Скачать или смотреть Lecture 49 : Relation between heat capacities (Cₚ - Cᵥ) | Applications of Maxwell's Relations

In this lecture, we derive the fundamental relation between heat capacities at constant pressure and constant volume using Maxwell’s relations. This topic is extremely important in thermodynamics as it links measurable quantities like thermal expansion and compressibility with heat capacities, providing deep physical insight into the behaviour of real systems.

Topics Covered:

1. Heat Capacities

Definition of heat capacity at constant volume (Cv)
Definition of heat capacity at constant pressure (Cp)
Physical interpretation of Cp and Cv


2. Maxwell Relations and Thermodynamics

Role of Maxwell relations in connecting thermodynamic derivatives
Use of entropy-based relations to derive heat capacity identities


3. Relation between Cp and Cv

Derivation of Cp − Cv using Maxwell relations
Dependence on thermal expansion and compressibility
Importance for gases, liquids, and solids


4. Key Thermodynamic Result

Why Cp is always greater than Cv
Special case of ideal gas
Applications in atmospheric physics and engineering systems


Why This Lecture Is Important:

Core concept in thermal physics
Frequently asked in competitive exams
Builds strong conceptual understanding of thermodynamic identities


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