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First law of thermodynamics

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For a closed thermodynamic system, the first law of thermodynamics may be stated as: δ Q = d U + δ W {\displaystyle \delta Q=\mathrm {d} U+\delta W} , or equivalently, d U = δ Q − δ W , {\displaystyle \mathrm {d} U=\delta Q-\delta W,} where δ Q {\displaystyle \delta Q} is the quantity of energy added to the system by a heating process, δ W {\displaystyle \delta W} is the quantity of energy lost by the system due to work done by the system on its surroundings and d U {\displaystyle \mathrm {d} U} is the change in the internal energy of the system. The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the d U {\displaystyle \mathrm {d} U} increment of internal energy (see Inexact differential). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energ...
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Conservation of energy

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In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. This law, first proposed and tested by Émilie du Châtelet, means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. Classically, conservation of energy was distinct from conservation of mass; however, special relativity showed that mass is related to energy and vice versa by E = mc2 , and science now takes the view that mass–energy as a whole is conserved. Theoretically, this implies that any object with ma...
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Quantum theory

In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the Hilbert space (or a space of wave functions) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position-momentum uncertainty principle, and merely holds in specific cases (see Uncertainty principle). Energy at each fixed time can in principle be exactly measured without any trade-off in precision forced by the time-energy uncertainty relations. Thus the conservation of energ...
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