Process identification – law p * v^n = constant When expansion or compression follows the law p * v^n = C, the process is known as a:

Introduction / Context:Many real processes lie between isothermal and adiabatic extremes. The polytropic relation p * v^n = constant provides a flexible model with index n capturing heat transfer and non-idealities.

Given Data / Assumptions:

• Quasi-equilibrium path for a compressible substance.
• n is constant during the process.
• Ideal-gas approximations often used for closed-form results.

Concept / Approach:Special cases of the polytropic family include n = 1 (isothermal for ideal gases), n = gamma (adiabatic for ideal gases), and n → ∞ (isochoric). Thus, the general name for p * v^n = C is the polytropic process.

Step-by-Step Solution:Recognize the given law p * v^n = C.Map n to special cases to confirm understanding.Select the general term: polytropic process.

Verification / Alternative check:Work and heat expressions reduce correctly to isothermal and adiabatic forms when n takes the corresponding values.

Why Other Options Are Wrong:

• Isothermal and adiabatic are specific cases within the polytropic family.
• Hyperbolic describes the curve shape for n = 1, not the general family.
• Isochoric keeps v constant, which is not the given law unless n → ∞.

Common Pitfalls:Assuming a single value of n applies universally; n depends on heat transfer and process details.

Final Answer:polytropic process