Thermodynamic Property Classification – Identify Specific Volume In engineering thermodynamics, the specific volume v (volume per unit mass) describes how much volume is occupied by a unit mass of a substance at a given state. Specify whether specific volume is an extensive or intensive property.

Difficulty: Easy

Correct Answer: intensive

Explanation:


Introduction / Context:
Correctly classifying properties as intensive or extensive is foundational for applying mass and energy balances, formulating equations of state, and scaling processes. Specific volume, denoted v, is widely used in steam tables, gas tables, and compressible-flow relations, so knowing its category prevents conceptual mistakes.


Given Data / Assumptions:

  • Specific volume v is defined as V/m, where V is total volume and m is total mass.
  • System can be subdivided into non-overlapping parts without changing local thermodynamic state.
  • We are considering equilibrium states (uniform properties within each part).


Concept / Approach:

An extensive property scales with system size and is additive over subsystems (e.g., total mass, total volume, total internal energy). An intensive property does not scale with system size and remains the same for subsystems at the same state (e.g., temperature, pressure, density). Since specific volume is the ratio V/m, it is independent of the overall size of the system at a fixed state, hence intensive. Equivalently, density rho = 1/v is also intensive.


Step-by-Step Solution:

Start with the definition: v = V/m.Consider doubling system size: V → 2V and m → 2m.Compute the ratio: v_new = (2V)/(2m) = V/m = v.Conclude v does not depend on system size → intensive property.


Verification / Alternative check:

Tabulated thermodynamic property data (e.g., steam tables) list v alongside p and T. When a uniform system is split into equal halves at identical p and T, each half has the same v as the original, confirming intensiveness. Meanwhile, total volume V halves and mass m halves—both extensive—yet v remains unchanged.


Why Other Options Are Wrong:

'Extensive' is incorrect because extensive properties scale with size; v does not. 'State-dependent but neither' is vague and ignores standard definitions. 'Path property' conflates state functions with process-dependent quantities; v is a state property. 'Extrinsic only for solids' is meaningless here; intensiveness is not restricted by phase.


Common Pitfalls:

Confusing specific properties (per unit mass) with total properties; assuming any property involving volume must be extensive. Remember: ratios of extensive properties (like V/m) typically yield intensive properties.


Final Answer:

intensive

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