Adiabatic process | Adiabatic process equation

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A process without transfer of heat or mass between a thermodynamic system and surroundings. Thus, Q = 0 is called the adiabatic process and such a system is said to be an adiabatically isolated system. Unlike an isothermal process, an adiabatic process transfer energy to the surrounding called work done. 

What is the adiabatic process?


An adiabatic process, in which the working substance neither receives nor given out heat or mass to the surroundings, during the expansion or compression is called an adiabatic process. In the adiabatic process following point is important. 
  • No heat leaves or enters the gas
  • The internal energy of the gas changes is equal to the work done.
  • The temperature of the gas changes equal to the work done. 
Now, let us check what is an adiabatic expansion and adiabatic compression process?

What is adiabatic expansion?


The process when an ideal behaviour for a closed system, in which the pressure remains constant and temperature decreasing is called adiabatic expansion process. 

What is adiabatic compression?


The process of compression in which no heat is added or subtracted from the air and internal energy of the air is increased which is called work done is called adiabatic compression of air. 

Theoretical explanation: 


Adiabatic process
Adiabatic process

We know that, 

Q1-2 = dU + W1-2  OR  dU = - W1-2

A negative sign indicates that for an increase in internal energy, work must be done on the gas, and a positive sign indicates for decrease internal energy, work must be done by the gas. 

Now, m kg of a perfect gas being expanded adiabatically which is shown by the curve in the above figure. 

Let, V1 = Initial vomule of gas, 
P1 = Initial pressure of a gas, 
V2 = Final volume of gas,
P2 = Final pressure of a gas

The work done during the adiabatic process is given by 

 P1 V1 - P2 V2 / ϒ - 1 = m R (T1 - T2) / ϒ - 1 ( For expansion )

P2 V2 - P1 V1 / ϒ - 1 = m R (T2 - T1) / ϒ - 1 ( For compression ) 

 From the above equation, the adiabatic process equation is PVϒ = Constant

Where ϒ is the adiabatic index, 

ϒ = Specific heat at constant pressure Cp / Specific heat at constant volume Cv

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