First law of thermodynamics in the context of "Climate model"

The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. Without a thermodynamic process, the internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics. The notion has been introduced to describe the systems characterized by temperature variations, temperature being added to the set of state parameters, the position variables known in mechanics (and their conjugated generalized force parameters), in a similar way to potential energy of the conservative fields of force, gravitational and electrostatic. Its author is Rudolf Clausius. Without transfer of matter, internal energy changes equal the algebraic sum of the heat transferred and the work done. In systems without temperature changes, internal energy changes equal the work done by/on the system.

The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of substance, or of energy, as heat, or by thermodynamic work. These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property.

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into work in a cyclic process." These are informal definitions, however; more formal definitions appear below.

The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.

James Prescott Joule (/dʒuːl/; 24 December 1818 – 11 October 1889) was an English physicist. Joule studied the nature of heat and discovered its relationship to mechanical work. This led to the law of conservation of energy, which in turn led to the development of the first law of thermodynamics. The SI unit of energy, the joule (J), is named after him.

He worked with Lord Kelvin to develop an absolute thermodynamic temperature scale, which came to be called the Kelvin scale. Joule also made observations of magnetostriction, and he found the relationship between the current through a resistor and the heat dissipated, which is also called Joule's first law. His experiments about energy transformations were first published in 1843.

In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system. The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy. Several free energy functions may be formulated based on system criteria. Free energy functions are Legendre transforms of the internal energy.

An adiabatic process (adiabatic from Ancient Greek ἀδιάβατος (adiábatos) 'impassable') is a type of thermodynamic process whereby a transfer of energy between the thermodynamic system and its environment is not accompanied by a transfer of entropy nor of amounts of constituents. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work and/or mass flow. As a key concept in thermodynamics, the adiabatic process supports the theory that explains the first law of thermodynamics. The opposite term to "adiabatic" is diabatic.

Some chemical and physical processes occur too rapidly for energy to enter or leave the system as heat, allowing a convenient "adiabatic approximation". For example, the adiabatic flame temperature uses this approximation to calculate the upper limit of flame temperature by assuming combustion loses no heat to its surroundings.

Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work indefinitely without an external energy source. This kind of machine is impossible, since its existence would violate the first and/or second laws of thermodynamics. These laws of thermodynamics apply regardless of the size of the system. Thus, machines that extract energy from finite sources cannot operate indefinitely because they are driven by the energy stored in the source, which will eventually be exhausted. A common example is devices powered by ocean currents, whose energy is ultimately derived from the Sun, which itself will eventually burn out.

In 2016, new states of matter, time crystals, were discovered in which, on a microscopic scale, the component atoms are in continual repetitive motion, thus satisfying the literal definition of "perpetual motion". However, these do not constitute perpetual motion machines in the traditional sense, or violate thermodynamic laws, because they are in their quantum ground state, so no energy can be extracted from them; they exhibit motion without energy.

A thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. If at every point in the cycle the system is in thermodynamic equilibrium, the cycle is reversible. Whether carried out reversibly or irreversibly, the net entropy change of the system is zero, as entropy is a state function.

During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities (or path quantities), such as heat and work are process dependent. For a cycle for which the system returns to its initial state the first law of thermodynamics applies: