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In thermodynamics, an adiabatic process is a process in which no heat is gained or lost in the working fluid. For example, there are no chemical process es taking place in the fluid and there is no heat transfer from the environment. The term "adiabatic" describes things that are impermeable to heat transfer; for example, an adiabatic boundary is a boundary that is impermeable to heat transfer. An insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process which is also reversible is called an isentropic process.

The opposite extreme, in which the maximum heat transfer with its surroundings occurs, causing the temperature to remain constant, is known as an isothermal process.

Adiabatic heating and cooling are processes that commonly occur due to a change in the pressure of a gas. This can be quantified using the ideal gas law.

There are three rates of adiabatic cooling for air.

1. The ambient atmosphere lapse rate, which is the rate that air cools as one goes up in altitude.
2. The dry adiabatic lapse rate, -10°C per 1000m rise.
3. The wet adiabatic lapse rate, about -6° per 1000m rise.

The first rate is used to describe the temperature of the surrounding air that the rising air is passing through, and the second and third rates are in reference to a parcel of air that is rising through the atmosphere. The dry adiabatic lapse rate applies to air which is below its dew point, ie which is not saturated by water vapor, whereas the wet adiabatic lapse rate applies to air which has reached its dew point. Adiabatic cooling is a common cause of cloudThis article is about clouds in meteorology. For the musical concept of clouds, see Cloud (music). For the Final Fantasy VII character, see Cloud Strife. A cloud is a visible mass of condensed water droplets or ice crystals suspended in the atmosphere abo formation.

Adiabatic cooling does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above absolute zero) is adiabatic demagnetisation , where the change in magnetic fieldIn physics, a magnetic field is an entity produced by moving electric charges ( electric currents) that exerts a force on other moving charges. The quantum-mechanical spin of a particle produces magnetic fields and is acted on by them as though it were a on a magnetic material is used to provide adiabatic cooling.

1 Formula

The mathematical equation for an adiabatic process is

where P is pressure, V is volume, and

For a monatomic ideal gas, , and for a diatomic gas (such as nitrogenNitrogen is the chemical element in the periodic table that has the symbol N and atomic number 7. A common normally colorless, odorless, tasteless and mostly inert diatomic non-metal gas, nitrogen constitutes 78 percent of Earth's atmosphere and is a cons and oxygenOxygen is the chemical element in the periodic table that has the symbol O and atomic number 8. The element is very common, found not only on Earth but throughout the universe. Molecular oxygen (O, often called free oxygen on Earth is thermodynamically un, the main components of air)

1.1 Derivation of Formula

The definition of an adiabatic process is that heat transfer to the system is zero, . Then, according to the first law of thermodynamics,

where E is the internal energy of the system and W is work done by the system. Any work (W) done must be done at the expense of internal energy E, since no heat Q is being supplied from the surroundings. Pressure-volume work W done by the system is defined as

However, P does not remain constant during an adiabatic process but instead changes along with V.

It is desired to know how the values of and

It will now be assumed that the system is a monatomic gas, so that

where R is the universal gas constant.

Given and then

Now plug equations (2) and (3) into equation (1) to obtain

simplify,

divide both sides by PV,

From the differential calculus it is then known that

which can be expressed as

for certain constants and of the initial state. Then

Exponentiate both sides,

eliminate the minus sign,

therefore

and

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Topics: Adiabatic Process Heat Adiabats Air Rate Constant Gas Isotherms...

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Adiabatic processThis article covers adiabatic processes in thermodynamics. For adiabatic processes in quantum mechanics, see adiabatic process (quantum mechanics). In thermodynamics, an adiabatic process is a process in which no heat is gained or lost in the working flui Adiabatic indexThe adiabatic index of a gas, usually denoted by the symbol κ ( kappa) (also called γ), is the ratio of its specific heat at constant pressure (c) to its specific heat at constant volume (c). kappa; c/c One can easily understand the relation i Adiabatic theoremThe adiabatic theorem is of major importance in quantum mechanics and provides the fundament for perturbative quantum field theory. There are different versions of this theorem. The original one has been proven by Max Born and V. Fock in 1928: A physical Adiabatic lapse rateAn adiabatic lapse rate is the rate at which a fluid's temperature changes when it is subjected to pressure changes. Most commonly, the term refers to the adiabatic lapse rate of air in the earth's atmosphere and is expressed in temperature degrees per 10 Adiabatic process (quantum mechanics)In quantum mechanics, an adiabatic process is a sufficiently slow change in the Hamiltonian which would result only in a change of eigenvalues, not eigenstates. Hence, if a system starts in the ground state, it will remain in the ground state of the syste