first law of thermodynamics

physics
Also known as: law of conservation of energy
Also called:
law of conservation of energy

first law of thermodynamics, thermodynamic relation stating that, within an isolated system, the total energy of the system is constant, even if energy has been converted from one form to another. This law is another way of stating the law of conservation of energy. It is one of four relations underlying thermodynamics, the branch of physics concerning heat, work, temperature, and energy.

The first law of thermodynamics is put into action by considering the flow of energy across the boundary separating a system from its surroundings. Consider the classic example of a gas enclosed in a cylinder with a movable piston. The walls of the cylinder act as the boundary separating the gas inside from the world outside, and the movable piston provides a mechanism for the gas to do work by expanding against the force holding the piston (assumed frictionless) in place. If the gas does work W as it expands, and/or absorbs heat Q from its surroundings through the walls of the cylinder, then this corresponds to a net flow of energy WQ across the boundary to the surroundings. In order to conserve the total energy U, there must be a counterbalancing change ΔU = QW in the internal energy of the gas. The first law provides a kind of strict energy accounting system in which the change in the energy account (ΔU) equals the difference between deposits (Q) and withdrawals (W).

There is an important distinction between the quantity ΔU and the related energy quantities Q and W. Since the internal energy U is characterized entirely by the quantities (or parameters) that uniquely determine the state of the system at equilibrium, it is said to be a state function such that any change in energy is determined entirely by the initial (i) and final (f) states of the system: ΔU = UfUi. However, Q and W are not state functions. Just as in the example of a bursting balloon, the gas inside may do no work at all in reaching its final expanded state, or it could do maximum work by expanding inside a cylinder with a movable piston to reach the same final state. All that is required is that the change in energy (ΔU) remain the same. By analogy, the same change in one’s bank account could be achieved by many different combinations of deposits and withdrawals. Thus, Q and W are not state functions, because their values depend on the particular process (or path) connecting the same initial and final states. Just as it is more meaningful to speak of the balance in one’s bank account than its deposit or withdrawal content, it is only meaningful to speak of the internal energy of a system and not its heat or work content.

Rudolf Clausius
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thermodynamics: The first law of thermodynamics

From a formal mathematical point of view, the incremental change dU in the internal energy is an exact differential, while the corresponding incremental changes dQ and dW in heat and work are not, because the definite integrals of these quantities are path dependent. These concepts can be used to great advantage in a precise mathematical formulation of thermodynamics.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.
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conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant. The first kind of energy to be recognized was kinetic energy, or energy of motion. In certain particle collisions, called elastic, the sum of the kinetic energy of the particles before collision is equal to the sum of the kinetic energy of the particles after collision. The notion of energy was progressively widened to include other forms. The kinetic energy lost by a body slowing down as it travels upward against the force of gravity was regarded as being converted into potential energy, or stored energy, which in turn is converted back into kinetic energy as the body speeds up during its return to Earth. For example, when a pendulum swings upward, kinetic energy is converted to potential energy. When the pendulum stops briefly at the top of its swing, the kinetic energy is zero, and all the energy of the system is in potential energy. When the pendulum swings back down, the potential energy is converted back into kinetic energy. At all times, the sum of potential and kinetic energy is constant. Friction, however, slows down the most carefully constructed mechanisms, thereby dissipating their energy gradually. During the 1840s it was conclusively shown that the notion of energy could be extended to include the heat that friction generates. The truly conserved quantity is the sum of kinetic, potential, and thermal energy. For example, when a block slides down a slope, potential energy is converted into kinetic energy. When friction slows the block to a stop, the kinetic energy is converted into thermal energy. Energy is not created or destroyed but merely changes forms, going from potential to kinetic to thermal energy. This version of the conservation-of-energy principle, expressed in its most general form, is the first law of thermodynamics. The conception of energy continued to expand to include energy of an electric current, energy stored in an electric or a magnetic field, and energy in fuels and other chemicals. For example, a car moves when the chemical energy in its gasoline is converted into kinetic energy of motion.

With the advent of relativity physics (1905), mass was first recognized as equivalent to energy. The total energy of a system of high-speed particles includes not only their rest mass but also the very significant increase in their mass as a consequence of their high speed. After the discovery of relativity, the energy-conservation principle has alternatively been named the conservation of mass-energy or the conservation of total energy.

When the principle seemed to fail, as it did when applied to the type of radioactivity called beta decay (spontaneous electron ejection from atomic nuclei), physicists accepted the existence of a new subatomic particle, the neutrino, that was supposed to carry off the missing energy rather than reject the conservation principle. Later, the neutrino was experimentally detected.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
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Energy conservation, however, is more than a general rule that persists in its validity. It can be shown to follow mathematically from the uniformity of time. If one moment of time were peculiarly different from any other moment, identical physical phenomena occurring at different moments would require different amounts of energy, so that energy would not be conserved.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Adam Augustyn.
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