Thermodynamic Paths — Law Governing a Hyperbolic Process A “hyperbolic process” on a p–V diagram is governed by which gas law or relation?

Introduction:
Different thermodynamic processes trace distinctive curves on the pressure–volume plane. Recognizing these shapes allows quick identification of the underlying relation. The term “hyperbolic” typically refers to the rectangular hyperbola characterized by a constant p * V product for ideal gases.

Given Data / Assumptions:

• Ideal-gas behavior for the working fluid.
• Quasi-static process representation on a p–V diagram.
• Temperature variations allowed unless constrained by the law.

Concept / Approach:
Boyle’s law states p * V = constant at constant temperature (isothermal) for a given mass of ideal gas. The locus p = C / V is a rectangular hyperbola in the p–V plane. Hence, “hyperbolic process” commonly denotes the isothermal ideal-gas path governed by Boyle's law.

Step-by-Step Solution:
Start from p * V = constant.Express p = C / V, which is the mathematical form of a rectangular hyperbola.Therefore, the hyperbolic process is identified with Boyle’s law.

Verification / Alternative check:
On semilog plots, isothermal compression/expansion of an ideal gas aligns with hyperbolic behavior; experimental deviations occur at high pressures where real-gas effects appear.

Why Other Options Are Wrong:
Charles’ law relates volume to temperature at constant pressure; Gay-Lussac relates pressure to temperature at constant volume; Avogadro’s law connects volume to moles at fixed T and p—none generate a hyperbola in p–V like Boyle’s law.

Common Pitfalls:
Assuming any curved p–V line is “hyperbolic”; forgetting that isothermal ideal-gas paths are the canonical hyperbolas.

Final Answer:
Boyle's law