4°C water expands normally when heated; Becomes a gas at 4°C: water remains liquid at 4°C; it becomes gas only at 100°C under standard pressure.

Correct Answer: C. 3 : 2 : 1

• **3 : 2 : 1** = For an isotropic solid, γ ≈ 3α and β ≈ 2α, giving the ratio γ:β:α = 3α:2α:α = 3:2:1. • **γ = 3α, β = 2α** — These relationships arise because volume expands in 3 directions and area in 2 directions simultaneously for isotropic materials. • 💡 Wrong-option analysis: 3 : 1 : 2: this incorrectly places β below α; 2 : 3 : 1: this reverses γ and β; 1 : 2 : 3: this lists them from smallest to largest (α : β : γ) in reverse of what the question asks (cubical : superficial : linear).

Correct Answer: A. Numerically the same

• **Numerically the same** = Since a temperature difference of 1°C is equal to 1 K, the coefficient α per °C and per K are numerically identical — only the zero-point of the scales differs, not the interval size. • **ΔT(°C) = ΔT(K)** — The expansion coefficient is defined in terms of temperature differences, not absolute temperatures; since the intervals are equal, the numerical value of α is the same. • 💡 Wrong-option analysis: Different by a factor of 273: the scales differ by 273.15 in zero-point, but not in interval size; Not comparable: they are perfectly comparable — numerically equal; Different by a factor of 2: no factor of 2 exists between kelvin and Celsius intervals.

Correct Answer: D. Allow thermal expansion and contraction

• **Allow thermal expansion and contraction** = Bridge spans expand in summer heat and contract in winter cold; expansion joints (gaps) accommodate this dimensional change without causing dangerous thermal stress or buckling. • **ΔL = αLΔT** — A 100-metre steel bridge span can expand by ~6 cm between winter (−20°C) and summer (40°C), a 60 K range. • 💡 Wrong-option analysis: Stop corrosion completely: expansion joints do not prevent corrosion; Reduce wind resistance only: wind loads are handled by structural design, not expansion joints; Increase the bridge's weight: expansion joints are lightweight sliding mechanisms.

Correct Answer: B. Mass

• **Mass** = Thermal expansion changes the dimensions (length, area, volume) of a metal rod, but no material is added or removed — the mass remains constant. • **Conservation of mass** — Heating rearranges the atomic spacing (average separation increases) but does not change the number of atoms or their masses. • 💡 Wrong-option analysis: Temperature: temperature changes when the rod is heated (that is the cause of expansion); Volume: volume increases due to thermal expansion; Length: length increases due to linear thermal expansion.