Adiabatic Process Derivation

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Adiabatic Process

The process of adiabatic is said to be Unlike an isothermal process an adiabatic process probably transfers the energy to the surroundings only in the form of work. It is also conceptually recognized as undergirds the theory which used to expound the first law of thermodynamics and is therefore a key of thermodynamic concept.

Some of the processes which include chemical as well as the physical occur very rapidly for energy to leave or enter the system as heat or allows a convenient approximation. For example if we see the adiabatic flame temperature uses the approximation which is to calculate the upper limit of flame and the temperature by assuming combustion that loses no heat to its surroundings.

In the study of oceanology and meteorology the adiabatic cooling produces condensation of moisture and the process of salinity or oversaturating the parcel. We can see that the excess must be removed. The process of pseudo adiabatic is defined for expansion because a compressed parcel becomes warmer and then it remains undersaturated.

Adiabatic Heating and Cooling Process 

The compression of adiabatic gas causes a rise in temperature of the gas. Which is known as the Adiabatic expansion against pressure or at times a spring causes a drop in temperature. In contrast, if we see the free expansion is an isothermal process for a gas which is ideal.

The process of Adiabatic heating occurs when there is pressure on a gas and this pressure is increased by work which is done on it by its surroundings that is a piston that is compressing a gas that is contained within a cylinder. And then the raising the temperature process occurs where in many practical situations heat strats conduction through walls can be slow compared with the time of compression. This practical application is found in the diesel engines which rely on the lack of heat that is dissipated during the compression stroke to elevate the fuel vapor temperature that is sufficient to ignite it.

Expression of Gas

For an free expression of an adiabatic ideal gas, the gas is supposed to be contained in an insulated container and then after that the gas is allowed to expand in a vacuum. As  there is no pressure from the external side the  gas to expand against the work done by or on the system is said to be zero. Since this whole process does not involve any heat transfer or work, which is  the first law of thermodynamics then implies that the net internal energy that changes the system is zero. 

For an ideal gas, the temperature remains constant because the energy which is internal energy which only depends on temperature in that case. Since at the constant temperature the entropy is proportional to the volume the entropy increases according to the volume in this case, therefore this process is said to be irreversible.


The curve of an adiabat is a curve of constant entropy which is in the diagram. Some of the properties of adiabats which are on a P–V diagram are indicated. Every process of adiabat asymptotically approaches both the P-axis and the V axis just like isotherms processes.

  1. Each process of adiabat intersects each isotherm exactly once.

  2. Process of the adiabat looks similar to an isotherm except for that during an expansion and adiabatic gas loses more pressure than an isotherm so it can be said that it has a steeper inclination  which is more vertical.

  3. The exception of adiabatic gas is very near to absolute zero, whereas if we look at  the density of adiabats drops sharply and they become rare, that is we shall refer to Nernst's theorem.

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A process of the adiabatic gas is a thermodynamic process such that there is no heat transfer out or in of the system and is generally obtained by using a strong insulating material which is surrounding the entire system.

Adiabatic Process examples are mentioned:

  • The flow which is vertical flow of air in the atmosphere

  • When the gas which is an interstellar cloud contracts or expands.

  • The turbine is a very good example of the process of adiabatic as it uses the heat as a source to produce the work.

The adiabatic processes which occur naturally are irreversible if entropy is produced.

In one of such kinds no entropy is produced within the system that is no friction or  viscous dissipation, etc. and the work is only on the pressure-volume work that is denoted by P dV. This ideal kind in  nature occurs only approximately because it demands an infinitely slow process and no sources of dissipation.

FAQ (Frequently Asked Questions)

Q1. How do we derive the Adiabatic Equations?

Ans: The process of derivation of the adiabatic can be done from the first law of thermodynamics which is relating to the change in internal energy dU to the work W done by the system and the heat which is dQ added to it. The work done that is dW for the change in volume denoted by V or by dV is given as PdV. This equation is very true for a process like an adiabatic process in an ideal gas.

Q2. What does Adiabatic Process mean?

Ans: An process like adiabatic is defined as a process in which no transfer of heat takes place. This does not mean that the constant temperature is there, but rather that no heat is transferred into or out from the system. The actual definition of an isentropic process is an adiabatic process which is reversible in nature.

Q3. What is Cv and Cp?

Ans: In heat capacity of thermodynamics the ratio or ratio of specific heat capacities that is Cp:Cv is also known as the index which is adiabatic. It is the ratio of the two specific heat capacities that are Cv and Cp is given by The capacity of Heat at Constant Pressure  that is Cp/ Heat capacity at Constant Volume that is Cv.