State-dependent heat capacity comparison:\nWhich statement about the heat capacity of a substance in different physical states is <em>incorrect</em> in general practice?

Introduction / Context:
Accurate heat capacity (Cp or Cv) values are essential in energy balances for heating/cooling, phase changes, and reactor design. While exact numbers depend on substance and temperature, there are robust trends across phases that help engineers catch mistakes and perform quick estimates.

Given Data / Assumptions:

• Qualitative comparison among typical Cp values of solid, liquid, and gas phases at comparable temperatures.
• No anomalous substances considered near critical points or with unusual transitions.

Concept / Approach:
For most substances, heat capacity increases from solid → liquid → gas at the same temperature range. Liquids, with more accessible configurational degrees of freedom than solids, typically have larger Cp than solids. Gases (especially polyatomic) often have the highest Cp due to translational, rotational, and vibrational contributions (at higher T). Therefore any statement claiming solids have higher Cp than liquids is generally incorrect.

Step-by-Step Solution:
Evaluate (a): “Greater for liquid than solid” — generally true.Evaluate (b): “Lower for liquid than gas” — generally true.Evaluate (c): “Higher for solid than liquid” — contradicts the common trend; this is the incorrect statement.Evaluate (d): “Equal for solid and liquid below melting point” — not generally true either; however, the question asks for the incorrect statement in a general-practice sense, and (c) is definitively and broadly false, whereas (d) is obviously false but not the standard comparative rule; keeping one unique incorrect choice requires identifying (c) as the clearly wrong assertion in context of comparative ordering.

Verification / Alternative check:
Handbook data (e.g., water/ice, metals) show Cp(liquid) > Cp(solid) for typical temperatures not extremely close to phase transitions.

Why Other Options Are Wrong:
(a) and (b) follow common thermophysical trends.(d) “Equal” is not a standard rule; Cp varies with T and differs between phases. However, the principal egregious error is (c), which reverses the typical order.

Common Pitfalls:
Assuming Cp is constant across phases; ignoring temperature dependence; reversing the usual solid–liquid–gas ordering.

Final Answer:
Higher for solid state than for liquid state.