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A closed system can exchange energy even though no matter crosses its boundary. Its energy stays constant only when the net energy transfer is zero; an isolated system excludes both matter and energy exchange.
By Matan · Updated
Define the boundary before claiming constancy
With negligible changes in bulk kinetic and potential energy, the first law for a closed system is ΔU = Q − W when W is work done by the system. Heat supplied or work extracted changes the system’s energy. Conservation is the balance, not a requirement that every chosen subsystem keep the same energy. [1]
Worked heated piston
A sealed gas receives 500 J of heat and does 200 J of expansion work. Its internal energy increases by 300 J. No gas escapes, so the system is closed; its energy nevertheless changes. If an additional 300 J of heat then leaves with no work, its internal energy returns to the initial value.
Friction changes the form of energy
A slowing pendulum loses mechanical energy to internal energy and sound in its surroundings. Including the relevant surroundings restores the full accounting. Mechanical energy K + U is constant only under the corresponding restrictions on nonconservative work.
Conservation and useful energy differ
A process can conserve total energy while reducing the amount available for useful work under specified environmental conditions. That is why efficiency remains meaningful. In more advanced physics, global energy definitions can require care; this article uses ordinary laboratory thermodynamics.
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How this article was checked
Sources checked; calculations checked where shown. Main claims and model assumptions were checked against the references below. Example arithmetic and units were checked separately. Numerical examples are illustrative calculations, not experimental measurements.
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Cite this article
Matan. “When is a system’s total energy constant? Closed versus isolated systems.” Your Physicist. Originally published 2023-05-17; updated 2026-09-10. https://your-physicist.com/why-is-the-total-energy-of-a-closed-system-conserved/
Revision history
10 September 2026: Corrected closed versus isolated systems and added explicit heat/work accounting. Added references and a transparent verification record.
