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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 ΔQ = 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.
    Since, these two conditions are not fully realized in practice, so no process is perfectly adiabatic.

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 γ = constant, By differentiating, we get
    dPV γ + PγVγ – 1 dV = 0
    ∴ Slope of adiabatic curve 55688.png
    But we also know that slope of isothermal curve, tan φ = –P/V. So,
Adiabatic elasticity For adiabatic process, PV γ = constant.
Differentiating both sides, dPVγ PγVγ –1d V = 0
Eφ = γ P
i.e., adiabatic elasticity is γ times that of pressure but we know isothermal elasticity Eθ = 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 55657.png
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 = 0
If Ui and Uf be the initial and final internal energies of the gas, then
Thus, the final and initial energies are equal in free expansion.

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