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Transfers of energy between closed systems

Adiabatic transfer of energy as work between two bodies

A body can be connected to its surroundings by links that allow transfer of energy only as work, not as heat, because the body is adiabatically isolated. Such transfer can be of two pure kinds, volume work, and isochoric work. Volume work means that the initial volume and the final volume of the body are different, and that mechanical work is transferred through the forces that cause the changes in the deformation parameters. Isochoric work is done on the body by the surroundings when the initial and final volumes and all deformation parameters of the body are unchanged. For example, the surroundings can do work through a changing magnetic field that rotates a magnetic stirrer within the body. Another example is 'shaft work', in which an externally driven shaft rotates fan- or paddle-blades within the body. Another example is rubbing, considered as tangential motion of a wall that contains the body. Stirring and rubbing were the main forms of work in Joule's experiments.

[edit]Transfers of energy as heat between two bodies

Referring to conduction, Partington writes: "If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a quantity of heat has passed from the hot body to the cold body."[26]

Referring to radiation, Maxwell writes: "In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot."

Diathermal wall

In considering transfer of energy between two bodies, it is customary to allow the existence of a wall between them which is permeable only to heat. This allowance is a presupposition of thermodynamics. Such a wall is called diathermal. It is usual for many theoretical discussions to allow that the wall itself has negligibly small internal energy. Then the only property of interest in the wall is that it allows conduction and radiation of heat between the two bodies of interest. While walls are readily found which are permeable only to heat, and impermeable to matter, it is very exceptional indeed to find walls which are permeable to matter but not to entropy. Such a rare exception is a wall penetrated by fine capillaries, which allow the passage of the superfluid of helium II but not of the normal fluid.[29] Transfer of energy as heat is uniquely defined only between closed systems, while for open systems, 'transfer of energy as heat through a wall that allows transfer of matter' is not uniquely defined; such a wall, however, does allow transfer of internal energy.

It is sometimes allowed that the diathermal wall is substantial and has properties of its own including a temperature of its own, and it is considered that the wall is a body in its own right, but is still considered as a closed system not permitted to exchange matter. Then when there is thermal equilibrium between the two bodies of interest, there is also thermal equilibrium between each of them and the wall, and all three have the same temperature. Then from the viewpoint of states of thermal equilibrium, all diathermal walls are equivalent; this is proposed as a possible statement of the zeroth law of thermodynamics. If heat is considered with respect to diathermal walls, then, because all diathermal walls are equivalent, all heat is of the same kind.

When the two bodies are initially separate and not connected by a substantial wall, and at different temperatures, and are then connected with the substantial wall as connecting medium, the properties and state of the wall need to be taken into account for the process of transfer of energy as heat. If the substantial wall contains fluid, and there is a gravitational field, then transfer of energy as heat between the two bodies of interest may involve convective circulation within the wall, with no transfer of matter into or out of the wall. In this sense, it can be said that convective circulation is a mechanism of transfer of energy as heat, but in this case, the transfer of energy as heat is complex, because of change of internal energy and temperature of the wall. Thermal convective circulation is always opposed by friction, and consequently occurs only above a threshold of thermal difference between source and destination of the transferred energy. Thermal equilibrium between source and destination is therefore finally reached by a non-convective stage, of conduction and radiation. In discussions of thermodynamics, such a diathermal wall and process of transfer of energy as heat is not usually intended unless they are explicitly expressed.

[edit]Transfers of energy involving more than two bodies

[edit]Heat engine

In classical thermodynamics, a commonly considered model is the heat engine. It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often. Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed. But two thermal reservoirs are needed, because transfer of energy as heat is irreversible. A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir. The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy. The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.

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