Closed System

Thermodynamic system that can exchange energy but not matter with its surroundings.

Conceptual context

Thermodynamics classifies systems according to the exchanges they allow with their surroundings. The closed system occupies the intermediate position between the isolated system (no exchange at all) and the open system (with matter exchange): it allows energy to pass in the form of heat and work through its boundary, but prohibits matter flow. This configuration is the most common in laboratory and engineering thermodynamic analyses, accurately describing piston engines, closed combustion chambers, electric batteries, and sealed reaction vessels.

The closed system is the natural setting for the first law of thermodynamics in its most complete form, where the change in internal energy results from the interaction of two qualitatively distinct energy transfer processes: heat, driven by temperature gradients, and work, driven by pressure, tension, or other generalized force gradients.

🟢 Essential level

A closed system is a system that neither gains nor loses mass, but can gain or lose energy. Think of a sealed syringe: the plunger can move (work exchange) and the walls can transmit heat, but the gas inside the syringe does not escape. That is a closed system.

The most direct consequence is that the internal energy $U$ of the system —the total energy stored in the microscopic motion and interactions of its molecules— can change, and that variation $\Delta U$ depends exactly on how much heat $Q$ enters or leaves and how much work $W$ enters or leaves. If more energy enters than leaves, $\Delta U$ increases. If more leaves than enters, $\Delta U$ decreases. The closed system boundary is permeable to energy but not to matter. In other words, energy exchange is possible, but exchange of substance is not.

A sealed pressure cooker follows the same logic: the steam and water inside do not change in amount while the valve stays shut, but the internal temperature and pressure do change depending on how much heat enters from the stove. If it is taken off the heat and left to cool on the counter, its internal energy decreases even though not a single gram of matter has crossed its walls.

🔵 Formal level

Basic formulas

The first law of thermodynamics establishes the exact relationship between $\Delta U$, $Q$, and $W$ for any process in a closed system:

First law of thermodynamics for a closed system

This expression states that the change in $\Delta U$ equals the sum of the heat $Q$ received by the system and the work $W$ received by the system. The sign convention is fundamental: $Q$ positive when the system absorbs heat from the surroundings; $W$ positive when the surroundings perform work on the system (IUPAC convention).

The second law imposes a constraint on the entropy change $S$ of the closed system. The Clausius inequality states that:

Second law for a closed system (Clausius inequality)

Real student questions

Why do Q and W depend on the path if $\Delta U$ does not?

Because $\Delta U$ reflects the difference between state properties (which are unique for each system state), while $Q$ and $W$ describe how the transfer occurs, which can vary enormously. The final state can be reached by a path where almost everything is heat and almost nothing is work, or by a path where almost everything is work and almost nothing is heat. In both cases $\Delta U$ is the same, but $Q$ and $W$ are very different.

Can the entropy of a closed system decrease?

Yes. A refrigerator is an everyday example: the refrigerant (a closed system that does not lose mass) has an entropy that decreases when it releases heat to the condenser. This decrease is possible because the compressor provides work, and that work pays the thermodynamic cost of the decrease in system entropy. The entropy of the universe (system plus surroundings) never decreases.

What is the practical difference between a closed system and an isolated system?

In an isolated system, $\Delta U$ is always zero because neither $Q$ nor $W$ can be non-zero. In a closed system, $\Delta U$ can change freely through $Q$ and $W$. The practical difference is that the closed system can be used as an engine, refrigerator, or heater, while the isolated system cannot exchange useful energy with the surroundings.

Final synthesis

The closed system is the canonical setting of the first law: $\Delta U$ equals $Q$ plus $W$. Its matter-impermeable boundary ensures that every change in internal energy has an identifiable energetic cause. The second law adds the constraint that $S$ can decrease in the system if heat is extracted, but the total entropy of the universe never decreases.