Skip to main content

Test for property; state and path function

Short answer

A quantity is a property if its cyclic integral is zero and change depends only on endpoints (exact differential). State functions (e.g., internal energy) are path-independent; path functions (heat, work) are inexact and path-dependent.

Explain how will you find out whether a given variable is a thermodynamic property or not. Also define state function and path function.

Test for a thermodynamic property

A quantity is a thermodynamic property only if:

  1. It has a definite value at each equilibrium state of the system.
  2. Its change between two states depends only on the end states, not on the path. Mathematically its differential is exact: ∮ dX = 0 for any cycle, and ∫₁² dX = X₂ − X₁.
  3. For X = f(x, y), the mixed derivatives are equal: ∂²X/∂x∂y = ∂²X/∂y∂x (Euler's test).

If the cyclic integral is not zero or the value depends on the process followed, it is not a property. Example: pressure, volume, T are properties; heat and work are not.

State function (point function)

A quantity whose value depends only on the state of the system, not on how the state was reached. Its differential is exact (dU, dH, dP, dV). Examples: internal energy, enthalpy, entropy.

Path function

A quantity whose value depends on the path (process) followed between two states. Its differential is inexact (δQ, δW). The area under a process curve on a P-V diagram (work) changes with the path. Examples: heat and work.

 P |1
   | \  path A: W_A
   |  \_____
   |   path B: W_B   (W_A != W_B)
   |        \__2
   +--------------- V

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Fundamental of Thermodynamics & Heat Transfer chapter 1 questions →