Adiabatic process

An adiabatic change (large α a " not " and διαβαίνειν diabaínein " pass ") is a thermodynamic process, in which a system is transferred from one state to another, without heat exchange with its surroundings.

Importance

In general, a thermodynamic system change its internal energy by exchanging both ( mechanical or different type ) work as well as heat with its surroundings. According to the first law of thermodynamics, this applies to a closed system when external energy ( kinetic and potential ) can be disregarded:

In an adiabatic change of state is no heat exchange with the environment (), so that the total work done in the working system is completely in the internal energy or a part of the internal energy is completely converted into work, that is performed by the system:

Calculations and theoretical considerations can be greatly simplified or made possible in some cases only.

There are both irreversible and reversible running adiabatic change. In the first case entropy in the system during the process generated in the latter case not. Because no heat energy is exchanged with the environment, no entropy flows to or from. Is the change in state is reversible, the entropy of the system remains the same, therefore, it is then an isentropic change of state. The reverse is not true: An isentropic change of state can also be irreversible and non- adiabatic, when exactly the entropy generated flows outward. Another example is the behavior when approaching the absolute zero temperature: Here the state changes are due to the third law of thermodynamics (almost) always isentropic, but only in exceptional cases adiabatic.

Reversible adiabatic state changes play an important role in the axiomatic justification of thermodynamics according to Carathéodory. Starting from the axiom " There are in the vicinity of each reversible achievable state conditions that are not adiabatic, reversible, therefore only irreversible or not available", the existence of a new state variable shown entropy. States between which only irreversible transitions are possible, in fact differ in their entropy, so that no reversible adiabatic (ie isentropic ) can transition between them exist.

Approximate realization

An ideal adiabatic change requires that the system in which the change of state takes place, is perfectly insulated from the heat flows in any form. It would heat conduction, convective heat transfer and radiation exchange to completely stop. The system must be traversed by a heat current, where no heat from it remains in the system; the heat flow can not be considered as belonging to the system (examples: a completely transparent subject illuminated by the solar system, a flooded from non-interacting neutrinos System).

In reality, a complete thermal insulation is not available, but real processes can occur adiabatically to a good approximation when

• They take place in a well insulated container (eg chemical reactions in an adiabatic calorimeter ),
• The state change proceeds so rapidly that in the short time can flow little heat to or ( for example in a combustion engine, wherein an air pump or the sound propagation ) or
• The volume of the system is very large, so that heat flows play virtually no role at its edge (eg thermally ascending air parcels ).

In reality, there is probably always at least partially diabatic processes so that it can be assumed only approximately by an adiabatic change of state.

Examples

• The compression of the air in air pump is an adiabatic change. If the compression is performed with a sufficiently high speed, a significant temperature increase is noticeable. The work is done at the pump, directly increases the internal energy and the temperature of the air mixture. This first No heat energy is transferred to the pump or taken from it. Only after completion of the process you notice a warming of the bicycle pump and hence a flow of heat energy. A pneumatic lighter uses this method. The extremely fast primary heating of the air during re-entry of spacecraft is due to the extremely high compression rates, an approximately adiabatic process. However, the heat in the connection then spread very rapidly through conduction, flow and radiation processes.
• Conversely, the compression causes a pressure drop of adiabatic cooling of the air. This is done for example in an ascending air stream ( at a thermal buoyancy or as it flows over a mountain ), or on the top of airplane wings. On cooling, the saturation concentration of water vapor decreases. Falls below the actual water content condenses the overlying water content to small water droplets (formation of clouds or fog).

Work in a reversible adiabatic ( isentropic ) change of state of an ideal gas

In the case of an ideal gas is true for the internal energy:

Because of this:

Denote this

This holds because for the adiabatic case of reversible ( isentropic ) change of state work done (volume work):

Here, denote the initial temperatures and volumes and the final temperatures and volumes and the molar heat capacity at constant volume.

It also follows that the work of the process, a higher temperature difference is larger. This has among others the temperature of the lower atmosphere result.

From the equation of state of an ideal gas these relationships follow:

These equations can be rewritten in such a way that:

They are also called Poisson equations. here is the isentropic exponent. The equations in this form, however, can only be used for non-dimensional variables, for example, if they are related to the sizes at standard conditions.

Since the mass of the gas volume remains constant, the transformation to the change in density is easy to calculate:

Isentropengleichung

The general Isentropengleichung for dimensionless quantities (see above) is:

Which is true. It is the ratio of isobaric and isochoric heat capacity and the f denotes the number of degrees of freedom of the gas. For an ideal monatomic gas yields with and from and for the Isentropenindex.