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Asked in JEE Main 1st Feb 1st Shift 2023 · Gas laws and P-V-T processes
Every term added to P must itself be a pressure, so [a/(V²)]=[P], giving [a]=[P][V²].
Every term subtracted from V must be a volume, so [b]=[V].
[(b²)/a]=([V]²)/([P][V]²)=1/([P]).
A reciprocal pressure is compressibility, the reciprocal of bulk modulus.
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