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What does it mean that energy is conserved?
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Saying “energy is conserved” means that in a closed (isolated) physical system the total amount of energy does not change with time — it can be transferred from place to place and converted between different forms (kinetic, potential, thermal, chemical, electromagnetic, mass–energy, …) but the sum stays constant.
Key points
- Practical statement: For an isolated system, dE/dt = 0. Energy can move between objects or change form, but the total is constant.
- Local form: Conservation is expressed by a continuity equation for energy density u and energy flux S, ∂u/∂t + ∇·S = 0, meaning energy is not lost but flows.
- Origin in theory: Conservation of energy follows from time-translation symmetry of the laws of physics (Noether’s theorem).
- Open systems: If a system exchanges heat or work with its surroundings, its energy can change — energy conservation then applies to the system plus its surroundings.
- Apparent exceptions: Dissipative processes (friction) convert organized mechanical energy into microscopic thermal energy; nothing mystical is lost — energy is redistributed. In relativity mass and energy are unified (E = mc^2), so mass–energy is conserved. In general relativity global energy bookkeeping is more subtle, but local energy–momentum conservation still holds (∇·T = 0).
Examples
- A swinging pendulum exchanges kinetic and potential energy while its total mechanical energy (neglecting air resistance) stays the same.
- A battery chemically converts stored chemical energy into electrical energy; the total energy (including heat losses) is conserved.
- In a nuclear reaction mass is partly converted into energy, but total mass–energy is conserved.
In short: energy conservation means you cannot create or destroy energy in an isolated system — you can only move it or change its form.
Key points
- Practical statement: For an isolated system, dE/dt = 0. Energy can move between objects or change form, but the total is constant.
- Local form: Conservation is expressed by a continuity equation for energy density u and energy flux S, ∂u/∂t + ∇·S = 0, meaning energy is not lost but flows.
- Origin in theory: Conservation of energy follows from time-translation symmetry of the laws of physics (Noether’s theorem).
- Open systems: If a system exchanges heat or work with its surroundings, its energy can change — energy conservation then applies to the system plus its surroundings.
- Apparent exceptions: Dissipative processes (friction) convert organized mechanical energy into microscopic thermal energy; nothing mystical is lost — energy is redistributed. In relativity mass and energy are unified (E = mc^2), so mass–energy is conserved. In general relativity global energy bookkeeping is more subtle, but local energy–momentum conservation still holds (∇·T = 0).
Examples
- A swinging pendulum exchanges kinetic and potential energy while its total mechanical energy (neglecting air resistance) stays the same.
- A battery chemically converts stored chemical energy into electrical energy; the total energy (including heat losses) is conserved.
- In a nuclear reaction mass is partly converted into energy, but total mass–energy is conserved.
In short: energy conservation means you cannot create or destroy energy in an isolated system — you can only move it or change its form.
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