Thermodynamic Work

Definition

Work ($W$) is the energy transfer associated with a force acting through a displacement. In thermodynamics, it is path-dependent (not a property).

Formula

General Reversible Work (Closed System)

$W_{12} = \int_{V_1}^{V_2} P(V)\,dV$

Specific Forms

Type	Differential Form	Remarks
Boundary (Expansion)	$\delta W_b = P\,dV$	Quasi-static (reversible) closed systems.
Shaft Work	$\delta W_s = \tau\,d\theta$	Rotating shafts (turbines, compressors).
Electrical	$\delta W_e = E\,dq$	Voltage $\times$charge.
Flow Work	$\delta W_{flow} = P\,dv$	Energy required to push mass into/out of a CV.

Relationships

• Related: [[first-law|First Law of Thermodynamics]], [[polytropic-process|Polytropic Process]]
• Contrast: Heat