Thermodynamic property concept: The heat-related energy stored within a gas that manifests as a rise in its temperature is known as what property?

Introduction / Context:
When a gas is heated, its microscopic motions (translation, rotation, vibration) intensify. The energy associated with these microscopic degrees of freedom is tracked via a state property that dictates temperature changes and appears in the first law. Identifying this property correctly is fundamental for energy balance problems.

Given Data / Assumptions:

• Closed system perspective for a simple compressible gas.
• No phase change; heating changes temperature and possibly volume/pressure.
• Microscopic interpretation via kinetic theory and molecular structure.

Concept / Approach:
Internal energy, U, is the energy contained within the system due to molecular motions and interactions. For ideal gases, changes in internal energy depend only on temperature and are quantified by ΔU = m * cv * ΔT. External energy is not a standard thermodynamic property; kinetic energy typically refers to macroscopic bulk motion; “molecular energy” is an informal phrase encompassing internal energy components but is not the standard property name used in balances.

Step-by-Step Solution:

Verification / Alternative check:
Applying the first law for a closed system: ΔU = Q − W (neglecting KE and PE changes). A positive heat input at constant volume leads directly to ΔU = m * cv * ΔT, confirming the role of internal energy.

Why Other Options Are Wrong:

• External energy: Not a defined thermodynamic property.
• Kinetic energy: Refers to bulk motion of the system as a whole.
• Molecular energy: Vague wording; the formal property is internal energy.

Common Pitfalls:
Mixing up path functions (heat, work) with properties (U, H, T, p).

Final Answer:
internal energy