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Asked in NEET 2013 Karnataka · Adiabatic Relations
Start from the adiabatic condition PV^γ= constant and use PV=nRT to swap out one variable at a time.
Replacing P by (nRT)/V: (nRT)/VV^γ= constant, so TV^γ-1= constant.
Replacing V by (nRT)/P: P((nRT)/P)^γ= constant, so P^1-γT^γ= constant.
Those are the only two P-T and T-V forms, and the P-T one carries 1-γ on P and γ on T.
P^γT^1-γ= constant has the two exponents exchanged, so it is the relation that does not hold.
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