Introduction

In thermodynamics, an adiabatic process is a change that occurs within a system as a result of the transfer of energy to or from the system solely in the form of work; that is, no heat is transferred throughout. The rapid expansion or contraction of a gas is almost adiabatic. The process that takes place in a container that is a good thermal insulator is also adiabatic. Adiabatic processes are characterized by an increase in entropy or degree of disorder when they are irreversible and there is no change in entropy when they are reversible. Adiabatic processes cannot reduce entropy.

What is Adiabatic Process

In thermodynamics, an adiabatic process is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its surroundings. 

In contrast to an isothermal process, in an adiabatic process energy is only transferred off to the environment as work. A key concept in thermodynamics is that the adiabatic process also supports the theory that explains the first law of thermodynamics.

Gas temperature increases when adiabatic compression occurs and gas temperature decreases when adiabatic expansion occurs. 

A detailed discussion of adiabatic cooling and adiabatic heating is provided below. 

Adiabatic Cooling: When the pressure of an isolated adiabatic system decreases, the gas expands, causing the gas to do work on the environment. This lowers the temperature. This phenomenon is responsible for the formation of lenticular clouds in the sky. 

Adiabatic Heating: When working on an isolated adiabatic system, the pressure of the system increases and because of it the temperature also increases. Adiabatic heating finds its application in the diesel engine during the compression stroke to raise the temperature of the fuel vapour sufficiently to ignite it.

Equation of Adiabatic Process

In an adiabatic process, the system is isolated from the environment and the shared heat  is zero. 

Therefore

PV=constant

Where, P = Pressure of the system, V = volume of the system, = Adiabatic Index

Work Done in Adiabatic Process

Imagine an isolated non-conductive cylinder with a non-conductive piston, and then pull the piston out a little outward, which results in a change in the physical conditions of the gas, and then find the work done to make the change. Suppose we have a one gram molecule of a perfect gas that is enclosed in a non-conductive cylinder that has a non-conductive piston. If we slowly move the piston outwards, the gas expands and thus does work without external energy input and adiabatic expansion takes place. And since the energy was not consumed from the outside, the temperature of the gas in the bottle drops.

Let’s assume that the initial temperature, pressure and volume of the cylinder are T1, P1 and V1 and in its final state are T2, P2and V2. Now let A be the cross-sectional area of ​​the piston and we move the piston a small distance dx, causing the gas to expand by a volume of dV. And with a small expansion, the change in pressure will be almost the same, say P.

For the adiabatic Change

PV=K

Hence,

P=KV

Work done,

W=V1V2PdV

W=V1V2KV=KV1V2V–dV

W=KV–1-=K1-(V21-–V11-)

Since, 

P1V2=P2V2=K

Therefore,

W=11-(P2V2V21-–P1V1V11-)

W=11-[P2V2–P1V1]

By using PV=RT, The work done can also be written as

W=R1-[T2–T1]

The expression which we get is the equation for the work done in an adiabatic process.

Adiabatic Compression and Expansion

Adiabatic Compression

Compression, in which no heat is added to or removed from the air and the internal energy of the air is increased by an amount equal to the external work done on the air. The increase in air temperature during adiabatic compression tends to result in an increase in pressure only due to the decrease in volume. Therefore, during adiabatic compression, pressure increases faster than the rate at which volume decreases.

Adiabatic Expansion

Adiabatic expansion is the expansion of a gas with no heat or mass exchange with the environment. As such it is an idealized concept, but it is very useful for understanding heat flow and duty cycles in heat engines. In practice, it is a very rapid expansion of a compressed gas in a low-pressure container, such that heat exchange with the environment is minimal due to the lack of time for heat flows across the system boundaries.

Conclusion

The article consists of the concept of adiabatic process, moreover the derivation of the work done by adiabatic process is also explained so that anyone will get a clear idea of adiabatic process and it’s work done. The compression due to adiabatic process and expansion due to adiabatic process is discussed i.e. in compression no heat is added or removed and in expansion or no heat is exchanged with the environment. This article is going to help you a lot in your academics.