Adiabatic Expansion: In this expansion, no heat is allowed to enter or leave from the system, hence, Δq = 0.

         The first law of thermodynamics states that,

                              ΔE = q+w      Thus ΔE = w

         work is done by the gas during the expansion at expense of internal energy. In the expansion, ΔE decreases while in the compression ΔE increases.

         The molar specific heat capacity at the constant volume of an ideal gas can be given by

         and for finite change               

   The value of ΔT depends upon the process whether it is reversible or irreversible.

         (i) Reversible adiabatic expansion : The following relationships are followed by an ideal gas under reversible adiabatic expansion.

         where, P = External pressure, V = Volume

         where, C_p = molar specific heat capacity at constant pressure, C_v =  molar specific heat capacity at constant volume.

         Knowing ϒ, P₁, P₂ and initial temperature T₁, the final temperature T₂ can be evaluated.

         (ii) Irreversible adiabatic expansion : In the process of free expansion, external pressure is zero, which means work done is zero. Accordingly, ΔE  which is equal to w is also zero. If ΔE is zero, ΔT should be zero. Therefore, in free expansion (the adiabatically), ΔT=0, ΔE=0, w=0 and ΔH=0 .

   In the intermediate expansion, volume changes from V₁ to V₂ against the external pressure, P_ext.

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