Trend in heat capacity by phase:\nFor most substances, in which phase is the heat capacity typically the greatest?

Introduction / Context:
Heat capacity indicates how much energy is required to raise temperature. Recognizing broad trends across phases helps in estimating energy requirements in heating/cooling operations when detailed data are unavailable.

Given Data / Assumptions:

• Comparison is qualitative and typical; exceptions exist.
• Consider molar or mass heat capacities at common conditions.

Concept / Approach:
Liquids generally exhibit higher heat capacities than solids due to additional configurational degrees of freedom (molecular rearrangements) and stronger interactions than gases, which at comparable conditions possess lower heat storage per unit mass or per mole for many common substances. Water is a prime example with an unusually high heat capacity among liquids.

Step-by-Step Solution:
Compare typical values: water C_p ≈ 4.18 kJ/kg·K (liquid); ice ≈ 2.1 kJ/kg·K (solid); water vapor near 1.9–2.1 kJ/kg·K at 1 atm.Most organic liquids also exceed their solid counterparts in C_p.Hence, “liquid phase” is the best general choice.

Verification / Alternative check:
Handbooks commonly list C_p(liquid) > C_p(solid) for the same substance near ambient; gases depend on composition and temperature but are often lower on a per-mass basis for common materials.

Why Other Options Are Wrong:
“Solid” typically lower; “gas” can be higher on a molar basis for some species but not as a broad rule; “no consistent trend” ignores widely observed patterns; “plasma” is beyond the intended scope.

Common Pitfalls:
Confusing per mole versus per mass comparisons; cherry-picking exceptions.

Final Answer:
liquid phase