Work done during an Adiabatic Process

Today we’re going to find work done during an adiabatic process.For this,
 Let us consider one gm. mole of perfect gas enclosed in cylinder having perfectly insulated walls.

Let it expands adiabatically from an initial volume V1 to a final volume V2. Then work done by gas during the expansion is given by :

       

 
where P is the instantaneous pressure of the gas while suffering infinitesimal expansion dV.
Now during an adiabatic process :-

Hence, the work done in adiabatic process depends only upon initial & final temperature T1 & T2. Thus the work done along any adiabatic between two isothermal is independent of particular adiabatic.
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