Work reservoir

A work reservoir is an idealized part of the surroundings that can exchange energy with a thermodynamic system as work while maintaining (approximately) constant “driving” parameters—typically one or more intensive generalized forces such as an externally imposed pressure, force, torque, electric potential, etc.

The key idealization is stiffness/size: the reservoir is so large (or so strongly constrained) that the generalized force(s) it applies do not change appreciably when it gives or absorbs a finite amount of work. Physically, examples include:

• a weight-and-pulley or gravitational field acting as a mechanical work store,
• a piston with weights producing an (approximately) fixed external pressure ,
• a large battery acting as an (approximately) fixed voltage source.

Work exchange is described by the inexact differential of work $\delta W$, emphasizing that work depends on the process (it is a path function ), not just the endpoints.

General form (conjugate pairs).
Many work interactions can be written schematically as

where each $X_i$ is an extensive “displacement-like” variable and each $Y_i$ is its conjugate intensive “force-like” variable. A work reservoir is often modeled as fixing one or more $Y_i$ values externally.

PV-work as the canonical example.
For boundary work involving volume $V$, an external pressure $P_{\text{ext}}$ set by the work reservoir gives

If $P_{\text{ext}}$ is constant, then $W = P_{\text{ext}}(V_f - V_i)$. Whether $W$ is counted positive for “work done by the system” or “work done on the system” depends on the site’s work sign convention and, for PV work in particular, the pressure–volume work convention .

Process dependence and reversibility.
In a quasistatic process , the system’s internal pressure can track the externally imposed pressure closely; in the ideal reversible limit, they coincide throughout (see reversible vs. irreversible ).

Work reservoirs are often paired with energy bookkeeping via the first law , which relates work and heat exchanges to changes in internal energy . For controlled heat exchange at fixed temperature instead, one uses a thermal reservoir .