Closed system

A closed system is a thermodynamic system for which no matter crosses the boundary , while energy exchange may occur with the surroundings as heat and/or work .

This is the standard “control mass” setting of classical equilibrium thermodynamics.

Physical interpretation

Examples include:

• A sealed piston–cylinder device, where the boundary can move and mechanical work occurs, but no mass enters or leaves.
• A rigid sealed container placed in thermal contact with a bath through a diathermal wall , allowing heat flow without mass flow.

A closed system differs from:

• an open system , which allows matter exchange across a permeable boundary, and
• an isolated system , which allows neither matter nor energy exchange.

Key relations

• Fixed amount of matter: For a single-component closed system, the particle number $N$ is constant:

  $$dN = 0.$$

• First-law form: The first law of thermodynamics relates changes in internal energy to boundary transfers. Using the common convention that $\delta W$ is work done by the system on the surroundings,

  $$dU = \delta Q - \delta W.$$

  (If $\delta W$ is instead defined as work done on the system, the sign changes accordingly.)

• Mechanical boundary work: For a simple compressible closed system, one common contribution to work is pressure–volume work of magnitude $p\,dV$; sign details are set by the pressure–volume work sign convention . The variables pressure $p$ and volume $V$ are then central state variables.

Process viewpoint

Because heat and work are path dependent , specifying a closed system is not enough to determine $U$-changes; one must also specify the process (e.g., the boundary constraints and driving protocol) that dictates how energy is exchanged with the surroundings.