# Adiabatic Process

When a thermodynamic system undergoes a change in such a way that no exchange of heat takes place between it and the surroundings, the process is known as adiabatic process. In this process

*P*,*V*, and*T*change, but Î”*Q*= 0.**Fig. 8**

# Essential conditions for adiabatic process

- There should not be any exchange of heat between the system and its surroundings. All walls of the container and the piston must be perfectly insulating.
- The system should be compressed or allowed to expand suddenly so that there is no time for the exchange of heat between the system and its surroundings.

# Examples of some adiabatic processes

- Sudden compression or expansion of a gas in a container with perfectly non-conducting walls.
- Sudden bursting of the tube of bicycle tyre.
- Propagation of sound waves in air and other gases.

**Equation of state**

Equation (2) is called equation of state for adiabatic change and can also be re-written as

# Indicator diagram

- Curve obtained on
*PV*graph is called adiabatic curve (Fig. 9).

**Fig. 9**

- Slope of adiabatic curve: From
*PV*= constant, By differentiating, we get^{Î³}*dPV*+^{Î³}*P*_{Î³}*V*^{Î³}^{ }^{â€“ 1}*dV*= 0*Ï†*= â€“*P*/*V*. So,

**Adiabatic elasticity**For adiabatic process,

*PV*

*= constant.*

^{Î³}Differentiating both sides,

*dPV**Î³*+*P*_{Î³}*V*^{Î³}^{ }^{â€“1}*d V*= 0*E*=

_{Ï†}*Î³*

*P*

i.e., adiabatic elasticity is

*Î³*times that of pressure but we know isothermal elasticity*E*=_{Î¸}*P.*So,i.e., the ratio of two elasticities of gases is equal to the ratio of two specific heats.

# Work done in adiabatic process

*W*

**Free expansion**Free expansion is an adiabatic process in which no work is performed on or by the system. Consider two vessels placed in a system which is enclosed with thermal insulation (asbestos-covered). One vessel contains a gas and the other is evacuated. The two vessels are connected by a stopcock. When suddenly the stopcock is opened, the gas rushes into the evacuated vessel and expands freely. The process is adiabatic as the vessels are placed in thermal insulating system (

*dQ*= 0) moreover, the walls of the vessel are rigid and hence no external work is performed (

*dW*= 0).

Now according to the first law of thermodynamics,

*dU*= 0If

*U*and_{i}*U*be the initial and final internal energies of the gas, then_{f}Thus, the final and initial energies are equal in free expansion.