Temperature dependence of heat capacity:\nAs temperature rises (within ordinary ranges), how does the heat capacity of a typical substance tend to change?

Introduction / Context:
Heat capacity measures how much heat is needed to raise temperature by one degree. For most solids and liquids over moderate temperature ranges, Cp increases slightly with temperature as additional vibrational or configurational modes become accessible. Many gases also show increasing Cp with temperature due to activation of vibrational degrees of freedom.

Given Data / Assumptions:

• Moderate pressures; no phase changes.
• Ordinary temperature spans used in engineering data.
• We are asking for the general trend, not exceptions.

Concept / Approach:
Empirical correlations (e.g., Shomate or polynomial Cp equations) typically show positive temperature coefficients for Cp in common ranges. While there are exceptions near transitions or decomposition, the general statement “Cp increases with T” is valid and widely used for preliminary calculations.

Step-by-Step Solution:
Consider common data tables for water, air, metals.Cp(T) generally exhibits a gentle upward slope with T.Therefore, select “increases.”

Verification / Alternative check:
Plotting Cp vs T for air (200–1000 K) or for water (liquid, 0–100 °C) confirms a mild increase.

Why Other Options Are Wrong:
“Decreases” and “unchanged” contradict typical data; “depends” is too vague for the standard generalization taught at this level.

Common Pitfalls:
Confusing specific cases (e.g., near critical points) with general behavior in standard ranges.

Final Answer:
increases